Chapter 8: Patent Protection of Software:
Statutory Subject Matter in the
Supreme Court and the Federal Circuit

B. The Analysis of Statutory Subject Matter
in the First Decade After the Trilogy

In re Grams
United States Court of Appeals for the Federal Circuit
888 F.2d 835 (1989)

Archer, Circuit Judge.

Applicants appeal from the decision of the PTO Board of Patent Appeals and Interferences (Board), affirming the examiner’s rejection of all claims. The claims were rejected under 35 U.S.C. § 101 as being directed to nonstatutory subject matter because they in essence claim either a mathematical algorithm or a method of doing business. We affirm.


The invention provides a method of testing a complex system to determine whether the system condition is normal or abnormal and, if it is abnormal, to determine the cause of the abnormality. As disclosed in the specification, the invention is applicable to any complex system, whether it be electrical, mechanical, chemical, biological, or combinations thereof. The system comprises a plurality of constituent subsystems or parts, some characteristic of which is represented by a set of correlated parameters susceptible of measurement and representative of the overall system. The disclosed invention involves considering the entire set of parameters, diagnosing the existence of an abnormality, and identifying which particular parameters of the set are responsible for the abnormality.

The claims limit the disclosed invention to the diagnosis of an individual. Claim 1, on which the other claims depend, reads:

Thus, step [a] requires the performance of clinical laboratory tests on an individual to obtain data for the parameters (e.g., sodium content). The remaining steps, [b]-[e], analyze that data to ascertain the existence and identity of an abnormality, and possible causes thereof. In that regard, steps [b]-[e] are in essence a mathematical algorithm, in that they represent “a procedure for solving a given type of mathematical problem.” See Gottschalk v. Benson. (It is of no moment that the algorithm is not expressed in terms of a mathematical formula. Words used in a claim operating on data to solve a problem can serve the same purpose.)

Applicants do not dispute that claim 1 includes a mathematical algorithm. However, they contend that the mere recital of an algorithm does not automatically render a claim nonstatutory. They are correct, in that regard, but the inclusion of a mathematical algorithm in a claim can render it nonstatutory if the claim in essence covers only the algorithm. The Board held that was the case here.


Whether the algorithm-containing claims at issue are drawn to statutory subject matter.


Intuitively, one might conclude that § 101's “any . . . process” would include the diagnostic method claimed by applicants. Indeed, even without physical step [a] present in the claims, application of the algorithm in steps [b]-[e] seems to be a type of “process.” The Supreme Court recognized as much in Flook.

Flook makes clear, however, as did its forerunner, Benson, that even though the application of an algorithm to data is a “process” in the literal sense, it is not one that is contemplated by § 101, i.e., it is “nonstatutory subject matter.” Thus, mathematical algorithms join the list of non-patentable subject matter not within the scope of § 101, including methods of doing business, naturally occurring phenomena, and laws of nature.

Construing § 101 as excluding mathematical algorithms seems somewhat at odds with the liberal view of that section expressed in a more recent Supreme Court opinion, Diamond v. Chakrabarty. There, the Court decided that a living man-made microorganism fell within the terms “manufacture” or “composition of matter” in § 101. In choosing such “expansive terms,” stated the Court, “modified by the comprehensive [word] 'any,' Congress plainly contemplated that the patent laws would be given wide scope.” The Court went so far as to note that Congress intended statutory subject matter to include “anything under the sun that is made by man.” Chakrabarty.

Chakrabarty expressly rejects the argument that patentability in a new area, “microorganisms, cannot qualify as patentable subject matter until Congress expressly authorizes such protection.” Although the Court distinguished Flook in its opinion, the court's rejection of this argument seems to reflect a change from Flook's admonition that “we must proceed cautiously when we are asked to extend patent rights into areas wholly unforeseen by Congress.”

Another recent case, Diehr, repeats the “anything under the sun” statement of Chakrabarty, in the context of determining that the algorithm-containing claim at issue there was statutory subject matter under § 101. Diehr adds that in cases of statutory construction, which is involved here because the issue is whether applicants' claims fall within the statutory meaning of “process,” “we begin with the language of the statute” and, unless otherwise defined, “words will be interpreted as taking their ordinary, contemporary, common meaning.” Diehr notes that the Court has “more than once cautioned that ‘courts should not read into the patent laws limitations and conditions which a legislature has not expressed.’ ”

Notwithstanding those statements in Diehr and Chakrabarty, Benson remains the law. Indeed, it is cited in both Diehr and Chakrabarty, with no apparent attempt in either opinion to overrule or disapprove of it. Thus, “an algorithm, or mathematical formula . . . like a law of nature . . . cannot be the subject of a patent.” Diehr.

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 PTO upon an applicant[.]” In re Sarkar, 588 F.2d 1330, 1333 (CCPA 1978). Thus, if there are physical steps included in the claim in addition to the algorithm, the claim might be eligible for patent protection. As stated in In re Walter:

Once a mathematical algorithm has been found, the claim as a whole must be further analyzed. If it appears that the mathematical algorithm is implemented in a specific manner to define structural relationships between the physical elements of the claim (in apparatus claims) or to refine or limit claim steps (in process claims), the claim being otherwise statutory, the claim passes muster under § 101.

Though satisfaction of the Walter test necessarily depicts statutory subject matter, failure to meet that test does not necessarily doom the claim. As stated in Abele, “Walter should be read as requiring no more than that the algorithm be ‘applied in any manner to elements or process steps,’ ” That statement is followed by this proviso: “provided that its application is circumscribed by more than a field of use limitation or non-essential post-solution activity.” Thus, if the claim would be “otherwise statutory,” albeit inoperative or less useful without the algorithm, the claim likewise presents statutory subject matter when the algorithm is included.

In all instances, this critical question must be answered: “What did applicants invent?” And in answering this inquiry:

Each invention must be evaluated as claimed: yet semantogenic considerations preclude a determination based solely on words appearing in the claims. In the final analysis under § 101, the claimed invention, as a whole, must be evaluated for what it is. Hence, the analysis requires careful interpretation of each claim in light of its supporting disclosure.

In re Sarkar, supra, Though that analysis can be difficult, it is facilitated somewhat if, as here, the only physical step involves merely gathering data for the algorithm. As stated in In re Christensen, 478 F.2d 1392, 1394 (CCPA 1973):

Given that the method of solving a mathematical equation may not be the subject of patent protection, it follows that the addition of the old and necessary antecedent steps of establishing values for the variables in the equation cannot convert the unpatentable method to patentable subject matter.

The reason for this was explained in In re Sarkar, 588 F.2d at 1335:

No mathematical equation can be used, as a practical matter, without establishing and substituting values for the variables expressed therein. Substitution of values dictated by the formula has thus been viewed as a form of mathematical step. If the steps of gathering and substituting values were alone sufficient, every mathematical equation, formula, or algorithm having any practical use would be per se subject to patenting as a “process” under § 101. Consideration of whether the substitution of specific values is enough to convert the disembodied ideas present in the formula into an embodiment of those ideas, or into an application of the formula, is foreclosed by the current state of the law.

Whether § 101 precludes patentability in every case where the physical step of obtaining data for the algorithm is the only other significant element in mathematical algorithm-containing claims is a question we need not answer. Analysis in that area depends on the claims as a whole and the circumstances of each case. Rather, we address only the claims and other circumstances involved here.

The sole physical process step in Grams' claim 1 is step [a], i.e., performing clinical tests on individuals to obtain data. The specification does not bulge with disclosure on those tests. To the contrary, it focuses on the algorithm itself, although it briefly refers to, without describing, the clinical tests that provide data. Thus, it states: “The [computer] program was written to analyze the results of up to eighteen clinical laboratory tests produced by a standard chemical analyzer that measures the levels of the chemical and biological components listed.” The specification also states that “[t]he invention is applicable to any complex system, whether it be electrical, mechanical, chemical or biological, or combinations thereof.” From the specification and the claim, it is clear to us that applicants are, in essence, claiming the mathematical algorithm, which they cannot do under Benson. The presence of a physical step in the claim to derive data for the algorithm will not render the claim statutory.

Applicants argue that Abele warrants a reversal. We disagree. Allowed claim 6 in Abele required operation of an algorithm on X-ray attenuation data, with a subsequent display. The data were available for the algorithm only after the production and detection steps, i.e., after an X-ray beam was passed through an object using a CAT scanner, and detected upon exit. The court concluded that in the absence of the algorithm, “the production, detection, and display steps would still be present and would result in a conventional CAT-scan process.” Thus, the production and detection steps were not viewed as mere antecedent steps to obtain values to solve the algorithm; instead:

We are faced simply with an improved CAT-scan. . . . The improvement in either case resides in the application of a mathematical formula within the context of a process which encompasses significantly more than the algorithm alone.

In Abele, therefore, the algorithm served to improve the CAT-scan process. As such, the algorithm satisfied the Walter guideline of “refining a step in a process that is otherwise statutory,” and hence, it presented statutory subject matter. In this case, because algorithm steps [b]-[e] do not operate to change any aspect of the physical process of step [a], the claim does not satisfy the Walter guideline. Though this by itself is not dispositive (see discussion of Walter, supra), patentability here is precluded by the fact that physical step [a] merely provides data for the algorithm.

Thus, claim 1 is unpatentable. Claims 3-15 were not argued separately from claim 1; hence they fall with our treatment of that claim. Claim 16, which requires that the method be performed with a programmed computer, is argued separately but applicants have not persuaded us that performing the method of claim 1 with a computer requires a different result.

Because we affirm the Board's holding that the applicants' claims are unpatentable under § 101 as being drawn to a nonstatutory mathematical algorithm, we need not address the issue of whether they are also unpatentable as a method of doing business.


1. What is Grams's invention, in plain English? Perhaps, it is something like this:

Does that appear to be a mathematical algorithm? Is that a "procedure for solving a given type of mathematical problem"? The court says that Grams did not dispute that the claim "includes a mathematical algorithm." Without that concession, would the court have been able to characterize the claim as one directed to a mathematical algorithm? (What about set theory?) What about classifying it as a method of doing business? (The court found it unnecessary to reach that issue.) A law of nature? A series of mental steps?

2. Compare Judge Archer's approach in Grams in which he painfully struggles to harmonize as much of the case law as possible with Judge Rader's approach in Arrhythmia (below) in which he calls for slashing the Gordian Knot to bits and reshaping the law on a simpler basis—"anything under the sun goes." This opinion reflects the courts' early struggles to deal with the confusing and seemingly conflicting cases.

3. How seriously do you think we should take the statement in Chakrabarty (based on a statement in the House Report, attributed to Pat Federico) about "anything under the sun that is made by man"? What does "made" mean? What if a man under the sun makes a thing that is not a Discovery? What if his activity is not that of an Inventor? How do you reconcile the breadth of the anything-under-the-sun maxim with the courts' repeated recognition that laws of nature, methods of doing business, and so on cannot be patented? Is a new method of doing business something made under the sun? Is a poem? A joke? A song? A legal argument? A fencing tactic?

4. Consider what is meant by: “In all instances, this critical question must be answered: ‘What did applicants invent?’ ” How do “semantogenic considerations preclude a determination based solely on words appearing in the claims”? Do these statements mean any more than — “We should look to the extent of the supporting disclosure, because the applicant is not entitled to claim more than was disclosed. If you invent, disclose, and enable just a telegraph you can't have a patent on the radio or TV.”

  se·man·to·gen·ic: adjective: arising from impairment in the use of language. (The Merriam-Webster Unabridged Dictionary - online)

5. Compare the concluding sentence[W]e need not address the issue of whether they are also unpatentable as a method of doing businesswith the earlier statement (second paragraph of Opinion) Thus, mathematical algorithms join the list of non-patentable subject matter not within the scope of § 101, including methods of doing business, naturally occurring phenomena, and laws of nature.

In re Iwahashi
United States Court of Appeals for the Federal Circuit
888 F.2d 1370 (1989)

Rich, Circuit Judge.

This appeal is from the decision of the PTO Board of Patent Appeals and Interferences (board), affirming the examiner's final rejection of the single claim of applicants' patent application serial No. 454,022, entitled "Auto-Correlation Circuit for Use in Pattern Recognition." The sole ground of rejection is that the subject matter claimed is nonstatutory under 35 U.S.C. § 101 because it is merely a mathematical algorithm. We reverse.

The opening sentence of the specification states: "This invention relates to an auto-correlation unit for use in pattern recognition to obtain auto-correlation coefficients as for stored signal samples." The embodiment more particularly discussed as a species of pattern recognition is voice recognition. The prior art calculation of auto-correlation coefficients is described as being based on a calculation formula involving a multiplication step. The specification states the disadvantage to be as follows:

Those state-of-the-art units for calculation of the auto-correlation coefficients have the disadvantage of requiring expensive multipliers and also complicated circuitry. As a result the auto-correlation unit circuitry within the entire pattern recognition apparatus is proportionately large and auto-correlation calculation demands a greater amount of time during recognition. . . .

The principal object of this invention is to provide an auto-correlation unit for pattern recognition which evaluates auto-correlation coefficients by means of a simple circuitry without the need for an expensive multiplier as well as eliminating the above discussed disadvantages.

Underlying the auto-correlation unit claimed, is a plethora of mathematical demonstration by which the applicants purport to show that the approximated value of the desired coefficient can be obtained without multipliers by obtaining the square of the sum of two of the factors in the equation and calculating the auto-correlation coefficient therefrom according to a stated formula. The specification concludes:

As explained in the foregoing, this invention offers a highly cost-effective auto-correlation unit for pattern recognition with simple circuitry without the need to use an expensive multiplier, but which has comparatively high accuracy and can, moreover, calculate auto-correlation coefficients at high speed.

Fig. 1 of the application drawings is described as "a block diagram schematically showing an embodiment of this invention." Fig. 2 is described as "a block diagram showing in more detail the embodiment of this invention."

We shall not attempt a description of the electronic circuitry shown by these drawings beyond explaining, for the better understanding of the claim, that the units designated "ROM" and "RAM" are, respectively, a read-only memory and a random access memory, terms well understood by those skilled in the art. "CPU" is a central processing unit. In this case, the function of the ROM, which is a permanent information-storage device, is to deliver as output the square of a number fed to it as input. It is the electronic equivalent of a table in which one can look up the square of numbers over a desired range.

We next reproduce the claim on appeal and do so by presenting a copy of the claim as it has been presented in the Solicitor's brief, to which we have added the letters in brackets designating at [a] the preamble or introductory clause and at [b] through [h] the several means-plus-function and other elements of the combination of elements recited. Element [d] is not in means-plus-function form but specifies a ROM.


[a] An auto-correlation unit for providing auto-correlation coefficients for use as feature parameters in pattern recognition for N pieces of sampled input values Xn(n = 0 to N - 1), said unit comprising:

[b] means for extracting N pieces of sample input values Xn from a series of sample values in an input pattern expressed with an accuracy of optional multi-bits;

[c] means for calculating the sum of the sample values Xn and Xn-r (t = 0 - P, P ≤ N);

[d] a read-only memory associated with said means for calculating;

[e] means for feeding to said read-only memory the sum of the sampled input values as an address signal;

[f] means for storing in said read-only memory the squared value of each sum, (Xn + Xn-r )2;

[g] means for fetching and outputting the squared values of each sum of the sample input values from said read-only memory when said memory is addressed by the sum of the sample input values; and

[h] means responsive to the output (Xn + Xn-r)2 of said read-only memory for providing an auto-correlation coefficient for use as a feature parameter according to the following formula:

          Σ   ( Xn + X n-r ) 2
        ———————— - 1
        2   ·   Σ   Xn 2

[Drawings shown below, at end of case]

This is one more in the line of cases stemming from the Supreme Court decision in Gottschalk v. Benson, decided by our predecessor, the CCPA. Out of these cases came the Freeman-Walter test to determine whether a claim defines nonstatutory subject matter. It was stated in Freeman as follows:

Determination of whether a claim preempts nonstatutory subject matter as a whole, in the light of Benson, requires a two-step analysis. First, it must be determined whether the claim directly or indirectly recites an "algorithm" in the Benson sense of that term, for a claim which fails even to recite an algorithm clearly cannot wholly preempt an algorithm. Second, the claim must be further analyzed to ascertain whether in its entirety it wholly preempts that algorithm.

The opinion next discusses the meaning of "algorithm":

Over-concentration on the word "algorithm" alone, for example, may mislead. The Supreme Court carefully supplied a definition of the particular algorithm before it [in Benson], i.e., "[a] procedure for solving a given type of mathematical problem." The broader definition of algorithm is "a step-by-step procedure for solving a problem or accomplishing some end." (Webster's New Collegiate Dictionary (1976).)

. . . It would be unnecessarily detrimental to our patent system to deny inventors patent protection on the sole ground that their contribution could be broadly termed an "algorithm".

In footnote 8 of the Freeman opinion the Court further said:

The preferred definition of "algorithm" in the computer art is: "A fixed step-by-step procedure for accomplishing a given result; usually a simplified procedure for solving a complex problem, also a full statement of a finite number of steps." (C. Sippl & C. Sippl, Computer Dictionary and Handbook (1972).)

Appellants state that the apparatus claimed "may properly be characterized as a computer."

We note these discussions of the meaning of "algorithm" to take the mystery out of the term and we point out once again that every step-by-step process, be it electronic or chemical or mechanical, involves an algorithm in the broad sense of the term. Since § 101 expressly includes processes as a category of inventions which may be patented and § 100(b) further defines the word "process" as meaning "process, art or method, and includes a new use of a known process, machine, manufacture, composition of matter, or material," it follows that it is no ground for holding a claim is directed to nonstatutory subject matter to say it includes or is directed to an algorithm. This is why the proscription against patenting has been limited to mathematical algorithms and abstract mathematical formulae which, like the laws of nature, are not patentable subject matter.

The above-listed line of CCPA cases held some claims statutory and other claims nonstatutory, depending entirely on what they said. We have to do the same here. Appellants cautiously admit that their claim "at least indirectly, recites an algorithm in some manner," and thus meets the first part of the Freeman-Walter test, but argue strenuously and convincingly that it does not meet the second part of the test, relying on the following statement in Walter:

Once a mathematical algorithm has been found, the claim as a whole must be further analyzed. If it appears that the mathematical algorithm is implemented in a specific manner to define structural relationships between the physical elements of the claim (in apparatus claims) or to refine or limit claim steps (in process claims), the claim being otherwise statutory, the claim passes muster under § 101.

Though the claim starts out by saying in clause [a] that it is a "unit," appellants prefer to characterize what they claim as apparatus with specific structural limitations. By the Solicitor's own analysis of the claim we are constrained to agree. Appellants emphasize that they specify a ROM in clause [d] to which is fed an input from an adder specified in clause [c]. The Solicitor states that [e] and [d] are connected together by a signal path. Next are means in the form of disclosed electronic circuitry which take from the ROM its output in the form of squares of numbers supplied as ROM input and feed them to a calculating circuit [h].

The claim as a whole certainly defines apparatus in the form of a combination of interrelated means and we cannot discern any logical reason why it should not be deemed statutory subject matter as either a machine or a manufacture as specified in § 101. The fact that the apparatus operates according to an algorithm does not make it nonstatutory. See Abele. See also the discussion of that case in Grams. We therefore hold that the claim is directed to statutory subject matter.

In the Solicitor's brief the summary of argument states that the claim "encompasses any and every means for performing the functions recited therein." We point out that the claim is a combination of means all but one of which is a means-plus-function limitation, the one exception being the ROM, clause [d], which is a specific piece of apparatus. The claim is therefore subject to the limitation stated in 35 U.S.C. § 112 ¶ 6 that each means-plus-function definition "shall be construed to cover the corresponding structure, material, or acts described in the specification and equivalents thereof."1 This provision precludes the Solicitor's interpretation of the claim. The Solicitor's summary also contends that since the claim should be interpreted as he does, we should regard it as though it were a method claim.

Since he is wrong on the first score, he is wrong on the second. Reversed.

  1. The "means" clause includes equivalents of the disclosed structure. Section 112 ¶ 6 cannot be ignored when a claim is before the PTO any more than when it is before the courts in an issued patent.

Fig. 1 - Block Diagram of Iwahashi Device

Fig. 2 - More Detailed Block Diagram of Device


1. Some matters that might be covered in Notes for this case are addressed in The Case of the Automated Substance Spreader, which follows and should be read with Iwahashi.

2. The officials of the PTO were dissatisfied with the ruling in Iwahashi, and issued a Notice for the benefit of PTO staff and others, which follows. The Notice "interprets" the Iwahashi decision in a manner with which the author of Iwahashi later expressed strong disagreement in the Alappat opinion (below). Among other things, the PTO Notice placed considerable emphasis on the ROM. Did the ROM carry the day for the applicants? Would its absence have led to a different outcome?

3. Explain how the ROM "is a specific piece of apparatus." What other devices would provide the same functionality in this circuitry as a ROM, and would operate in the same way to provide the same results?

4. Can you think of an example to belie the PTO Solicitor's assertion that the claim encompasses any and every means for performing the recited functions? (Do not ignore equivalents.)

5. Why does it matter whether the claim is in format directed to an apparatus or a method? Or regarded as though it were a method claim?

PTO Notice Interpreting In Re Iwahashi
1112 Off. Gaz. Pat. Off. 16 (Mar. 13, 1990)

The PTO's policy on the patentability of claims reciting mathematical algorithms and computer programs, published at 1106 0ff. Gaz. Pat. Office 5-12 (Sept. 5, 1989), is unaffected by In re Iwahashi, 888 F.2d 1370 (Fed. Cir. 1989). The following comments are intended as the PTO's interpretation of Iwahashi.

Iwahashi reversed a rejection of appellants'apparatus claim 1 (the sole claim) under 35 U.S.C. § 101. The rejection maintained that claim 1 was directed to nonstatutory subject matter in the form of a mathematical algorithm. Appellants developed an approximation to the conventional equation for auto-correlation coefficients for use in pattern recognition which uses a term which is the square of the sum of two variables, instead of the product of the two variables. Appellants' claim to an auto-correlation unit is in "means-plus-function" format except for a recited "read-only memory" ("ROM") for implementing the squaring term. The PTO argued that the term "read-only memory" as used in this claim is as broad as a means-plus-function recitation, with the result that the claim is effectively entirely in means-plus-function format and indistinguishable for § 101 purposes from a method claim; it was argued that such a corresponding method claim would be nonstatutory. The PTO also argued that appellants' apparatus claim is nonstatutory when directly analyzed according to the two-part Freeman-Walter test because (1) it recites a mathematical algorithm and (2) the algorithm does not "define" a structural relationship between physical elements and is not "applied" in any manner to physical elements.

The Federal Circuit determined that a read-only memory is a "term well understood by those skilled in the art," and that the claimed read-only memory element "is not in means-plus-function form," but "is a specific piece of apparatus." The Court states that appellants' apparatus claim does not meet the second part of the Freeman-Walter test, detailing the relationship between the ROM and the other means in the claim. Therefore, the Court concluded:

The claim as a whole certainly defines apparatus in the form of a combination of interrelated means and we cannot discern any logical reason why it should not be deemed statutory subject matter as either a machine or a manufacture as specified in § 101. The fact that the apparatus operates according to an algorithm does not make it nonstatutory. . . . We therefore hold that the claim is directed to statutory subject matter.

Because the Court determined a ROM to be a specific piece of apparatus for implementing a table look-up function, and not as broad as a means-plus-function recitation, appellants carried their burden of demonstrating that the claim is "truly drawn to specific apparatus distinct from other apparatus capable of performing the identical functions," Walter, 618 F.2d at 768. As a matter of claim interpretation, the claim cannot be treated as equivalent to a method. The Walter test for whether an apparatus claim is equivalent to a method claim is the same as applying the Freeman-Walter test to an apparatus claim. See In re Maucorps, 609 F.2d 481, 486 (CCPA 1979) (application of second part of two-part Freeman test to apparatus claim in "means for" format considers whether the "claimed invention as a whole comprises each and every means for carrying out a [mathematical algorithm]").

Once it is determined that the claim is truly drawn to specific apparatus, it necessarily follows that the apparatus is statutory subject matter under § 101. True apparatus does not invoke the mathematical algorithm exception, because the mathematical algorithm remains free for use by anyone not employing the specific apparatus, i.e., there is no preemption, in whole or part, of the mathematical algorithm itself. See In re Bernhart, 417 F.2d 395, 1399 (CCPA 1969) ("a member of the public would have to do much more than use the equations to infringe any of these [apparatus] claims"); In re Freeman, 573 F.2d 1237, 1247 n.11 ("the calculation method remained free for use by anyone not employing the entire apparatus of claim 9"). Importantly, as the Iwahashi Court notes: "the fact that apparatus operates according to an algorithm does not make it nonstatutory."

The Court's holding that the claim defines apparatus because a ROM is a specific piece of apparatus for implementing the mathematical algorithm is consistent with precedent and PTO policy as set forth at 1106 Off. Gaz. Pat. Office 5-12. Every case, however, must be determined on its facts and, to be consistent with previous decisions, Iwahashi does not "hold that the mere presence of apparatus language in a claim will, of itself, save that claim from rejection as nonstatutory." Under Walter, the inquiry with every apparatus claim should be whether the apparatus encompasses any and every means for performing the recited functions and, if this appears to be the case, the burden should be placed on the applicant to show that it does not.

The Court's dicta in note 1 (the sole footnote) suggests that § 112, ¶ 6 may require the PTO to construe means-plus-function as limited to the apparatus disclosed in the application and equivalents thereof. Under this suggestion, even a claim which is entirely in means-plus-function format could not be treated as indistinguishable from a corresponding method claim for § 101 purposes. Such a result would be directly contrary to precedent, including Freeman, Walter, Abele, and Meyer. In the opinion of the PTO, means-plus-function limitations should be not treated differently for § 101 purposes than for §§ 102 and 103 purposes for rejections over prior art. Indeed, during prosecution claims should be given their broadest reasonable interpretation [because the applicant can amend to narrow the claim expressly in order to overcome a rejection].

The issue of claim scope should be treated as a matter of burden of proof: PTO examiners should give "means for" limitations their broadest reasonable interpretation and then it is the applicant's burden to show that the functionally-defined disclosed means do not encompass any and every means for performing the recited functions.


1. The PTO states that "to be consistent with previous decisions, Iwahashi does not ‘hold that the mere presence of apparatus language in a claim will, of itself, save that claim from rejection as nonstatutory.'" Do you consider that a correct reading of Iwahashi? Is it wishful thinking? Myopia?

2. The PTO's position on § 112 ¶ 6 claims met its Waterloo in In re Donaldson, 16 F.3d 1189, 29 U.S.P.Q.2d 1845 (Fed. Cir. 1994), discussed in connection with Alappat (below).

Some ROM chips — the specific piece of apparatus

The Case of the Automated Substance Spreader
Adapted from Richard H. Stern, Tales From the
Algorithm War, 18 AIPLA Q.J. 371 (1991)

As you know from reading the Iwahashi decision, one feature of the voice pattern recognition systems with which Iwahashi and his co-workers were concerned is the use of autocorrelation coefficients to characterize a voice pattern. The state of the art was to use a great deal of number multiplication to determine these coefficients, and that required a considerable amount of circuitry or computer resources. Iwahashi's invention was using the squares of the sums of various factors instead of performing expensive and time-consuming multiplication operations. Iwahashi's procedure was faster and cheaper, and closely approximated the results of the usual method.

The Federal Circuit did not explain in its opinion the mathematics of how Iwahashi's invention achieved this result, other than to quote a part of the patent claim that said that squares were needed to place into the following formula:

As you know, the legal controversy was about whether Iwahashi's claim was one directed to the foregoing formula or algorithm or was one directed to a machine that used the formula or algorithm. Because the Federal Circuit did not explain how the invention or algorithm worked, you may find some difficulty in determining whether Iwahashi's claim was one directed to the foregoing formula or algorithm or was one directed to a machine that used the formula or algorithm. Accordingly, I will recast the issue in terms of one of my own inventions — a machine for use in (and a process for) spreading fertilizer onto a rectangular field or a field that can be treated as a set of rectangular fields. The process is highly sensitive to the amount of substance deposited per unit area. It is therefore important to meter the size of the field accurately so as to achieve a desired per-unit amount of substance deposition. (Thus, where f is the desired per-unit area amount of fertilizer to be deposited, A is the area, and F is the total amount of fertilizer required for the particular field, the parameters are related by the equation f · A = F.)

I must therefore calculate area parameters or "coefficients" to feed into my machine in accordance with a very precise equation for determining area, A = LW, where L refers to length and W refers to width.

As explained in Iwahashi, multiplication is a tedious, expensive, and time-consuming process that uses a great deal of computer resources. However, I am able to shortcut much of that by using the following equations in my machine, which permit me to use a look-up table of squares to determine the product LW, instead of having to multiply L by W or vice-versa:

By means of an algorithm based on these equations, I have invented (in Federal Circuit parlance) a machine for substituting use of a look-up table of squares for actual multiplication, I can rapidly and inexpensively derive the value of the product LW by simply taking the difference between a quarter of the square of the sum of L and W and a quarter of the square of the difference between L and W. Hence:

A = LW = 0.25(L+W)2 - 0.25(L-W)2

That is the core or heart of my invention of an apparatus and method for spreading fertilizer on rectangular fields. In point of fact, my invention is more general than that, and extends as well to applying other substances in a metered fashion to other rectangular surfaces, such as spreading herbicide on a field and painting a wall.

The application suggested by the illustration shown above is thus by no means the full extent of the utility of my apparatus and method, and I have considered it appropriate to claim it to the limits of the prior art. Moreover, I have a particular apparatus that I use in practicing the invention, a ROM of course, but in accordance with the practice suggested by the Federal Circuit's decision in the Iwahashi case, my claims are in means-for format.

First, I will describe for you my specific piece of apparatus, and then show you how my claim to that apparatus reads.

The apparatus is shown in the block diagram captioned "The Specific Piece of Apparatus." An L input and a W input each feed both an Add unit and a Subtract unit, providing an L+W signal and an L-W signal. These are each fed to a look–up ROM, each of whose locations stores a value one-quarter of the square of its address. The ROM provides signals for the L+W and L-W inputs that are, respectively, one-quarter of the squares of the inputs. These signals are fed to another Subtract unit, thus providing an output signal LW. (I have given only a drawing like that of Fig. 1 of the Iwahashi decision; if you insist, I could provide one like Iwahashi's Fig. 2, as well.)

The Specific Piece of Apparatus

The following claim is based on the claim that the Federal Circuit approved in the Iwahashi case. You will note that the claim includes a specific piece of apparatus, a ROM, as in that case.

The subject matter claimed is:

An apparatus for providing area coefficients for use as parameters in determining an amount of substance to be supplied to an applicator for applying a substance to a rectangular surface having length L and width W, said apparatus comprising:

    a ROM in which has been stored at each address thereof a signal representative of 0.25 the square of said address, said ROM having means for fetching and outputting said signal when said ROM is addressed by an address-input signal;

    summing means for summing a signal representative of said length L and a signal representative of said width W, for providing a sum-input signal representative of a sum L+W;

    first infeed means for feeding said sum-input signal from said summing means to said ROM as an address-input signal;

    first outfeed means for feeding from said ROM a sum-output signal representative of 0.25 (L+W)2;

    first subtracting means for subtracting from a signal representative of said length L a signal representative of said width W, for providing a difference-input signal representative of a difference sum L-W;

    second infeed means for feeding said difference-input signal from said subtracting means to said ROM as an address-input signal;

    second outfeed means for feeding from said ROM a difference-output signal representative of 0.25 (L-W)2; and

    second subtracting means for providing a signal representative of LW for use as a said area coefficient, said second subtracting means comprising:

      means for receiving from said first outfeed means said sum-output signal,

      means for receiving from said second outfeed means said difference-output signal, and

      means for subtracting said difference-output signal from said sum-output signal.

In all material respects, the foregoing claim is the same as that of the Iwahashi case.* Is the claim subject to rejection as nonstatutory subject matter? Does it preempt all ways to use the algorithm, at least in the described field of use?

      * I could have made the claim much shorter by eliminating the infeed and outfeed means and instead just saying that the first input of the ROM is connected to the output of the subtraction means, etc., but that is not how Iwahashi's claims read. For some reason, he insists on claiming all of the wires. So I did too, so that you could see the parallelism between his and my claim.

The Federal Circuit in Iwahashi apparently did not challenge the PTO's position about an algorithm-related claim that contains only a series of means and no specific apparatus elements (other than a general-purpose digital computer used to carry out the steps of the algorithm). The PTO said that such a claim must be regarded as no different from a method claim to the steps of the algorithm, unlimited by any requirement that particular apparatus be used, and thus a claim directed to the algorithm itself. Instead, the Federal Circuit held that a "specific piece of apparatus" — a ROM — was present as clause [d] of the claim. (In 1994, in Alappat, the Federal Circuit may have abandoned even this requirement, on the theory that a general-purpose digital computer is a specific piece of apparatus. Then again, Alappat may be a case in which an oscilloscope connected to a computer is the day-carrying specific piece of apparatus. In any event, as of 1989 when Iwahashi was decided, it appeared that some specific piece of apparatus other than a general-purpose digital computer was needed.) All elements of my claim are in means-for format except for the ROM, which — Iwahashi says — is "a specific piece of apparatus." Is it?

For the purpose of carrying out my invention, and presumably the invention involved in Iwahashi as well, the ROM has equivalents. According to § 112, a claim in means-for format is to be construed to cover the structures described for the means in the specification and also any equivalents of that structure. The look-up table therefore need not be a ROM chip to be covered by the claim, although that is certainly an appropriate expedient. You could also keep the look-up table in a floppy or hard disk, and load that into the RAM of a microcomputer or microprocessor to carry out my (or Iwahashi's) process. If you insisted, you could use tape, core memory or punched cards, too. An optical CD (compact disk) would also be satisfactory. Can you conceive of any information-storage device that would not work (assuming that an appropriate interface is provided)? Does the mention of the ROM, therefore, assuming that it is indeed a specific piece of apparatus, assure that I am not preempting the algorithm — taking into account the fact that I am entitled to the benefits of the equivalents? (If you have any question about what range of equivalents I am entitled to, we can settle that by putting a paragraph into the specification listing floppy disks, tapes, etc. as contemplated alternative devices to the ROM for storing the look-up table. That will nail it down.)

To be sure, you cannot practice my invention if you do not use some kind of look-up table device. But the whole point of my invention is to use a look-up table of squares of L and W instead of doing regular long multiplication of L and W. If you don't use a look-up table, it's not my invention any more.

My claim is directed to what we may call a "pseudomachine," meaning that it is a fake machine, the ROM notwithstanding. The apparatus format is illusory. You can also call the ROM "nominal hardware," meaning that nominal mention of the ROM does not actually place any meaningful limitation on the scope of the claim. Consider the effect of the following hardware limitations on the scope of claims:

As a practical matter, would any of these claims cover any less ground if you left out the hardware limitation? What the draftsman gives up, by writing a claim in the format I have suggested, is the speculative possibility that some day somebody will discover that the algorithm is good for some other, wholly unanticipated use. If that happens, third parties may be able to take a "free ride."

For example, at the time that I wrote the Algorithm Wars paper (1990) from which this commentary is excerpted and adapted, I was unaware that an algorithm for shape-pattern recognition was good for anything but use with robots and other object–manipulation devices. I knew that you could use shape-pattern recognition software for controlling how assembly-line robots pick up parts and the like, but I did not know that you could use such software to interpret aerial photographs to look for such things as SCUD emplacements. Gulf War television programs then educated me further.

Thus, if I had written a claim directed to a machine system using a shape-pattern recognition algorithm, at the time of the Algorithm Wars paper, I would have short-sightedly limited the claim to a system in which the output signal from whatever processed data according to the algorithm was fed to a robot or other object-manipulation device. (This would have avoided risk of PTO rejection on grounds that my claim was directed to the algorithm.) It would not have occurred to me to claim a system in which the output signal was used to cause the data sample from which it was derived to be "marked" in storage with an indicium or flag (e.g., the ASCII equivalent of "Hey, this is a SCUD site!"), so that the relevant data sample could later be retrieved from the mass of irrelevant data samples around it by appropriate means. I would have failed to foresee and claim all of the possibilities. That would have permitted a later comer to take a free ride on the invention.

Consider this hypothetical fact situation from a moral standpoint. Compare my (hypothetical) plight with that of Samuel Morse. Over the protests of Justice Grier, the Supreme Court struck claim 8 down as overbroad. Therefore, various other later-developed telecommunications devices (fax, TV, Internet) enjoyed a free ride at Morse's expense. Isn't it a purpose of the patent system to prevent free-loaders from taking that kind of free ride at inventors' expense? How would you assure securing inventors their just rights?

Arrhythmia Research Technology, Inc. v. Corazonix Corp.
United States Court of Appeals for the Federal Circuit
958 F.2d 1053 (Fed. Cir. 1992)

Rader, Circuit Judge, concurring.

The court upholds the ‘459 patent by applying a permutation of the Benson algorithm rule. In reaching this result, the court adds another cord to the twisted knot of precedent encircling and confining the Benson rule. While fully concurring in the court's result and commending its ability to trace legal strands through the tangle of post-Benson case law, I read later Supreme Court opinions to have cut the Gordian Knot. The Supreme Court cut the knot by strictly limiting Benson.

Relying on the language of the patent statute, the Supreme Court in Diamond v. Diehr turned away from the Benson algorithm rule. Thus, I too conclude that the ‘459 patent claims patentable subject matter — not on the basis of a two-step post-Benson test, but on the basis of the patentable subject matter standards in title 35. Rather than perpetuate a nonstatutory standard, I would find that the subject matter of the ‘459 patent satisfies the statutory standards of the Patent Act.

The questions presented by this case are whether the ‘459 patent claims a process and apparatus within the meaning of 35 U.S.C. § 101. According to this language, "any" invention or discovery within the four broad categories of "process, machine, manufacture, or composition of matter" is eligible for patent protection. "Any" is an expansive modifier which broadens the sweep of the categories. See Chakrabarty. The language of § 101 conveys no implication that the Act extends patent protection to some subcategories of machines or processes and not to others.

In Benson the Supreme Court, by reading a limitation not found in the statute into the term "process," determined the method of conversion did not satisfy § 101. In Flook the Court followed Benson. Flook claimed a method for updating alarm limits during catalytic conversion of hydrocarbons. The Court found Flook's method involving mathematical calculations — though applied to a post-solution use — unpatentable. Flook clearly limited the Benson rule to mathematical formulae and mathematical algorithms. By mixing the terms "formula" and "algorithm," however, Flook further confused the meaning of "mathematical algorithm." As used by Benson, that term meant "a procedure for solving a given type of mathematical problem." Thus, an "algorithm" required both a mathematical problem and a solution procedure. A "formula" does not present or solve a mathematical problem, but merely expresses a relationship in mathematical terms. A "formula," even under Benson's definition, is not an algorithm.

In the wake of Benson, the CCPA struggled to implement the algorithm rule. Much of the difficulty sprang from the obscurity of the terms invoked to preclude patentability — terms like "law of nature," "natural phenomena," "formulae," or "algorithm." When attempting to enforce a legal standard embodied in broad, vague, nonstatutory terms, the courts have floundered.

Congress has never stated that § 101's term "process" excludes certain types of algorithms. Therefore, as Diehr commands, this court should refrain from employing judicially-created tests to limit § 101.

Courts should give "process" its literal and predictable meaning, without conjecturing about the policy implications of that literal reading. If Congress wishes to remove some processes from patent protection, it can enact such an exclusion. Again, in the absence of legislated limits on the meaning of the Act, courts should not presume to construct limits. In Diehr, the Supreme Court directed this court to follow the Act.

With that preface, the Supreme Court in Diehr specifically limited Benson. In the first place, the Court acknowledged the narrow definition of "mathematical algorithm" set forth by Benson. Moreover, the Court expressly stated:

Our previous decisions regarding the patentability of "algorithms" are necessarily limited to the more narrow definition employed by the Court. . . .

Thus, after Diehr, only a mathematical procedure for solution of a specified mathematical problem is suspect subject matter.

The ‘459 patent discloses an apparatus and a method for analyzing electrocardiograph signals to detect heart-attack risks. The apparatus is a machine and is covered by the Iwahashi rule. The method converts an analog signal to a digital signal which passes, in reverse-time order, through the mathematical equivalent of a filter. The filtered signal's amplitude is then measured and compared with a predetermined value.

The ‘459 invention manipulates electrocardiogram readings to render a useful result. While many steps in the ‘459 process involve the mathematical manipulation of data, the claims do not describe a law of nature or a natural phenomenon. Furthermore, the claims do not disclose mere abstract ideas, but a practical and potentially life-saving process. Regardless of whether performed by a computer, these steps comprise a "process" within the meaning of § 101.

The district court granted summary judgment because "the claims of the ‘459 patent are drawn to a nonstatutory mathematical algorithm and, as such, are unpatentable pursuant to the provisions of 35 U.S.C. § 101." This erroneous conclusion illustrates the confusion caused by Benson and its progeny.


1. The court's opinion (omitted here) made a bow to Iwahashi, by pointing to an analog-to-digital converter (ADC) that Simson used at the front end of his signal processing. The ADC here appears to serve the same office, for § 101 purposes, as Iwahashi's ROM. The court called the ADC "a specific electronic device." Assume that an EKG machine is an analog device and that the anomalous low-voltage, high-frequency waveforms that appear toward the end of the QRS segment of the EKG signals of heart-attack patients can be detected and processed only by digital signal processing means. How much then does the presence of the ADC as a claim element limit the practical scope of Simson's apparatus claim? It limits the claim scope to signals that have been run through an ADC or its equivalent. What other ways can you think of to subject a set of analog signals to digital signal processing?

2. Is this concurring opinion's view of Benson and Flook consistent with the view of those cases in Diehr? By this time, the Standard Analysis — i.e., look for some apparatus in which or near which the algorithm is embedded — was rapidly approaching its Last Hurrah, at least in the Federal Circuit. Read on to the second decade of post-Trilogy case-law.

Link to section C of chapter 8

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