
    In re Andrew U. MEYER and William K. Weissman.
    Appeal No. 82-510.
    United States Court of Customs and Patent Appeals.
    Sept. 16, 1982.
    
      Karl F. Milde, Jr., Chappaqua, N.Y., for appellant.
    Joseph F. Nakamura, Sol., and Jere W. Sears, Deputy Sol., Washington, D.C., for the Patent and Trademark Office.
    Before MARKEY, Chief Judge, and RICH, BALDWIN, MILLER and NIES, Judges.
   MILLER, Judge.

This is an appeal from a decision of the Patent and Trademark Office (“PTO”) Board of Appeals (“board”) sustaining the examiner’s rejection under 35 U.S.C. § 101 of all claims in application serial No. 465,-574, filed April 30, 1974, entitled “Process and Apparatus for Identifying Locations of Probable Malfunction.” We affirm.

BACKGROUND

Appellants in their brief to this court describe their invention, in pertinent part, as follows:

The invention is a process and an apparatus for carrying out the process of testing a complex system and analyzing the results of these tests. The process proceeds by (1) dividing the complex system into a plurality of “elements” and (2) associating a factor of function or malfunction with each of these elements. The factors, which are initialized at the outset, are updated or modified during the course of the process in dependence upon the responses of this system to a series of tests. When the tests have been completed, the resultant factors so produced indicate a measure of probability of function or malfunction of the elements with which they are associated.

The term “elements” is used ... to identify any arbitrary subdivision of the complex system. For example, the complex system may be divided into a plurality of volume elements of uniform, or even nonuniform size. Where the complex system is a portion of the nervous system of a human body, each of the volume-elements may contain various neurogenerators and/or portions of neuropathways. Alternatively, each element of the complex system may constitute a “functional component,” or a portion or a set of functional components of the system. The term “functional component”, as used in the Application and in this Brief, is intended to denote any component of the complex system which is operative to produce, transmit, receive, or store signals or information. In the nervous system, the functional components include the neurogenerators and neuropathways. Thus, the elements into which the nervous system is divided may be individual neurogenerators and/or neuropathways, or may be portions of sets thereof.

For a given complex system, a table may be compiled of the possible responses or outcomes of the various tests. Each test outcome necessarily falls into one of the following categories:

(a) A specific set of system elements is functioning.

(b) Malfunction is likely to be present in a specific set of system elements; function of another specific set of system elements may also be indicated.

(e) The test outcome has no interpretative significance and no inference can be made concerning function or malfunction of the system elements.

For example, as part of a clinical neurological examination, a patient may be asked to close both his eyes (test). Given this test, the patient may respond in one of three ways (test outcome):

(1) The patient closes both his eyes;
(2) The patient closes his right eye only; or
(3) The patient does not close either eye.

These three test outcomes fall, respectively, into the three categories (a), (b) and (c) described above. Test outcome (1) shows that a specific set of elements (e.g., volume elements containing neurogenerators and pathways) of the nervous system is functioning. Test outcome (2) indicates a malfunction in one or more specific sets of elements (e.g., the volume elements containing those neuropathways leading to the left eyelid). On the other hand, test outcome (2) also shows that certain elements of the nervous system are functioning (e.g., those volume elements containing neuropathways leading to the right eyelid). The test outcome (3) is an example of a response for which no inference can be made. The patient may be deaf, may not understand the language or other unknown factors may be present which remove the interpretative significance of the test outcome.

A realistic computation of malfunction probabilities for all elements in a complex system, based on a large number of test outcomes, is a rather complex task. This problem may be avoided by using a rather simple algorithm to locate elements of probable function and malfunction in a complex system....

Pursuant to the algorithm, each element of the complex system is identified by some suitable code. For the purpose of illustration, let there be K elements designated by numbers k = 1,... ,K. A “function factor” NF(k) and a “malfunction factor” M(k) are associated with each element k. Initially the function factor NF(k) and the malfunction factor M(k) are set equal to zero for all k = 1,... ,K. Whenever a test outcome indicates function or malfunction in certain ones of the elements, NF(k) or M(k), respectively, are incremented by some value or set of values for all the elements k involved.

When an element k is described herein as “functioning” or “malfunctioning”, it will be understood that, in reality, it is one or more of the functional components contained in the element which is either functioning or malfunctioning.

Each outcome of each test applied to the complex system is also identified by some suitable code. For the purpose of illustration, for all the tests performed let there be a total of I test outcomes considered; these are designated by numbers i = 1,... ,1.

For each possible test outcome i in categories (a) or (b) there is a set ^ (i) of elements k which are functioning and/or a set77l(i) of elements k which are malfunctioning. For all values of k in the set y (i) let there be an incrementation factor of probable function ANF(i,k), and for all the values of k in the set77£(i) let there be an incrementation factor of probable malfunction AM(i,k). These incrementation factors, as indicated, may be a function of the test outcome i as well as the elements k with which they are associated. If and when the test outcome i should occur, the function factors NK(k) and the malfunction factors M(k) are increased by the incrementation factors ANF(i,k) and AM(i,k) for the elements in the sets ^ (i) and ?7¿(i), respectively.

... [T]he algorithm begins by initializing the function factors NF(k) and malfunction factors M(k) to zero for all elements: i.e., NF(k) = 0 and M(k) = 0 for all k = 1,... ,K. Thereafter, a series of tests is applied to the complex system and the test outcomes that occur are read into the computer. Since I is the total number of possible test outcomes considered, the number N of test outcomes that do occur during an entire examination will be less than I.

During or after the examination, the computer compares each of the N test outcomes that have occurred with its prestored data giving the inference, if any, which can be made from each test outcome.

Let i(n) be the nth of these test outcomes considered by the computer. If no inference from this test outcome i = i(n) is indicated — that is, this test outcome belongs in category (c) — the next test outcome i = i(n + 1) is considered. If the test outcome i = i(n) indicates any set (i) of elements k are functioning, then the function factors NK(k) for all elements k in the set ^ (i) are increased by the previously stored incrementation factors of probable function NF(i, k). Likewise, if the test outcome i = i(n) indicates any set7?£(i) of elements k are malfunctioning, then the malfunction factors M(k) for all elements k in the set77L(i) are increased by the previously stored incrementation factors of probable malfunction AM(i,k). That is:

where the symbol S means “belonging to the set”; i.e., “for all k S ^ (i)” means: “for all values of k belonging to the set ^ (i)”, and “for all k S 77J.(i)” means: “for all values of k belonging to the set 77L(i)”.

The incrementation factors of probable function ANF(i,k) and the incrementation factors of probable malfunction AM(i,k) are preselected and stored in the computer. The simplest choice is to take ANF(i,k) = 1 for all k s ^ (i) and AM(i,k) = 1 for all k S77J, (i) for every test outcome i for which an inference concerning the functioning or malfunctioning of the elements of the complex system can be made. More involved configurations of incrementation factors may be chosen depending on knowledge of the relevance and relative weight of various test outcomes.

The output display depends upon the nature of the complex system and the nature of the system elements. The simplest form of output would consist of separate lists of the function factors and the malfunction factors together with the elements with which they are associated. A more informative output would be a video display of the function and malfunction factors (by number or by color) superimposed on an image of the complex system or a particular cross section thereof.

Independent claims 1 (for a process) and 55 (for an apparatus) are representative:

1. A process for indentifying [sic] locations of probable malfunction in a complex system, said process comprising the steps of:
(a) selecting a plurality of elements in the complex system, said elements having known locations;
(b) initializing a factor associated with each of said elements;
(c) testing the complex system for a response, which response, if effective, requires proper functioning of certain said elements, the probable indentity [sic] of at least some of these certain elements being known;
(d) determining whether said response of the complex system was at least partially effective or ineffective;
(e) modifying the factor associated with at least some of said elements known to be possible [sic] involved in the response in accordance with the effectiveness of the response; and
(f) repeating steps (c), (d) and (e) for further responses of the complex system to obtain resultant factors for at least some of said elements,
whereby said resultant factors are indicative of probable malfunction of their associated elements and thereby indicative of probable malfunction at the locations of these elements.
55. Apparatus for indentifying [sic] locations of probable malfunction in a complex system in dependence upon individual responses to a plurality of tests of said system, whereby each response, if effective, requires the proper functioning of certain ones of a plurality of elements of said system, the locations of said plurality of elements and the probable indentity [sic] of at least some of said certain ones of said elements being known, said apparatus comprising, in combination:
(a) means for initializing a factor associated with each of said elements;
(b) means for modifying the factor associated with at least some of said elements known to be possibly involved in a test response, in accordance with the effectiveness of the response, thereby to obtain resultant factors for at least some of said elements which are indicative of probable malfunction of their associated elements and thereby indicative of probable malfunction at the location of these elements; and
(c) means for displaying the resultant factors associated with at least some of said elements.

During oral argument, appellants’ counsel explained that a doctor may perform fifty or more tests when conducting a standard neurological examination such as tapping the knee and pricking the skin. According to counsel, doctors know the relationship between these tests, the responses they should receive, and the patient’s neurological system. After observing the patient’s response indicating that a neurological area or pathway is functioning or malfunctioning, the doctor, utilizing appellants’ invention, inputs this information to the computer. The Solicitor characterized the invention, without objection, as a “diagnostic” or “memory” aid for a physician and emphasized that the invention does not conduct a diagnosis in and of itself, but is used by a doctor when performing a diagnosis to store and to accumulate test responses obtained by this standard process of elimination and to narrow the neurological area of possible malfunction. In fact, the Solicitor indicated that these standard tests have been employed for many years and that the more experienced the doctor and the better his memory, the less would be his need (if any) for this invention.

The examiner rejected all claims under 35 U.S.C. § 101 as drawn to nonstatutory subject matter citing Gottschalk v. Benson, 409 U.S. 63, 93 S.Ct. 253, 34 L.Ed.2d 273 (1972) and Parker v. Flook, 437 U.S. 584, 98 S.Ct. 2522, 57 L.Ed.2d 451 (1978). In the examiner’s view, the claims were drawn not only to an algorithm but to a mathematical algorithm which, like any law of nature or scientific truth, “cannot be the subject of a patent.” Responding to appellants’ arguments that no mathematical formula or expression was recited in the claims, the examiner quoted the following passage from In re Richman, 563 F.2d 1026, 1030, 195 USPQ 340, 344 (Cust & Pat App. 1977):

That a claim includes a mathematical expression is not determinative. The decisive factor is whether a claimed method is essentially a mathematical calculation. If it is, deletion from the claims of the mathematical formula involved and substitution of “words which mean the same thing” would not transform the claimed method into statutory subject matter.

The board sustained the rejection stating:

The claims are drawn to a technique of statistical analysis. Data is accumulated from a series of test operations and conclusions are drawn in accordance with a mathematical algorithm....
If we take claim 1 as typical, the first step “selecting” relates to nothing more than the selection of a source for the accumulation of data to be used in the analysis.
The factor recited in step (b) is a factor which relates to the probability that the particular element is malfunctioning. At the beginning of the test procedure a proper factor would be zero.
The third step (c), testing for a response, is nothing more than a data gathering step. Such a step cannot make an otherwise nonstatutory claim státutory. In re Richman, 563 F.2d 1026, 195 USPQ 340 (Oust. & Pat. App. 1977).
Step (d) provides information that is read into the computer. Step (e) takes place in the computer by a comparison process in which test outcomes are compared with stored data. The computer infers from this comparison that certain elements are functioning or not functioning. Factors are added to the elements designated (step e) in accordance with the results.... The process goes on, step (f), and the results are eventually displayed, claim 21 for example. Claim 1 merely says that results are obtained. They are not displayed.
The process recited is an attempt to patent a mathematical algorithm rather than a process for producing a product as in Diamond v. Diehr, [450 U.S. 175, 101 S.Ct. 1048, 67 L.Ed.2d 155 (1981) ].

Appellants argue that no mathematical algorithm is claimed, and, even assuming, arguendo, that there is, any such mathematical algorithm is not wholly preempted by these claims. According to the Solicitor, the claims are directed to a mathematical algorithm; steps (a) and (b) are “arbitrary and merely set the stage for the exercise ... steps (c) and (d) are necessary input producing steps. As recognized by the Board, data gathering steps ‘cannot make an otherwise nonstatutory claim statutory.’ ” Further, according to the Solicitor, step (e) “calls for ‘modifying the factor associated with at least some of said elements known to be [possibly] involved in the response in accordance with the effectiveness of the response,’ whereas step (f) calls for repetition of steps (c), (d) and (e) for further test results. At the very least, successive incrementation and/or decrementation is involved, i.e., addition and/or subtraction.” Having concluded that a mathematical algorithm is involved, the Solicitor argues that the second of the two-part test of In re Freeman, 573 F.2d 1237, 197 USPQ 464 (Oust. & Pat. App. 1978), as modified by In re Walter, 618 F.2d 758, 205 USPQ 397 (Oust. & Pat. App. 1980), has been satisfied, and, as a consequence, the claims wholly preempt the mathematical algorithm.

OPINION

Both the Senate and the House Committee Reports accompanying the bill that became the 1952 Patent Act indicate that 35 U.S.C. § 101 was intended to encompass a broad range of subject matter. S. Rep. No. 1979, 82d Cong. 2d Sess. 5, reprinted in [1952] U.S. Code Cong. & Ad. News 2394, 2399; H.R. Rep. No. 1923, 82d Cong. 2d Sess. 6 (1952). Discoveries not encompassed by 35 U.S.C. § 101 — those excluded from subject matter that Congress chose to protect — are narrowly confined. One type of discovery that the Supreme Court has in recent years determined that the Congress did not choose to protect is the mathematical algorithm. Diamond v. Diehr, 450 U.S. 175, 101 S.Ct. 1048, 67 L.Ed.2d 155 (1981); Parker v. Flook, 437 U.S. 584, 98 S.Ct. 2522, 57 L.Ed.2d 451 (1978). This exclusion from protection is consistent with the Court’s long-standing exclusion from patentable subject matter of scientific principles, laws of nature, ideas, and mental processes.

Scientific principles, such as the relationship between mass and energy, and laws of nature, such as the acceleration of gravity, namely, a = 32ft./sec., can be represented in mathematical format. However, some mathematical algorithms and formulae do not represent scientific principles or laws of nature; they represent ideas or mental processes and are simply logical vehicles for communicating possible solutions to complex problems. The presence of a mathematical algorithm or formula in a claim is merely an indication that a scientific principle, law of nature, idea or mental process may be the subject matter claimed and, thus, justify a rejection of that claim under 35 U.S.C. § 101; but the presence of a mathematical algorithm or formula is only a signpost for further analysis.

The Supreme Court has recognized that scientific principles and laws of nature, even when for the first time discovered, have existed throughout time, define the relationship of man to his environment, and, as a consequence, ought not to be the subject of exclusive rights of any one person. Leroy v. Tatham, 55 U.S. (14 How.) 155, 175, 14 L.Ed. 367 (1852). As the concurring opinion in O’Reilly v. Morse, 56 U.S. (15 How.) 61, 132-33, 14 L.Ed. 601 (1853) said:

The mere discovery of a new element, or law, or principle of nature, without any valuable application of it to the arts, is not the subject of a patent. But he who takes this new element or power, as yet useless, from the laboratory of the philosopher, and makes it the servant of man; who applies it to the perfecting of a new and useful art, or to the improvement of one already known, is the benefactor to whom the patent law tenders its protection.

In Rubber-Tip Pencil Co. v. Howard, 87 U.S. (20 Wall.) 498, 507, 22 L.Ed. 410 (1874), the Supreme Court stated that “[a]n idea of itself is not patentable, but a new device by which it may be made practically useful is.”

In considering a claim for compliance with 35 U.S.C. § 101, it must be determined whether a scientific principle, law of nature, idea, or mental process, which may be represented by a mathematical algorithm, is included in the subject matter of the claim. If it is, it must then be determined whether such principle, law, idea, or mental process is applied in an invention of a type set forth in 35 U.S.C. § 101. This is consistent with In re Freeman, 573 F.2d 1237, 197 USPQ 464 (Cust. & Pat. App. 1978), as modified by In re Walter, 618 F.2d 758, 205 USPQ 397 (Cust. & Pat. App. 1980), and the more recent decisions by this court in In re Pardo, 684 F.2d 912 (Cust. & Pat. App. 1982) and In re Abele, 684 F.2d 192 (Cust. & Pat. App. 1982). In Abele, this court said that “all of the claims may be directed to nonstatutory subject matter as each presents a mathematical formula or a sequence of mathematical operations.” At 907. (Emphasis supplied.) And, in order to determine whether they set forth a statutory invention, it is necessary to determine whether the mathematical formula is “applied in any manner to physical elements or process steps” (citing In re Walter, supra). At 907.

Appellants’ specification and arguments indicate that their invention is concerned with replacing, in part, the thinking processes of a neurologist with a computer. Counsel for appellants acknowledged in oral argument that the claims recite a mathematical algorithm, which represents a mental process that a neurologist should follow. Thus, the decisive question is whether that mental process is applied to physical elements or process steps in an otherwise statutory process, machine, manufacture, or composition of matter, in accordance with 35 U.S.C. § 101. Although the second of the two-part test of In re Freeman is whether a scientific principle, law of nature, idea or mental process (represented by a mathematical algorithm or formula) is preempted by the claim, this court, in In re Walter, supra, modified Freeman to require that a positive approach be taken to determine what, as a whole, is claimed, saying:

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. [Footnote omitted.]

618 F.2d at 767, 205 USPQ at 407. The above statement from Walter complements prior statements by the Supreme Court, but, as with those statements, it was not intended to be the exclusive test for determining the presence of statutory subject matter. A more comprehensive test for cases involving mathematical algorithms is set forth in In re Abele, supra, and Walter must be interpreted in light of that opinion.

In answering the decisive question, the claims are to be given their broadest reasonable interpretation consistent with the specification. In re Prater, 56 CCPA 1381, 1395-96, 415 F.2d 1393, 1404-05, 162 USPQ 541, 550-51 (1969). On this basis, we conclude that appellants’ independent claims are to a mathematical algorithm representing a mental process that has not been applied to physical elements or process steps and is, therefore, not limited to any otherwise statutory process, machine, manufacture, or composition of matter.

This court is aware of its directive in In re Bernhart, 57 CCPA 737 at 742, 417 F.2d 1395 at 1399, 163 USPQ 611 at 615, that, in accordance with 35 U.S.C. § 112, paragraph 6, claims under 35 U.S.C. § 101 drafted in means plus function format are to be examined in light of the “corresponding structure, material, or acts described in the specification and equivalents thereof.” We have done so here.

In view of the foregoing, we hold that appellants’ claims were properly rejected.

The decision of the board is affirmed.

AFFIRMED. 
      
      . The Constitution empowers Congress to protect an inventor’s “discoveries.” However, Congress has chosen to protect only a “useful process, machine, manufacture, or composition of matter or any ... useful improvement thereof.” 35 U.S.C. § 101.
     
      
      . However, the second step in Freeman, as modified by Walter, is subject to misinterpretation, see notes 4 and 5 and accompanying text, infra.
      
     
      
      . Appellants’ apparatus claims differ from the method claims by reciting “means for” performing the steps set forth in the method claims, and “means for displaying” the results. However, for purposes of section 101, such claims are not treated differently from method claims. As we stated in In re Pardo, 684 F.2d 912, 916 n. 6 (Cust. & Pat. App. 1982):
      Although some of appellants’ claims are drawn to a “general purpose data processor of known type operating under the control of a stored program,” such claims are treated as indistinguishable from the method claims for purposes of section 101 unless it is demonstrated that the claims are drawn to specific apparatus distinct from other apparatus capable of performing the identical functions. In re Walter, supra [618 F.2d] at 768, 205 USPQ at 407-08.
     
      
      . The Freeman approach, looking for preemption, has led to a number of “negative” rules for determining the presence of patentable subject matter, such as: mere antecedent data gathering steps do not render the claims statutory (In re Richman, 563 F.2d 1026, 195 USPQ 340 (Cust. & Pat. App. 1977)); mere reference to apparatus does not render a claim statutory (In re Castelet, 562 F.2d 1236, 195 USPQ 439 (Cust & Pat. App. 1977)); reading out the results of calculations does not render the claim statutory, id. However, these statements were not intended to be separate tests for determining whether a claim positively recites statutory subject matter.
     
      
      . In Gottschalk v. Benson, supra, the Court stated that “Transformation and reduction of an article ‘to a different state or thing’ is the clue to the patentability of a process claim that does not include particular machines.” 409 U.S. at 70, 93 S.Ct. at 256. But the Court also cautioned:
      It is argued that a process patent must either be tied to a particular machine or apparatus or must operate to change articles or materials to a “different state or thing.” We do not hold that no process patent could ever qualify if it did not meet the requirements of our prior precedents. [Emphasis supplied.]
      
        Id. at 71, 93 S.Ct. at 257.
     
      
      . Before the PTO, in the examination of claims in view of prior art, the claims are not limited by reference to the specification. See in re Reuter, 651 F.2d 751, 210 USPQ 249 (Cust. & Pat. App. 1981).
     
      
      . The dependent claims have not been separately argued and, therefore, fall with the independent claims.
     