## Summary

stating the determination of whether a claimed method is a `process' within the meaning of 35 U.S.C. § 101 is unaffected by the particular apparatus for carrying out the method.

Summary of this case from Ductmate Industries, Inc. v. Famous Supply Corp.## Opinion

Appeal No. 78-555.

March 8, 1979.

Sheldon Kanars, U.S. Army Communications Electronics Material Research Command, Fort Monmouth, N. J., for appellants; Jeremiah G. Murray, Edward Goldberg, U.S. Army Communications Electronics Material Readiness Command, Fort Monmouth, N. J., of counsel.

Joseph F. Nakamura, Washington, D.C., for the Commissioner of Patents; Thomas E. Lynch, Associate Sol., Washington, D.C., of counsel.

Appeal from the Patent and Trademark Office Board of Appeals.

Before MARKEY, Chief Judge, and RICH, BALDWIN, LANE and MILLER, Judges.

This is an appeal from the decision of the Patent and Trademark Office Board of Appeals (board) affirming the rejection under 35 U.S.C. § 101 of claims 1-10 in application serial No. 113,471, filed February 8, 1971, and entitled "Optimal Seeking Process for the Design of Microwave Circuits." We affirm.

### *The Invention*

The invention relates to a process for determining a set of values for use in a mathematical model of a microwave circuit. The model comprises mathematical equations that describe both the functional characteristics, e. g., impedance, capacitance and inductance of the circuit components, and the manner in which the components interrelate to determine a circuit response. The purpose of the mathematical model is to select by arithmetical computations values for the functional characteristics of the circuit components so that the "modeled" microwave circuit, if it is ever built, would exhibit a specified response. Appellants' specification states that typical responses for microwave circuits are defined by one or more of the following parameters: (1) power gain versus frequency, (2) input voltage standing wave ratio (VSWR) versus frequency, (3) output VSWR versus frequency, (4) insertion phase versus frequency, (5) terminal reflection coefficient versus frequency, and (6) input-output impedance versus frequency. The specification further states that the equations representing these circuit responses in the mathematical model involve hyperbolic or other types of transcendental functions.

*Van Nostrand's Scientific Encyclopedia,* D. Van Nostrand Company, Inc. (3d ed. 1958) at p. 1705, defines "transcendental," as used in its mathematical context, as:

TRANSCENDENTAL. A term applied tonumbers, equations,orfunctionswhich are notalgebraic.The word comes from the Latin,scandere,to climb, and it is intended to suggest only that transcendental operations cannot be defined by elementary methods ("Quod algebrae vires transcendit"). No special difficulty in understanding their properties is signified nor is there any religious or philosophical connotation to the word.

A transcendental number is not arootof apolynomialin one unknown, with integral coefficients. Typical examples are:e,the base of naturallogarithmsand II, the area of acirclewith unit radius.

Some transcendental functions are:trigonometricandhyperbolic,with their respective inverses;exponentialandlogarithmic;betaandgamma;elliptic;Bessel,etc. They may be subdivided into a class defined as the solution to adifferential equation,which is true for those listed in the previous sentence and one not so defined, like theRiemann zeta function.

Transcendental equations contain one or more transcendental functions. They cannot, in general, be solved by direct analytical means and someapproximate methodmust be used. [Emphasis in original.]

### *The Invention as Claimed and Described*

Claim 1 is representative of the claims and it reads:

1. A computer method of automatically determining, from a set of initial reference parameters, a set of optimal microwave circuit element parameters for producing data defining a predetermined objective circuit response function of a given microwave circuit configuration comprising the steps of;

(1) calculating data defining a reference circuit response function from the latest set of said reference parameters;

(2) comparing said data defining said calculated reference circuit response function and said predetermined objective circuit response function for obtaining a reference error proportional to the difference;

(3) perturbing the values of a subset of said latest set of reference parameters to determine a new set of reference parameter values for producing a new reference error less than the penultimate reference error;

(4) increasing, by a common factor, each of said last mentioned perturbations to obtain a new set of reference parameter values and a new reference error in accordance with steps (1) and (2);

(5) comparing said new reference error with the penultimate reference error and then returning to step (4), if said new reference error is less, and redefining the penultimate reference parameter values as said latest set of reference parameter values and returning to step (3), if said new reference error is not less; and

(6) storing said latest set of reference parameters as said set of optimal microwave circuit element parameters when said reference error has been reduced to a predetermined value.

A meaningful analysis of the process as claimed can only begin when some of the mystery is removed from terms such as "transcendental equations," "initial reference parameters," "optimal microwave circuit element parameters" and "predetermined objective circuit response."

First, it should be understood that a microwave circuit is merely an electronic circuit for generating and/or receiving signals which lie in the electromagnetic spectrum between the far infrared and the conventional radio frequency portion, i.e., frequencies of 1,000 to 300,000 megahertz and corresponding wavelengths of between 30 cm and 1 mm. A microwave circuit is generally comprised of a combination of active elements, e.g., transistors, and passive elements, e.g., transmission lines, resistors, capacitors and inductors. Each active and passive element can be characterized by assigning numerical values to its electrical properties, inter alia, gain, impedance, inductance and capacitance. Appellants teach that the microwave circuits are designed by selecting the proper values for the electrical properties characterizing the active and passive circuit elements so that a microwave circuit comprised of these elements is responsive over a particular band of microwave frequencies.

*Van Nostrand's Scientific Encyclopedia,* supra note 1 at 1062.

The foregoing explanation of a microwave circuit should be helpful in understanding other terms recited in claim 1. The "initial reference parameters" are numerical values for the electrical properties characterizing the active and passive elements. For the sake of simplicity, these numerical values will be called a set of process inputs. The "predetermined objective circuit response" is a numerical target frequency or range of frequencies within which the microwave circuit is to be responsive in some manner if it is ever built. A shortened name is "goal response." The "optimal microwave circuit element parameters" are numerical values to be assigned to the electrical properties of the circuit elements after the steps in the claimed "computer method" (process) have been completed. Again, these values are merely numbers, and for the purposes of this analysis they will be called the "process outputs."

The initial values for the process inputs are disclosed to be educated guesses of values which will generate a calculated response within the numerical range of the goal response. Appellant acknowledges, however, that it is very unlikely that the first calculated response will be acceptably close to the goal response and, thus, iterative numerical changes and arithmetical calculations must be performed to arrive at a set of process inputs which will produce an acceptable calculated response.

With these definitions in mind, the recited steps of the method will be analyzed. Step (1) arithmetically calculates a reference circuit response from the current numerical values for a set of process inputs. In step (2) a comparison is made between the calculated reference circuit response and the goal response to obtain a "reference error" or response error which is proportional to the difference between the two. The specification reveals that this proportional response error is a number determined by an arithmetic calculation.

In step (3), the numerical values of the set of process inputs are "perturbed" (numerically changed), and the proportional response error is recalculated. The specification states that each perturbing step is an exploratory search for changes in the numerical values for the set of process inputs that result in a reduction in the response error. The sets of process inputs which provide smaller response errors are memorized or stored for use in subsequent calculations.

Step (4) comprises what appellants call a pattern search. This entails first incrementing the numerical values of a pseudorandomly selected subset of each set of previously stored process inputs by a fixed amount and then iteratively calculating response errors by the repeated execution of the mathematical calculations of steps (1) and (2).

Step (5) requires steps (3) and (4) to be iteratively performed if the newly calculated response errors are decreasing in numerical value. A decreasing response error signifies that the changes in the sets of process inputs are effecting calculated responses approaching the value or range of values of the goal response. When these iteratively performed calculations no longer effect a decreasing response error, step (6) is performed. This step requires that the numerical values for the last set of process inputs be stored as the "process outputs." These "process outputs" define the numerical values for the electrical properties characterizing the circuit elements in the microwave circuit being designed. These values presumably would be used to select the components if the microwave circuit is ever built.

The claimed process as above-explained can be further simplified as follows:

(1) arbitrarily select a set of numbers;

(2) calculate an answer by means of equations which use the selected set of numbers;

(3) computationally check to see whether the calculated answer is acceptable; if not,

(4) repeatedly calculate different sets of numbers from previous sets and do the calculations of (2) and (3) until an acceptable answer is calculated;

(5) call the last set of numbers selected the "process outputs."

As thus simplified from the complex terminology of microwave circuits, claim 1 merely comprises an iterative method for arithmetically determining a set of process outputs which provide the calculated response most nearly equivalent to a goal response for a mathematical model of a microwave circuit.

### *The Board Opinion*

The pertinent portion of the board's opinion is as follows:

If for the purposes of discussion, the claimed subject matter here under consideration is a machine process, as appellants would have it, we think such a process falls within the purview ofBenson,supra, [Gottschalk v. Benson,409 U.S. 63 [ 93 S.Ct. 253, 34 L.Ed.2d 273], 175 USPQ 673 (1972)] for it is apparent that as a practical matter it can only be performed by the computer, as evidenced by appellants' commentary on the difficulty of hand computation.

Any subject matter remaining in the public domain, as for example, the capability to perform the calculations by hand, would be trivial.

The nature of the steps recited in the claims are such as to pre-empt whatever is carried out by the computer, be it characterized as algorithm, formula, machine process, program or the like. We draw this conclusion from the fact that we know of no way of operating a digital computer of the character employed for appellants' disclosed invention except by some form of programming. In this case the language inBensonis clear:

"_ _ _ We have, however, made clear from the start that we deal with a program only for digital computers.

### * * * * * *

If these programs are to be patentable, considerable problems are raised which only committees of Congress can manage, for broad powers of investigation are needed, including hearings which canvass the wide variety of views which those operating in this field entertain. The technological problems tendered in the many briefs before us indicate to us that considered action by the Congress is needed."

From this language, it appears that the board held the claims to recite nonstatutory subject matter for one or both of the following reasons: (1) the process is performed by a computer, or (2) the process is reduced to practice in the form of a computer program.

### *Appellants' Arguments*

Appellants, in their briefs before this court, argue that instead of analyzing the recited claim limitations, the board opinion erroneously and overbroadly concludes that the Supreme Court in *Gottschalk v. Benson,* 409 U.S. 63, 93 S.Ct. 253, 34 L.Ed.2d 273, 175 USPQ 673 (1972), held that all computer programmable processes are, prima facie, nonstatutory. Further, appellants argue that claims 1, 3-7, 9 and 10 do not recite a mathematical formula or algorithm because there are no formulas recited in the claims which relate mathematical objects or quantities. Appellants state that step 1 of claim 1 which calls for "calculating data defining a reference circuit response function from the latest set of said reference parameters" does not comprise a mathematical calculation, formula or equation because no formula is directly or indirectly recited in the steps.

The specification describes the calculations associated with step 1 as follows:

The next step would be to perform a circuit analysis using the initial input information to determine the error E between the actual and objective response. The first step in the analysis process 22 is set forth in box 32, i. e., the process of forming the ABCD matrix for each element. The ABCD matrix for the first element is determined from the initial values of the variables Z1 and L1 and the type of element specified. For example, for a shorted stub transmission line, the ABCD matrix is of the following form:

| 1 0 | | | ABCD = | 1 | | 1 ---------- | | Z tanh L |

Additional ABCD matrices may be formed in accordance with current microwave circuit design techniques * * *. An entire set of ABCD matrices would be stored in a library routine which when automatically called would produce p matrices, one for each element in the circuit. The p matrices are first stored, step 33, and then multiplied together, step 34, to form the total ABCD matrix.

A calculation step 35 is performed to obtain the circuit responses (PG, VSWR, etc.) stated in the input objective. For example, a subroutine which calculates the power gain from the total ABCD matrix is also stored in the library and is automatically called at this point.

The set of the ABCD matrices for all of the proposed circuit elements comprises a mathematical model of the circuit and appellants' statement that step 1 does not recite mathematical calculations is clearly in error.

As an alternative argument, appellants state that even if it is assumed that independent claims 1 and 7 recite steps which are mathematical calculations, formulas or algorithms, the claimed inventions are still statutory because the equations are merely being used by a computer in performing a statutory method, i. e., the use of a mathematical model to compute numerical "process outputs." In essence, appellants argue that these claims on appeal are not nonstatutory methods of calculation because there is no formula into which the process can be "plugged" to compute the "process outputs." Appellants characterize their use of mathematical equations merely as a means for testing a set of process inputs and not as a law of nature (formula) expressing relationships between the process inputs and outputs.

### OPINION

The determination of whether particular method claims recite statutory processes within 35 U.S.C. § 101 has been a recurring issue before this court. *See,* e. g., *In re Sarkar,* 588 F.2d 1330, 200 USPQ 132 (Cust. Pat.App. 1978), *In re Johnson,* 589 F.2d 1070, 200 USPQ 199 (Cust. Pat.App. 1978); *In re de Castelet,* 562 F.2d 1236, 195 USPQ 439 (Cust. Pat.App. 1977); *In re Richman,* 563 F.2d 1026, 195 USPQ 340 (Cust. Pat. App. 1977); *In re Flook,* 559 F.2d 21, 195 USPQ 9 (Cust. Pat.App. 1977); *In re Chatfield,* 545 F.2d 152, 191 USPQ 730 (Cust. Pat.App. 1976); *In re Christensen,* 478 F.2d 1392, 178 USPQ 35 (Cust. Pat. App. 1973); *In re Benson,* 58 CCPA 1134, 441 F.2d 682, 169 USPQ 548 (1971). Two of these cases have been further considered by the Supreme Court. *See Parker v. Flook,* 437 U.S. 584, 98 S.Ct. 2522, 57 L.Ed.2d 451, 198 USPQ 193 (1978) (hereinafter *Flook*); *Gottschalk v. Benson,* 409 U.S. 63, 93 S.Ct. 253, 34 L.Ed.2d 273, 175 USPQ 673 (1972) (hereinafter *Benson*). The results of the Supreme Court's considerations include legal principles with which to analyze the claims of each appeal and the acknowledgement that "[t]he line between a patentable `process' and unpatentable `principle' is not always clear." *Flook,* supra, 437 U.S. at 589, 98 S.Ct. at 2525, 198 USPQ at 197.

None of the above cases, however, supports the board's reasons for holding the claims under consideration nonstatutory. The fact that the claimed process is performed on a computer is not a proper basis for rejection as is evident from decisions of this court which have held computer-implemented processes to constitute statutory subject matter. *See,* e. g., *In re Chatfield,* supra (method of reassigning priorities within a computer); *In re Deutsch,* 553 F.2d 689, 193 USPQ 645 (Cust. Pat.App. 1977) (method of controlling a processing plant by means of a computer); *In re Johnson,* supra (computer-implemented method for removing noise from seismic signals). The determination of whether a claimed method is a "process" within the meaning of 35 U.S.C. § 101 is unaffected by the particular apparatus for carrying out the method.

To the extent that the board's second ground for holding the claims nonstatutory is understood, i. e., that appellants' method is implemented by a computer, that computers are operated by programs, and that programs are nonstatutory under *Benson,* supra, and *Flook,* supra, we find this basis unsupported by legal precedent and irrelevant to the issue at hand. First, the Supreme Court has stated that the ultimate determination of the propriety of patent protection for computer programs, as such, is within the domain of Congress. *See Flook,* supra, 437 U.S. at 595, 98 S.Ct. 2522, 198 USPQ 199-200; *Benson,* supra, 409 U.S. at 73, 93 S.Ct. 253, 175 USPQ at 676-7. Having stated its position, the Court considered the claimed inventions and held Flook's claims to be for a nonstatutory method of calculation and Benson's claims to improperly preempt a mathematical algorithm. Thus, the board's proposed basis of rejection is not supported by either the considerations or holdings of these two cases. Furthermore, as stated by this court in *Chatfield,* supra, 545 F.2d at 155, 191 USPQ at 733, "the mere labeling of an invention as `a computer program' does not aid in decision making." While a program may configure a computer in a manner to carry out a process, it is the process, i. e., what the computer does, which is the subject of examination under 35 U.S.C. § 101, *et seq.* This distinction was further explained in *Johnson,* supra, 589 F.2d at 1081, n. 12, 200 USPQ at 210-1, n. 12, where we stated:

Very simply, our decision today recognizes that modern technology has fostered a class of inventions which are most accurately described as computer-implemented processes. Such processes are encompassed within 35 U.S.C. § 101 under the same principles as other machine-implemented processes, subject to judicially determined exceptions, inter alia, mathematical formulas, methods of calculation, and mere ideas. The overbroad analysis of the PTO errors in failing to differentiate between a computer program, i. e., sets of instructions within a computer, and computer-implemented processes wherein a computer or other automated machine performs one or more of the recited process steps. This distinction must not be overlooked because there is no reason for treating a computer differently from any other apparatus employed to perform a recited process step.

Thus, we agree with appellants' first contention that the board did not properly consider the method as claimed.

Appellants' further arguments, which comprise the substance of this appeal, are an attempt to show that the claims on appeal do not recite mathematical algorithms, formulas or methods of calculation as rejected by *Benson, Flook* and the relevant decisions of this court. Appellants contend that to fall within the scope of these decisions the claim must recite a formula or algorithm in the form of a relationship between mathematical objects or quantities. Appellants claim that no such relationship exists between the first set of process inputs and the "process outputs" (the last set of process inputs) and, thus, conclude that the recited method is a statutory process.

In the context of appellants' method, this statement means that instead of merely claiming the equations which comprise the mathematical model for a microwave circuit, appellants are claiming the use of these equations (step 1 of claim 1) in combination with other steps for the purpose of arithmetically determining a set of numerical "process outputs." Appellants, in essence, argue that although a mathematical model may not be statutory, its use in performing computations is a statutory process.

In determining whether a method constitutes statutory subject matter, this court, in *In re Sarkar,* supra, indicated that any analysis must start from the premise that "a series of steps is a `process' within § 101 *unless* it falls within a judicially determined category of nonstatutory subject matter exceptions." *Id.,* 588 F.2d at 1333, 200 USPQ at 137. It is an obligation of this court to analyze claims on appeal in the light of the legal precedents establishing the categories of nonstatutory subject matter to determine whether the claims fall into one of the exceptions.

In *Gottschalk v. Benson,* the Supreme Court considered claims for converting binary coded decimal (BCD) numbers into pure binary numbers. Claim 13 of the Benson application reads as follows:

"A data processing method for converting binary coded decimal number representations into binary number representations comprising the steps of

"(1) testing each binary digit positioni,beginning with the least significant binary digit position, of the most significant decimal digit representation for a binary `0' or a binary `1';

"(2) if a binary `0' is detected, repeating step (1) for the next least significant binary digit position of said most significant decimal digit representation;

"(3) if a binary `1' is detected, adding a binary `1' at the (i + 1)th and (i + 3)th least significant binary digit positions of the next lesser significant decimal digit representation, and repeating step (1) for the next least significant binary digit position of said most significant decimal digit representation;

"(4) upon exhausting the binary digit positions of said most significant decimal digit representation, repeating steps (1) through (3) for the next lesser significant decimal digit representation as modified by the previous execution of steps (1) through (3); and

"(5) repeating steps (1) through (4) until the second least significant decimal digit representation has been so processed." [Id.,409 U.S. at 74, 93 S.Ct. at 258, 175 USPQ at 677.]

After considering the claims, the Supreme Court concluded that they recited a formula for converting BCD to binary, and that a "patent would wholly pre-empt the mathematical formula and in practical effect would be a patent on the algorithm itself." *Id.* at 72, 93 S.Ct. at 257, 175 USPQ at 676. Although the Court stated that the process involved a formula, it is readily apparent that the claims did not recite a mathematical formula per se, *e. g.,* E = MC[2]. The method, in fact, constituted what the Court defined as an algorithm, i. e., "[a] procedure for solving a given type of mathematical problem," *Id.* at 65, 93 S.Ct. at 254, 175 USPQ at 674, and the claims recited iteratively performed steps for computing a binary number from a corresponding BCD number. Although every BCD number has a known, corresponding binary representation, the claims recited a computational procedure rather than merely a simple or complex mathematical formula relating a BCD input to a binary output. Thus, it does not appear that applicants' claims necessarily fall outside of the *Benson* precedent.

The court, in *Parker v. Flook,* supra, considered claims for calculating and updating the value of an alarm limit in a process for the catalytic conversion of hydrocarbons. Claim 1 of the application reads as follows:

"1. A method for updating the value of at least one alarm limit on at least one process variable involved in a process comprising the catalytic chemical conversion of hydrocarbons wherein said alarm limit has a current value of

Bo+K

"Wherein Bo is the current alarm base and K is a predetermined alarm offset which comprises:

"(1) Determining the present value of said process variable, said present value being defined as PVL;

"(2) Determining a new alarm base, B1, using the following equation:

B1 = Bo(1.0-F) + PVL(F)

"wherein F is a predetermined number greater than zero and less than 1.0;

"(3) Determining an updated alarm limit which is defined as B1 + K; and thereafter

"(4) Adjusting said alarm limit to said updated alarm limit value."

[Id.,437 U.S. at 596-7, 98 S.Ct. at 2529, 198 USPQ at 200.]

Clearly, the mathematical formula of step (2) relates a set of input conditions to the calculated value of the alarm limit and would, therefore, be nonstatutory under the test proposed by appellants. The holding of the Court, however, did not rest on the mere presence of the formula but was articulated as follows: "Very simply, our holding today is that a claim for an improved method of calculation, even when tied to a specific end use, is unpatentable subject matter under [35 U.S.C.] § 101." 437 U.S. at 595, n. 18, 98 S.Ct. at 2528, n. 18, 198 USPQ at 199, n. 18.

Decisions of this court have held claims merely reciting methods of calculation to be nonstatutory. These decisions include: *In re Christensen,* supra (method of computing porosity of subsurface formation); *In re Richman,* supra (method of calculating a boresight correction angle); *In re de Castelet,* supra (method for solving a set of mathematical equations *per se*). In each of these appeals, specific mathematical formulas were recited for calculating numerical output values from one or more input values. Such was not the case in *In re Waldbaum,* 559 F.2d 611, 194 USPQ 645 (Cust. Pat.App. 1977), and *In re Sarkar,* supra.

The claims in *Waldbaum,* supra, were directed to a computer-controlled method for computing the number of busy and idle lines in a telephone network. *Waldbaum's* claim 9 reads as follows:

9. A method for controlling the operation of a data processor to determine the relative numbers of 0's and 1's in a data word; said data processor including a memory for storing data and instruction words at respective addresses; means for normally controlling the sequential execution of successively addressed instruction words; a plurality of registers; means for storing memory data words in said register; means for comparing the contents of predetermined ones of said plurality of registers; and means for controlling operations in the data processor in accordance with the instruction word being executed; comprising the steps of:

(1) controlling said storing means to store a memory data word whose relative numbers of 0's and 1's must be determined in a first one of said registers;

(2) executing a series of identical instruction words, each of which controls the data word in said one register to have one of its bits of a predetermined value changed to the opposite value, and controls a transfer to be made to the instruction word at a specified address and the address of the next instruction word to be placed in a second of said registers if said first register contains bits of only said opposite value, and

(3) controlling said comparing means to compare the address of a predetermined one of the instruction words in said series with the content of said second register when a transfer is made during the execution of one of the instruction words in said series to determine the relative numbers of 0's and 1's in said data word. [Id.at 614, 194 USPQ at 467.]

While, admittedly, the number of busy and idle telephone lines should equal the numbers finally computed by the process, claim 9 clearly does not recite a mathematical formula. As in *Benson,* when Waldbaum's method as claimed is analyzed, it is found to comprise a series of steps for manipulating binary numbers within a procedure for calculating the number of binary 1's and 0's present. Even though no formula was directly or indirectly recited, this court, in *In re de Castelet,* supra, 562 F.2d at 1243, 195 USPQ at 446, stated that Waldbaum's claims were nonstatutory because they were "directed solely to a process for calculating, i. e., to an algorithm per se."

This court, in *In re Sarkar,* supra, considered two distinct sets of claims in a method for open channel analysis and control using a mathematical model. The first set of claims is represented by claim 1 which reads:

1. A method of constructing a mathematical model of at least a portion of an open channel segmented into at least one reach and in which there is spatially varied unsteady flow and including the existence of at least one gravity wave during a given period of time comprising:

(a) measuring the cross-sectional dimensions of the channel at a specifically chosen, predetermined number of locations usable for schematizing said dimensions into a rectangularized cross-section for each regularly spaced but arbitrarily chosen distance x along the length of the channel irrespective of the chosen value of the interval of time t; [steps (b) — (h)] . . . .[] [Id.588 F.2d at 1331, 200 USPQ at 135.]

Steps (b) — (h) recited mathematical equations, additional data gathering steps and a procedure for solving the equations using the collected data. The substance of these steps was omitted from the decision pursuant to the court's granting of Sarkar's Motion for In Camera Proceedings and To Seal the Record under court Rule 5.13(g). *In re Sarkar,* 575 F.2d 870, 197 USPQ 788 (Cust. Pat.App. 1978). The precise recitation of these steps was not critical to the Court's consideration of the claims and are also unimportant to the analysis of the claims on appeal.

These claims are essentially directed to the mathematical model for open channel analysis and its use in computing flow parameters.

Claim 14 is representative of the second set of claims and it reads:

14. A method of locating an obstruction in an open channel to affect flow in a predetermined manner comprising:

a) obtaining the dimensions of said obstruction which affect the parameters of flow;

b) constructing a mathematical model of at least that portion of the open channel in which said obstruction is to be located in accordance with the method of claim 1 using those dimensions obtained in step (a) above;

c) adjusting the location of said obstruction within said mathematical model until the desired effect upon flow is obtained in said model; and thereafter

d) constructing said obstruction within the actual open channel at the specified adjusted location indicated by the mathematical model. [Id.at 1331, 200 USPQ at 135.]

The claim clearly recites the use of a mathematical model in an iterative manner to compute a set of parameters which will yield a desired flow result. Step (c) comprises adjusting the location of the obstruction by numerically changing its representation and then using the mathematical model to compute the effects of the change. When the result is within a certain error tolerance, the method proceeds to step (d).

This court, in considering claim 14, did not attribute any significance to step (d) under the reasoning that:

From the oral argument, we conclude that Sarkar no longer relies upon bridge or dam construction as post-solution activity steps effective to bring his process within § 101.It is unnecessary,therefore, to address that question orto consider claims 14-39 differently from claims 1-13.[Emphasis added.Id.at 1332, n. 6, 200 USPQ at 136, n. 6.]

The court went on to hold Sarkar's claimed invention to be mathematical exercises which do not comprise statutory subject matter under the rationale that:

Mathematical exercises, or methods of calculation, are within the myriad of mental processes of which the human mind is capable. Though they may be represented by written formulae, symbols, equations, or "algorithms," mathematical exercises remain disembodied. They may not, therefore, cross the threshold of § 101. On the other hand, the mere presence of a mathematical exercise, as a step or steps in a process involving nonmathematical steps, should not slam the door of the Patent and Trademark Office upon an applicant seeking eventual disclosure of that process. To hold otherwise would be to ignore the intent and purpose expressed ("any process") by Congress in § 101. [Id.at 1333, 200 USPQ at 137.]

Appellants seek to distinguish *Benson, Flook* and these other cases on the basis that the appealed claims do not recite methods of calculation because they do not set forth mathematical equations or relationships which determine an output value from a set of input values. In a sense this is true because the process claimed is best characterized as a solution technique for arithmetically determining the set of "process outputs" which are so inherently interrelated that they produce a specified goal response when operated upon by one or more transcendental equations within a mathematical model. This is different from the normal mode of calculating *only* in that appellants specify what the answer must be *before* performing the calculation. This simply amounts to a difference in the manner of calculating a set of acceptable "process outputs" and fails to make the claimed procedure any less a method of calculation. The type of mathematical computation involved does not determine whether a procedure is statutory or nonstatutory.

Stating a particular parameter, e. g., circuit response, current, wind resistance, etc., and then designing a structure by use of a mathematical model and computation techniques is a common way of computing the set of input parameters necessary to yield the specified output parameters. In fact, where the designed structure is to interface with other structures, it is necessary to work backwards because certain tolerances between structures will be interrelated.

As an example, appellants' process could be applied to a mathematical model of a simple resistor circuit. The circuit elements are interrelated by the well-known equation V=IR, in the same manner that appellants' elements are interrelated by transcendental equations. If the current, I, is specified to be not less than three amps, then according to the claimed procedure, calculations and substitutions would be iteratively performed to solve for acceptable numerical values of V and R. This is precisely what the method recited in claim 14 of *In re Sarkar,* supra, contemplates, i. e., adjustment in parameter values until a set is selected which will produce a desired output value or response from a mathematical model. It is readily apparent from such examples that appellants' process as claimed is just as much a method of calculation as was *Flook*'s procedure for calculating an updated alarm limit.

As has been previously explained, each of the steps of the claimed process, except perhaps the final step of equating the process outputs to the values of the last set of process inputs, directly or indirectly recites a mathematical computation. Appellants' process as a whole comprises a solution technique for a set of equations wherein sets of numbers are computed from other sets of numbers.

Appellants' claimed step of perturbing the values of a set of process inputs (step 3), in addition to being a mathematical operation, appears to be a data-gathering step of the type we have held insufficient to change a nonstatutory method of calculation into a statutory process. *See,* e. g., *In re Christensen* and *In re Sarkar.* In this instance, the perturbed process inputs are not even measured values of physical phenomena, but are instead derived by numerically changing the values in the previous set of process inputs.

As previously explained, the nature of the claims and the decisions in *Benson, Waldbaum* and *Sarkar* (in particular claims 14-39) rebut appellants' contention that methods of calculation or mathematical algorithms only exist when a mathematical formula relates a set of process inputs to a set of process outputs. To hold as appellant wishes would limit the meaning of "method of calculation" to a situation where process inputs are plugged into a formula to produce process outputs. There is no support in the decisions of this court or of the Supreme Court for such a narrow construction.

This is not to say, however, that the mere presence of calculations in a claimed process mandates a holding of nonstatutory subject matter. *See Flook,* 437 U.S. at 590, 98 S.Ct. 2522, 198 USPQ at 197. Numerous decisions of this court have properly determined computer-implemented processes to be statutory because any calculations involved were merely ancillary to more encompassing processes, *see,* e. g., *In re Chatfield,* supra; *In re Deutsch,* supra; and *In re Johnson,* supra.

Although the line separating statutory processes from nonstatutory processes is unclear, the mere presence of a calculation or the computer implementation of the method does not mandate a holding that the claimed procedure is not a "process" within the meaning of 35 U.S.C. § 101. But, where, as here, the claims solely recite a method whereby a set of numbers is computed from a different set of numbers by merely performing a series of mathematical computations, the claims do not set forth a statutory process.

In arguing that the claims on appeal are statutory, appellants place significance on the speculation that a trial and error substitution of physical circuit elements in a breadboard embodiment of a microwave circuit could possibly achieve the same results as appellants' process. Any weight given this possibility is misplaced, however, because it ignores the principle that it is the invention as claimed which must be examined. *See, In re Chatfield,* supra. Appellants have claimed a series of steps for computing a set of numbers and it is this claimed invention which is nonstatutory.

Nothing recited in claims 2-10 requires us to reach conclusions differing from that reached with respect to claim 1, and, therefore, the decision of the board holding claims 1-10 to not be directed to a "process" within the meaning of 35 U.S.C. § 101, is *affirmed.*

*AFFIRMED.*

With all due deference, I cannot agree that the presently claimed invention falls within any class of judicially established exceptions to § 101.

The majority opinion refuses to limit "method of calculation" to the plugging of inputs into a formula to produce outputs because it finds no judicial precedent for that limitation. But precedent is not required. The majority opinion elsewhere correctly recognizes that appellants' series of steps is a process "Within § 101 *unless*" (emphasis the majority's) it falls within an exception. Requiring judicial precedent for new technology would limit the patent system to the crusty molds of the past, and would frustrate disclosure of technological advances into areas unforeseen.

### *General*

The court is unanimous in holding erroneous the board's rejection, described in the board's brief opinion as based on the sole ground that the claimed process "falls within the purview" of *Benson* because "it can only be performed by the computer," and because the claims "pre-empt whatever is carried out by the computer, be it characterized as algorithm, formula, machine process or program or the like," and because the board knew "no way of operating a digital computer" except "by some form of programming."

In the interest of judicial economy, the court has elected not to remand the case to the board so that it might cure its inexplicable failure to conduct or supply an analysis of the claims.

The advent of a wholly new technology confronts the Patent and Trademark Office (PTO) with administrative problems in performing its vital service to the public interest in encouraging true progress of the useful arts. The solution to administrative problems does not lie, however, in so interpreting the law as to reduce an administrative burden. Avoiding a petition to Congress for increased funds or legislative relief, using § 101 to exclude new technology, presenting to the Supreme Court patentability issues not considered in the PTO or in this court, and employing phrases from the Court's opinions as rejection rubrics under § 101 in subsequent cases, is an approach long overdue for abandonment. Sadly, the exclusionary approach is extant in the board's treatment of the present appeal.

### *The Board*

The board decision is predicated on the notion that no process performed by use of a computer can be statutory. That approach is repeated in the solicitor's brief:

While others may have doubted that the broad proscription in the concluding paragraphs ofBensonis applicable, without exception[,] to computer programming cases, no room for doubt can exist any longer in view of the decision inFlook[Parker v. Flook,437 U.S. 584, 98 S.Ct. 2522, 57 L.Ed.2d 451, 198 USPQ 193 (1978)]. * * * [T]he mandate of the court is that it will not "extend patent rights into areas wholly unforeseen by Congress," and that claims directed to computer programming fall within this proscription.

A process invention cannot, however, be declared nonstatutory on the sole basis of the means employed in carrying out the process.

This court has patiently explained the impropriety of reading *Benson* so broadly as to exclude all processes performed with a computer. *See, e. g., In re Freeman,* 573 F.2d 1237, 1244-45, 197 USPQ 464, 470 (Cust. Pat.App. 1978); *In re de Castelet,* 562 F.2d 1236, 1240-43, 195 USPQ 439, 443-45 (Cust. Pat.App. 1977); *In re Chatfield,* 545 F.2d 152, 155-57, 191 USPQ 730, 733-34 (Cust. Pat.App. 1976), *cert. denied,* 434 U.S. 875, 98 S.Ct. 226, 54 L.Ed.2d 155, 195 USPQ 465 (1977).

Indeed, the Supreme Court attempted, in unequivocal language, to forestall such broad reading of its opinion in *Benson,* inserting an express caveat: "It is said that the decision precludes a patent for any program servicing a computer. We do not so hold." 409 U.S. at 71, 93 S.Ct. at 257, 175 USPQ at 676.

In *Flook,* the Court again declined to declare all process inventions involving "computer programs" nonstatutory per se. It characterized its holding in *Benson*: "In *Gottschalk v. Benson,* 409 U.S. 63, 93 S.Ct. 253, 34 L.Ed.2d 273, we held that the discovery of a novel and useful *mathematical formula* may not be patented," 437 U.S. at 585, 98 S.Ct. at 2523, 198 USPQ at 195 (emphasis added). It stated, "[w]e use the word `algorithm' in this case, as we did in *Gottschalk v. Benson,* 409 U.S. 63, 65, 93 S.Ct. 253, 34 L.Ed.2d 273, to mean `[a] procedure for solving a given type of *mathematical* problem * * *.'" 437 U.S. at 585 n. 1, 98 S.Ct. at 2523 n. 1, 198 USPQ at 195 n. 1 (emphasis added). It summarized its holding as, "Very simply, our holding today is that a claim for an improved *method of calculation,* even when tied to a specific end use, is unpatentable subject matter under § 101." 437 U.S. at 595 n. 18, 98 S.Ct. at 2529 n. 18, 198 USPQ at 199 n. 18 (emphasis added). It added:

Neither the dearth of precedent, nor this decision, should therefore be interpreted as reflecting a judgment that patent protection of certain novel and useful computer programs will not promote the progress of science and the useful arts, or that such protection is undesirable as a matter of policy. Difficult questions of policy concerning thekindsof programs that may be appropriate for patent protection and the form and duration of such protection can be answered by Congress on the basis of current empirical data not equally available to this tribunal.

437 U.S. at 595, 98 S.Ct. at 2528, 198 USPQ at 199-20 (emphasis added and footnotes omitted). Thus, until Congress decides that some kinds of programs are not statutory, it remains the duty of the PTO and the courts to carefully analyze the claimed inventions presented, and to determine whether each falls within or without the judicially established exceptions to § 101.

The solicitor quotes the Court's reference in *Flook* to "areas wholly unforeseen by Congress." That reference, however, must be read in the light of the facts then before the Court. In both *Benson* and *Flook,* the Court was dealing with claims it viewed as drawn to mathematical formulae. In *Benson* it referred to the necessity for Congress to speak if "these" programs are to be statutory. In *Flook* it spoke of the need for Congress to determine what "kinds" of programs may be patented. The Court nowhere described the invention in *Flook* as a "program," but merely responded to importunings of amici who sought a judicial pronouncement that "computer programs" were *per se* statutory or nonstatutory. It is just such pronouncement the Court refused to make. Hence it is improper to interpret *Flook* as holding nonstatutory all claims describable in the solicitor's (not the Court's) words as, "directed to computer programming." In all events, the words of the Court in *Benson* and *Flook* cannot be interpreted as condemning all claims to process inventions which are merely *carried out* by use of a computer. Congress and the courts having refrained from so directing, it should be manifest to all that "no basis exists for a moratorium on protection of inventions embodying or *using* computer programs." *In re de Castelet, supra,* 562 F.2d at 1240, 195 USPQ at 443 (emphasis added).

The reference to "areas wholly unforeseen" cannot be read literally, or in a vacuum. The Court was quoting from its opinion in *Deep-south Packing Co. v. Laitram Corp.,* 406 U.S. 518, 92 S.Ct. 1700, 32 L.Ed.2d 273 (1972), which dealt with *infringement,* and was merely refusing to revise its earlier views. The Court could not have meant that no invention in a new technology can be considered statutory until Congress says it is. Congress is not prescient. Nor can it be expected to continuously amend the statute, in a fruitless effort to stay ahead of burgeoning technology. Congress has for years broadly provided for patenting of "any process" meeting all requirements of the statute, leaving to the courts the interpretation of that phrase. *See In re Sarkar,* 588 F.2d 1330, 200 USPQ 132 (Cust. Pat.App. 1978).

The Court refused the same importunings in *Dann v. Johnston,* 425 U.S. 219, 220, 96 S.Ct. 1393, 1394, 47 L.Ed.2d 692, 189 USPQ 257, 258 (1976), saying "We find no need to treat that question in this case, however, because we conclude that in any event respondent's system is unpatentable on grounds of obviousness." It is at least incongruous for the PTO to argue that the Court made a pronouncement it has consistently and explicitly refused to make.

The board's inexplicably superficial consideration of the claims on appeal led it to find them preempting "whatever is carried out by the computer," and because computers are operated by "programs," the board held the invention nonstatutory on that ground alone. We explained our view of the error of that approach in a statement in *In re Freeman, supra,* reflecting the law applicable here:

Though the board gave no clear reasons for so concluding, its approach would appear to be that every implementation with a programmed computer equals "algorithm" in theBensonsense. If that rubric be law, every claimed method that can be so implemented would equal nonstatutory subject matter under 35 U.S.C. § 101. That reasoning sweeps too wide and is without basis in law. * * *

As a bare minimum, application ofBensonin a particular case requires a careful analysis of the claims, to determine whether, as inBenson,they recite a "procedure for solving a given type ofmathematicalproblem." [Gottschalk v. Benson,] 409 U.S. at 65, 93 S.Ct. 253, 175 USPQ at 674 (emphasis added).

573 F.2d at 1245, 197 USPQ at 470.

### *Mathematical Relationship*

This is the first computer-related case in which this court has affirmed a rejection of claims not drawn in essence to a mathematical relationship.

In clarifying the distinction between statutory and nonstatutory subject matter in these types of cases, this court has recognized that "[t]he mathematical expression of scientific truth or principle is itself not patentable," and has pointed out that the Supreme Court "viewed Benson's claims as effectively claiming the `effect,' principle, or law or force of nature (the algorithm) itself." *In re de Castelet, supra* at 1243, 195 USPQ at 445. In *Flook, supra,* 437 U.S. at 589, 98 S.Ct. at 2525, 198 USPQ at 197, the Court said, "Reasoning that an algorithm, or mathematical formula, is like a law of nature, *Benson* applied the established rule that a law of nature cannot be the subject of a patent." The import of that statement is that the meaning of "algorithm" is limited by its association with the "mathematical formula = law of nature" concept. Neither "algorithm" nor "mathematics" may alone serve as a label substitute for "nonstatutory."

Nor, as above indicated, is the term "program" an acceptable substitute for "nonstatutory." Confusion may be avoided if it be realized that what is at issue is not the "program," i. e., the software, but the process steps which the software directs the computer to perform.

The terms "mathematics" and "mathematical exercises" are so broad as to be applicable to any process in which numbers are involved. Not every process, however, in which the doer works with numbers should be declared nonstatutory on that ground alone. When the numbers involved satisfy a mathematical relationship, like the relationship defined in an equation, a formula, or a mathematical algorithm, and the invention is the mere plugging of numbers into that equation, formula, or algorithm, *i.e.,* a solution technique or method of calculation, that invention has been judicially declared nonstatutory. When the numbers involved satisfy no mathematical relationship, and the invention merely employs numbers in the place of physical elements, that invention may, in my view, be statutory.

The mathematical exercises referred to in *Sarkar, supra* note 2, are those expressible as equations, formulae, and mathematical algorithms. Sarkar's invention was found to be the provision of a formula, the substitution of values therein, and the making of formula-required calculations.

In *In re Richman,* 563 F.2d 1026, 1029, 195 USPQ 340, 343 (Cust. Pat.App. 1977), the nonstatutory process at issue was carefully described as "method of calcula[tion] (utilizing *mathematical formulae*)" (emphasis added). Some, perhaps most, computer software merely directs the performance of nonstatutory mathematical exercises, as those in *Richman, Benson,* and *Flook* were found to be. Other software, however, may be a means for directing the performance of clearly statutory process. Simply stated, the labeling approach risks freezing from the patent system disclosures of processes the claims to which, as here, are not in essence analogous to claims to mathematical formulae or laws of nature.

Every process may be called a "program," *i. e.,* a series of steps. Both the series of steps performed by a computer, and the software directing those steps, have acquired the name "computer programs." That fact alone, as indicated in the text, *supra,* does not warrant the view that no computer program can on analysis be shown to represent a statutory process. Some computer-performed processes may be statutory. Some may not.

Efforts to follow precedent in "computer program" type cases require repeated wrestling with the interpretation and effect of such terms as "program," "mathematical formula," "algorithm," "solution," "equation," and "calculation." *See, e. g., In re Toma,* 575 F.2d 872, 197 USPQ 852 (Cust. Pat.App. 1978); *In re Freeman, supra; In re Chatfield, supra.* In *Benson,* some of those terms were used interchangeably. "Algorithm" was defined as "[a] procedure for solving a given type of *mathematical* problem." 409 U.S. at 65, 93 S.Ct. at 254, 175 USPQ at 674 (emphasis added). The claimed process was variously described as "a method of programming a general purpose digital computer," 409 U.S. at 65, 93 S.Ct. at 254, 175 USPQ at 674; "a generalized formulation for programs to solve mathematical problems of converting one form of numerical representation to another," 409 U.S. at 65, 93 S.Ct. at 254, 175 USPQ at 674; and a "formula for converting BCD numerals to pure binary numerals," 409 U.S. at 71, 93 S.Ct. at 257, 175 USPQ at 676. It was said that a patent containing Benson's claims "would wholly pre-empt the mathematical formula and in practical effect would be a patent on the algorithm itself," 409 U.S. at 72, 93 S.Ct. at 257, 175 USPQ at 676.

In *Flook,* Benson's invention was characterized as "a novel and useful mathematical formula," 437 U.S. at 585, 98 S.Ct. at 2523, 198 USPQ at 195, and the definition of "algorithm" in *Benson* was employed in identifying steps (2) and (3) of Flook's claim 1 as an "algorithm" or "formula." *Id.* The claimed invention in *Flook* was described as a "method for calculating alarm limit values," 437 U.S. at 594, 98 S.Ct. at 2528, 198 USPQ at 199. *In re Richman, supra,* was quoted in the course of holding the invention in *Flook* nonstatutory, even if its formula's "solution is for a specific purpose," 437 U.S. at 595, 98 S.Ct. at 2528, 198 USPQ at 199.

In *Benson,* the claimed process presumed a fixed relationship between BCD numbers and pure binary numbers and included a series of manipulatory steps that, when practiced on the digits in a BCD number, converted that number to its pure binary equivalent. In *In re de Castelet, supra,* the claims recited a process for solving a set of mathematical equations to transform discrete coordinate points into a smooth curve. In *In re Waldbaum,* 559 F.2d 611, 194 USPQ 465 (Cust. Pat.App. 1977), the claimed process was a series of counting steps for determining the number of 1's in a binary data word. In *In re Richman, supra, In re Christensen,* 478 F.2d 1392, 178 USPQ 35 (Cust. Pat.App. 1973), *In re Sarkar, supra* note 2, and *Flook,* the claims were found to be directed essentially to the solution of mathematical equations and were not rendered statutory by the inclusion of data-gathering and post-solution steps dictated by the equations. In referring to the rule that the discovery of a law of nature cannot be patented, the Court in *Flook* said, "The underlying notion is that a scientific principle, such as that expressed in respondents' algorithm, reveals a relationship that has always existed." *Parker v. Flook, supra,* 437 U.S. at 593 n. 15, 98 S.Ct. at 2527, n. 15, 198 USPQ at 198 n. 15.

In short, the foregoing cases dealt with process claims that, upon careful analysis, were determined to be directed to nothing more than a mathematical *relationship* between quantities, *i. e.,* processes wherein input quantities are acted upon by a series of relationship-defining steps, expressed in mathematical symbols or in prose, to produce output quantities bearing the defined mathematical relationship to the input quantities.

Each so-called "computer program" case, like all cases turning on the nature of an invention, must be decided not on a rubric but on its own facts. In reviewing a rejection under § 101, the controlling facts must be developed from careful and detailed analysis of the invention as described and claimed. The Supreme Court and this court have made just such analysis in the "computer program" cases thus far presented. It is just such analysis that the PTO must make in each such case. That analysis includes a determination of the meaning of computer-world terms, and the role and effect of the elements or steps for which they stand, in the context of the invention as a whole. Justice requires that employment of labels, rubrics, and talismans, be eschewed.

The same is true in considering the nature of an invention in the light of § 103. To hold unpatentable, for example, all "combinations of old elements" would totally defeat the constitutional-statutory scheme for promoting progress in the useful arts. Every invention is a combination of old elements. Some combinations of old elements are not patentable, *e. g., Graham v. John Deere Co.,* 383 U.S. 1, 86 S.Ct. 684, 15 L.Ed.2d 545, 148 USPQ 459 (1966). Some are, *e. g., United States v. Adams,* 383 U.S. 39, 86 S.Ct. 708, 15 L.Ed.2d 572, 148 USPQ 479 (1966).

The analyses reached different conclusions concerning the *nature* of the claimed inventions in *Benson* and *Flook,* this court viewing them as a whole as processes within § 101, the Supreme Court viewing them as mathematical formulae not within § 101. The same dichotomy exists between the majority and dissenting opinions in this case.

It would ease the decisional burden, for example, to merely note that one step of the present process involves a transcendental equation, to cry "algorithm," "mathematics," or "method of calculation," and to affirm the rejection on that talismanic basis. But, analysis discloses that the present process as a whole is fundamentally different from processes found nonstatutory in prior "computer program" cases.

### *The Present Invention*

The real party in interest is the United States of America as represented by the Secretary of the Army.

Rejections under §§ 102, 103 were overcome because, in Gelnovatch and Arell's (Gelnovatch's) process, a different subset of parameters is perturbed in each exploratory search. In prior processes, all parameters were perturbed in each exploratory search. Gelnovatch's process decreases the error faster, thus requiring less computer time to execute. The pertinent reference of record is Murray-Lasso Kozemchak, *Microwave Circuit Design By Digital Computer,* IEEE Transactions on Microwave Theory and Techniques, vol. MTT-17, No. 8, August 1969, at 514. The examiner withdrew rejections under §§ 102, 103, and 112. The examiner also withdrew a "mental process" rejection when "computer" and "automatically" were inserted in the claims, viewing those words as limiting the processes to performance by computer. The board chose not to exercise its authority under PTO Rule 196(b) ( 37 CFR 1.196(b)) to reinstate the §§ 102, 103, 112 rejections, electing to treat performance by computer, the limitation that overcame those rejections, as the sole basis for its rejections.

The sole rejection being under § 101, we are not here concerned with considerations of novelty ( § 102) or obviousness ( § 103). Nor are we at liberty, as we never are when reviewing rejections under § 101 alone, 35 U.S.C. § 144, to determine whether the claimed invention is patentable, as distinguished from whether it is statutory.

The determinative question under § 101 is, "What did Gelnovatch invent?" If the claimed process be the input of quantities bearing a mathematical relationship to output quantities, it falls within the judicially declared class of nonstatutory inventions. The process of Gelnovatch is not such.

In Gelnovatch's process, a transcendental equation expresses a relationship between the output data produced and the desired microwave circuit response, but the claimed process is *not* directed to that relationship. Thus the present process is not one in which desired circuit response data ("input quantity") is substituted for variables in a transcendental equation ("a series of relationship-defining steps expressed in mathematical symbols"), and the equation then solved for parameter values capable of producing the desired response ("output quantity"). To so characterize the present process would not only be inaccurate, but would attribute to the process a capability for the impossible, namely, the exact solution of a transcendental equation.

Gelnovatch's claimed process is not directed to a relationship between quantities, there being *no relationship* whatsoever, even in theory, between his input data (arbitrarily estimated parameter values) and his output data (parameter values approaching a desired circuit response). The present process invention is best characterized as a systematic, exploratory, trial-and-error series of particular steps to produce parameter values capable of approximating a desired microwave circuit response.

The values produced by the present process are related to the desired microwave circuit response through the medium of a particular "law of nature," *i. e.,* a transcendental equation, but Gelnovatch is *not* claiming the equation itself. Nor is he claiming a formula, or mathematical algorithm, or calculation. Nor is he claiming anything describable as a law of nature. There being no preexisting relationship or natural law that correlates the input data and the output data, Gelnovatch's process is the *antithesis* of a mathematical relationship or law of nature. It is more akin to the "bread-board" experimental method employed in the development of physical products.

Indeed, the present process is technically identical with a process in which large supplies of circuit elements were one-by-one physically connected into a circuit, additional elements were substituted and resubstituted, within specific and different element groups, until a circuit was created having the desired circuit response. Such a purely physical process might or might not be patentable; it would clearly be statutory. That Gelnovatch has replaced each physical circuit element with its numerical representation, and substituted numerical representations instead of substituting the physical elements themselves, does not change the fundamental nature of the process in this case, and does not in my view render it nonstatutory.

That the claimed process may *use* a transcendental equation in a process step does not alone render the claimed invention as a whole nonstatutory. *In re Chatfield, supra,* 545 F.2d at 158-59, 191 USPQ at 736. "Yet it is equally clear that a process is not unpatentable [nonstatutory] simply because it contains a law of nature or a mathematical algorithm." *Parker v. Flook, supra,* 437 U.S. at 590, 98 S.Ct. at 2526, 198 USPQ at 197.

I would reverse the rejection.