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

C. Statutory Subject Matter in and
After 1994, the Year of the Algorithm
Continued (Second Section)

Archer, Chief Judge, with whom Nies, Circuit Judge, joins, concurring in part and dissenting in part.


I disagree with the majority's conclusion that Alappat's “rasterizer,” which is all that is claimed in the claims at issue, constitutes an invention or discovery within 35 U.S.C. § 101.

As I shall demonstrate, the majority's holding that Alappat's rasterizer represents the invention of a machine are illogical, inconsistent with precedent and with sound principles of patent law, and will have untold consequences.

B. Inventions Under § 101

The Patent Clause of the Constitution empowers the Congress to “promote the Progress of...useful Arts, by securing for limited Times to...Inventors the exclusive right to their...Discoveries.”

Congress has implemented this limited grant of power in 35 U.S.C. § 101 by enumerating certain subject matter, the invention or discovery of which may entitle one to a patent: “Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.” The terms used in § 101 have been used for over two hundred years—since the beginnings of American patent law—to define the extent of the subject matter of patentable invention.

Coexistent with the usage of these terms has been the rule that a person cannot obtain a patent for the discovery of an abstract idea, principle or force, law of nature, or natural phenomenon, but rather must invent or discover a practical application to a useful end. Thus patent law rewards persons for inventing technologically useful applications, instead of for philosophizing unapplied research and theory. Brenner v. Manson, 383 U.S. 519, 534-35 (1966) (“Unless and until a process is refined and developed to this point — where specific benefit exists in currently available form — there is insufficient justification for” the reward of a patent.).

Additionally, unapplied research, abstract ideas, and theory continue to be the “basic tools of scientific and technological work,” which persons are free to trade in and to build upon in the pursuit of among other things useful inventions. Even after a patent has been awarded for a new, useful, and nonobvious practical application of an idea, others may learn from the underlying ideas, theories, and principles to legitimately “design around” the patentee's useful application.

The requirement of the patent law that an invention or discovery reside in the application of an abstract idea, law of nature, principle, or natural phenomenon is embodied in the language of 35 U.S.C. § 101. A patent can be awarded to one who “invents or discovers” something within the enumerated classes of subject matter — “process,” “machine,” “manufacture,” “composition of matter.” These terms may not be read in a strict literal sense entirely divorced from the context of the patent law. Diehr (“[E]very discovery is not embraced within the statutory terms”); Schrader (use of terms of art in § 101 is presumed to be in accord with their well-established meaning). Rather they must be read as incorporating the longstanding and well-established limitation that the claimed invention or discovery must reside in a practical application. See Flook (the determination of “what type of discovery is sought to be patented must precede the determination of whether that discovery is, in fact, new or obvious”).

Consider for example the discovery or creation of music, a new song. Music of course is not patentable subject matter; a composer cannot obtain exclusive patent rights for the original creation of a musical composition. But now suppose the new melody is recorded on a compact disc. In such case, the particular musical composition will define an arrangement of minute pits in the surface of the compact disc material, and therefore will define its specific structure. Alternatively, suppose the music is recorded on the rolls of a player piano or a music box.

Through the expedient of putting his music on known structure, can a composer now claim as his invention the structure of a compact disc or player piano roll containing the melody he discovered and obtain a patent therefor? The answer must be no. The composer admittedly has invented or discovered nothing but music. The discovery of music does not become patentable subject matter simply because there is an arbitrary claim to some structure.

And if a claim to a compact disc or piano roll containing a newly discovered song were regarded as a “manufacture” and within § 101 simply because of the specific physical structure of the compact disc, the “practical effect” would be the granting of a patent for a discovery in music. Where the music is new, the precise structure of the disc or roll would be novel under § 102. Because the patent law cannot examine music for “nonobviousness,” the Patent and Trademark Office could not make a showing of obviousness under § 103. The result would well be the award of a patent for the discovery of music. The majority's simplistic approach of looking only to whether the claim reads on structure and ignoring the claimed invention or discovery for which a patent is sought will result in the awarding of patents for discoveries well beyond the scope of the patent law.

Patent cases involving the distinction between idea or principle may involve subtle distinctions. Section 101 embodies the very soul of the intangible nature of invention. Without particular claimed subject matter in mind, it is impossible to generalize with bright line rules the dividing line between what is in substance the invention or discovery of a useful application within § 101 versus merely the discovery of an abstract idea or law of nature or principle outside § 101. Each case presenting a question under § 101 must be decided individually based upon the particular subject matter at issue. There are however answers in every § 101 case. But they are found by applying precedent and principles of patent law to the particular claimed subject matter at issue.

C. Electronics and § 101

1. Discoveries and inventions in the field of digital electronics are analyzed according to the aforementioned principles as any other subject matter. The trilogy of Supreme Court cases in this area must be applied to determine whether an invention or discovery in the field of digital electronic related subject matter is within the scope of the patent law. These cases govern both product and process claims.

In the first case, Benson, the Supreme Court held that claims to a method of converting binary_coded decimal numbers into pure decimal numbers did not recite an invention or discovery within § 101, and thus were ineligible for patent protection. In Benson, the claimed method was to be performed specifically in a general purpose digital computer, and one of the claims (claim 8) contained express digital electronic structure limitations by reciting “signals” and a “reentrant shift register.” The Court found that the “practical effect” of a patent for the method would be the impermissible award of a patent for a discovery in mathematics because the whole of the subject matter sought to be patented was a mathematical formula that had “no substantial practical application except in connection with a digital computer.”

In the second case, Flook, the Court held that a claim to a method of updating “alarm limits” (numbers) did not recite an invention or discovery within § 101, and thus was ineligible for patent protection. The claims in Flook did not “wholly preempt” the claimed mathematical formula because they did not cover every application of the formula. The claimed method was expressly limited to operation “in a process comprising the catalytic chemical conversion of hydrocarbons,” and thereby to application in a particular technological environment. And the claim recited specific activity beyond the solution of the mathematical formula (so called “post-solution” activity), namely adjusting an “alarm limit” to the figure computed according to the formula. The Court reasoned that the updating of alarm limits in chemical processes was well known, and all that Flook purported to invent and claim was a new formula coupled to a computer for doing so (limited to certain post-solution activity in a technological environment). On these facts, the Court reasoned that the claimed invention or discovery was an alleged newly discovered mathematical formula, which was “not the kind of 'discover[y]' that the statute was enacted to protect.”

In the third case, Diehr, the Court held that a process for operating a rubber-molding press was within § 101. An element of the claimed process was a digital computer programmed to perform a mathematical function. It was known that temperature inside a rubber-molding press determined in part the time the press was required to remain closed. The problem faced in the art was that when the press opened during operation, it cooled, thereby changing the amount of time needed for curing. By including a thermocouple or other temperature-detecting device for measuring temperature inside the press, feeding signals to a computer which would repeatedly calculate the cure time and then cause the press to open at the right moment, the applicant claimed to have invented a new, useful, and nonobvious precision method of curing rubber. The Court reasoned that the claimed subject matter was, as a whole, a process for precision rubber curing that included a computer performing a mathematical formula; the totality of claimed subject matter was not just the mathematical formula. Therefore, held the Court, the claimed subject matter was eligible for patent protection.

The Court in Diehr distinguished its decision in Flook. Both cases involved claims including mathematical formulae to be performed by digital electronics, with application in chemical processes. Diehr's claims were neither to the mathematical formula nor to the “the isolated step of 'programming a digital computer.'” They were to a process “beginning with the loading of [a] mold and ending with the opening of [a] press and the production of synthetic rubber product that has been perfectly cured—a result [t]heretofore unknown in the art.” The chemical process in Flook was not the alleged invention or discovery but only was related tangentially to the mathematic formula; the applicant simply “limit[ed] the use of the formula to a particular technological environment” and claimed “insignificant postsolution activity.” All this demonstrated that in Diehr the applicant was, in substance, asserting and claiming to have invented a new and useful chemical process, thereby qualifying the subject matter for examination under the remaining provisions of the patent law, while in Flook as in Benson the applicant was, in substance, asserting and claiming as his invention or discovery a mathematical function (to be performed by a computer), thereby placing the subject matter outside the patent law.

Under Benson, Flook, and Diehr the posing and solution of a mathematic function is nonstatutory subject matter. It is nonstatutory even if the particular mathematics is limited to performance in digital electronic circuitry or a general purpose digital computer, even if the mathematic operations are alleged generally to have some application in one or various technologies, and even if the solution of the function is said generally to “represent” something of physical or technologic relevance. On the other hand, an invention or discovery of a process or product in which a mathematic operation is practically applied may be statutory subject matter. The fact that one element of the claimed process or product is a programmed digital computer or digital electronics performing a mathematic function does not necessarily preclude patent protection for the process or product. In this way, the door remains open to the advancement of technologies by the incorporation of digital electronics. But the mere association of digital electronics or a general purpose digital computer with a newly discovered mathematic operation does not per se bring that mathematic operation within the patent law.

2. Every case involving a § 101 issue must begin with this question: What, if anything, is it that the applicant for a patent “invented or discovered.”? To resolve this inquiry, the patent or patent application must be reviewed and the subject matter claimed as the invention or discovery “must be considered as a whole.”

In considering claimed subject matter for eligibility under § 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” claimed as the invention or discovery. When the claimed invention or discovery includes “a mathematical formula (or scientific principle or phenomenon of nature), an inquiry must be made into whether the claim is seeking patent protection for that formula in the abstract,” or whether the “claim containing a mathematical formula implements or applies that formula in a structure or process which, when considered as a whole, is performing a function which the patent laws were designed to protect.” Thus the dispositive issue is not whether the claim recites on its face something more physical than just abstract mathematics. If it were, Benson and Flook would have come out the other way and Diehr would have been a very short opinion. The dispositive issue is whether the invention or discovery for which an award of patent is sought is more than just a discovery in abstract mathematics. Where the invention or discovery is only of mathematics, the invention or discovery is not the “kind” of discovery the patent law was designed to protect and even the most narrowly drawn claim must fail. To come within the purview of § 101 and the patent law, a mathematical formula or operation must be “applied in an invention of a type set forth in 35 U.S.C. § 101.”

D. The Claimed Invention or Discovery

Alappat's specification discloses a digital oscilloscope. The majority is quite taken in by the structure and functioning of the oscilloscope. But as the majority recognizes, the oscilloscope is not claimed as Alappat's invention. Rather the claimed invention is, as the majority says, “a means for creating a smooth waveform display in a digital oscilloscope,” or an “anti_aliasing system” for an oscilloscope.

Thus, Alappat discloses a component of a digital oscilloscope to be a “display system,” and a component of the “display system” to be a “rasterizer.” Only the “rasterizer” and the immediate handling of its input and output are described in any structural detail. Figure 5 [in the specification — see prefatory note] provides an example of what the “rasterizer” does. The input to the rasterizer is given as two consecutive y coordinates. The rasterizer outputs an array of “I′” data. According to the preamble of the claim the data is to be displayed on a display means. The specification gives as an example a cathode–ray tube. The “I′” data produced above by “rasterizing” is “anti-aliased” when a cathode-ray tube is illuminated according to the data. This means that there would be no discontinuity, jaggedness, or oscillation that might otherwise appear had merely a line been attempted to be graphed. There is no discussion in the specification of the structure of the means for actually displaying the data or of the oscilloscope.

E. § 101 and the Claimed Invention

1. Of course, I agree that the means–for–function elements in claim 15 must be construed to cover the corresponding structure described in Alappat's specification and equivalents thereof. 35 U.S.C. § 112 ¶ 6; see In re Donaldson. Accordingly, Alappat correctly argues and the majority properly holds that when the “means” elements of the claim are construed under 35 U.S.C. § 112 ¶ 6, paragraphs (a) to (d) of the claim read as follows (the preamble has been shortened for brevity):

A rasterizer for converting vector list data ... into ... pixel illumination intensity data to be displayed ... comprising:

    (a) a first ALU;

    (b) a second ALU;

    (c) two barrel shifters; and

    (d) a ROM.

Further, pursuant to 35 U.S.C. § 112 ¶ 6, elements (a)_(d) also cover equivalents of the two ALUs, the two barrel shifters, and the ROM.

2. The § 112 ¶ 6, issue, however, is a red herring in this case. Although the reconsideration panel erred by ignoring specific structure recited in the claims, Alappat's claimed invention still is not the invention or discovery of a machine. The presence of structure on the face of the claims does not ipso facto make the claimed invention or discovery one of statutory subject matter.

To hold that a claim reciting structure necessarily defines an invention within § 101, the majority implicitly resurrects long-dead precedent of the Court of Customs and Patent Appeals in direct conflict with Supreme Court precedent and subsequent precedent of that court. Early precedent of the Court of Customs and Patent Appeals held that a claimed invention or discovery is outside § 101 only if the claim on its face recites in its entirety mathematics, because claims like that would wholly preempt the mathematical operation at issue. That was the extent of the boundaries of the patent law under § 101. E.g., In re Bernhart, 417 F.2d 1395, 1399 (CCPA). As a corollary, the court reasoned that if the claim does recite structure, the claim necessarily does not “wholly preempt” an abstract idea. E.g., In re Johnston, 502 F.2d 765, 771 (CCPA 1974), rev'd on other grounds sub nom. Dann v. Johnston, 425 U.S. 219 (1976). [Ed. Note: A claim reciting structure, such as that of a general–purpose digital computer, does not “wholly preempt” the subject matter because the claim does not cover the subject matter when it is practiced with other than a general–purpose digital computer and its equivalents. Use of the algorithm in wetware, for example, is not preempted.]

However, the Supreme Court expressly reversed the CCPA's wholesale preemption test in Flook. There the Supreme Court concluded that the claimed discovery was nonstatutory even though the applicant's claim did not wholly preempt the mathematic function involved. Flook should have made clear that satisfaction of § 101, and eligibility for the patent reward in general, requires a judgment that the applicant for the patent has actually invented or discovered something in the useful arts and for that reason is deserving of exclusive patent rights. To determine whether the applicant has invented or discovered something within the patent law, it makes no sense for the sole question to be, “Does the applicant happen to recite structure in the claims or not?” Because the wholesale preemption test cares nothing about the nature of the alleged invention or discovery, the Supreme Court not surprisingly rejected it.

Although the wholesale preemption test became outmoded, the inquiry into specific structure has survived, and indeed has been elevated to the inquiry under § 101, as this case evidences. See also Iwahashi (the claimed subject matter is a statutory “machine” or “manufacture” because the claim is to “apparatus with specific structural limitations” [ROM?] and the claim “defines apparatus in the form of a combination of interrelated means”). However, the majority's test under § 101 that looks simply to whether specific structure is claimed is as inconsistent with Supreme Court precedent as is the wholesale preemption test.

The Supreme Court has held that a claimed invention may represent merely the discovery of a law of nature and be outside the patent law, even though the claim entirely recites a specific and complete structure. See Funk Bros. Seed Co., 333 U.S. at 130 (claim to species of bacteria represented discovery of law of nature and was outside § 101). The Supreme Court has also held that a claimed process may be nonstatutory even if it implements a principle in a “specific fashion.” Flook. And the Supreme Court has held that a claimed invention may represent the discovery of mathematics alone and be outside § 101 even though the claim recites specific structural limitations. Benson.

As the Supreme Court and this court have said, and as the majority says now, the claimed subject matter must be considered as a whole to determine whether the invention or discovery is within § 101. A claim may thus include a limitation directed to a “mathematical formula, computer program or digital computer,” and yet the invention or discovery will be within § 101 so long as the claimed invention in total represents an application of such formula, program, or computer. Likewise, a claim may include the recitation of something physical (i.e., structure), and yet the invention or discovery is essentially only mathematical. Where the claimed invention is nothing more than a newly discovered mathematical formula or solution, the claimed subject matter will not be statutory simply because included in the claim are one or more references to structure.

3. So what did Alappat invent or discover? Alappat's specification clearly distinguishes between an “oscilloscope” and a “rasterizer,” and Alappat claims his invention in claims 15-19 to be only the “rasterizer.”

The “rasterizer” as claimed is an arrangement of circuitry elements for converting data into other data according to a particular mathematical operation. The rasterizer begins with vector “data”— two numbers. “[I]t does not matter how they are ascertained.” The two numbers, as they might to any algebra student, “represent” endpoints of a line. The claimed “rasterizer” ends with other specific “data” — an array of numbers, as the original and reconsideration panels of the board both expressly agreed.

Alappat admits that each of the circuitry elements of the claimed “rasterizer” is old. He says they are merely “form.” Thus, they are only a convenient and basic way of electrically representing the mathematical operations to be performed, that is, converting vector data into matrix or raster data. In Alappat's view, it is the new mathematic operation that is the “substance” of the claimed invention or discovery. Claim 15 as a whole thus claims old circuitry elements in an arrangement defined by a mathematical operation, which only performs the very mathematical operation that defines it. Rather than claiming the mathematics itself, which of course Alappat cannot do, Alappat claims the mathematically defined structure. But as a whole, there is no “application” apart from the mathematical operation that is asserted to be the invention or discovery. What is going on here is a charade. Alappat's brief asks the following:

An input to...a circuit or processing function is converted into a different thing at the output (otherwise why have the circuit or function in the first place?). If the process is new, useful, and nonobvious, does it really matter whether the implementation is in the form of analog components, digital components, programs for a computer, or a combination thereof? Isn't such a differentiation exalting form over substance?

The questions are properly answered thusly: “No,” in Alappat's claimed “rasterizer” it really does not matter how the mathematics is implemented; and “Yes,” assigning § 101 significance to the disclosed structure would be exalting form over substance. So, where the claimed structure does not matter and the invention or discovery is only of a “new, useful, and nonobvious” process for solving a mathematical formula, Benson, Flook, Diehr, and years of precedent command that the patent law shall not exalt form over substance, but rather recognize that the substance is outside § 101.

The subject matter of claim 15, as in Flook, has no substance apart from the calculations involved. The calculations are the beginning and end of the claim. Also as in Flook, the oscilloscope disclosed in Alappat's specification presents a general technological environment for the claimed “rasterizer,” insignificant in relation to it. Claim 15 is not even limited to the environment of an oscilloscope. The claimed rasterizer mathematical function presumably has application in conjunction with any current or future device that prints in an x-y coordinate grid, such as oscilloscopes, computer monitors, televisions, laser printers, mechanical printing devices, etc.

This is not to say that digital circuitry cannot be an element in an otherwise statutory machine. Under Diehr, it can. (Likewise, but not present in this case, improved digital circuitry itself, such as faster digital processors, would be statutory subject matter. Unlike the "rasterizer" in this case, they are not simply a claimed arrangement of circuit elements defined by a mathematical operation which does nothing more than solve the operation that defines it.) But Alappat in his brief expressly recognizes the distinction between a “machine,” even giving some examples, and the “digital processing” one of its components might perform:

In today's technological environment virtually every machine, from cars to washing machines to instruments [e.g., oscilloscopes], uses digital processing, either with specific digital circuitry and/or a microprocessor executing a program.

Thus, unlike the rubber curing process in Diehr, the claimed rasterizer here is not an application of mathematics in an otherwise statutory process or product. The rasterizer is simply the mathematical conversion of data. In Diehr, the input data were derived by a claimed component of the overall rubber curing process—the press and thermocouple—which fed data to the claimed computer. Here, however, as the specification and claims indicate, the waveform data converted by the claimed rasterizer are not required to come from a particular machine connected up to the rasterizer, and, as Alappat admits, it does not matter how the data are selected. The end product of the claimed rasterizer is not precisely cured rubber as it was in Diehr but rather different data as a mathematical function of the original data. Sure, the data have some use. Most data have uses, and that is why people spend time calculating data. But just having some use for data does not make the creation of particular data patentable. Like the subject matter in Flook and Benson, and unlike the subject matter in Diehr, Alappat's claimed rasterizer is newly discovered mathematics and not the invention or discovery of a process or product applying it. Even though it recites structure, claim 15 should be rejected under § 101.

Rejection under § 101 is especially important for the following reason. The examination of Alappat's “rasterizer” must focus on, as Alappat says, the “process” of the circuit elements — the mathematic function performed by them. Because the patent law does not examine abstract mathematics, if the “rasterizer” is held to be within § 101, there can be no meaningful examination for compliance with § 103, and other sections of the patent statute become inapplicable. The practical result is that there is patentability so long as the mathematics is “new.” This is reflected in Alappat's statement that the rasterizer is a “novel combination of conventional electronic circuits which, as functionally defined in the claims, is patentably distinct from prior art rasterizers.” But standing alone, “the novelty of the mathematical algorithm is not a determining factor at all.” Flook.

4. Finally, a “general purpose computer” issue has been raised as an aside in this case. The parties agree that each of the “means” elements in claim 15 would find an “equivalent” within the meaning of 35 U.S.C. § 112 ¶ 6, in a “general purpose digital computer.” Alappat goes so far as to plead emphatically for recognition of equivalency, saying, “Any employable circuit designer could readily design around” to two ALUs, two barrel shifters, and one ROM.

Yet Alappat also concedes that a claim drawn to “a method which amounted to a mathematical algorithm [without] any disclosed hardware or structure, other than a programmed general purpose computer,” is nonstatutory. Alappat's argument is that “bona fide hardware supporting the `means plus function' recitals” in claim 15 renders the claimed subject matter statutory, but then the claim may cover general purpose digital computers as equivalents through § 112 ¶ 6, even though that subject matter could not be claimed outright.

Alappat cannot have it both ways. If a programmed general purpose digital computer is not statutory subject matter, then a claim cannot be drawn to that subject matter whether outright or by application of equivalents under 35 U.S.C. § 112 ¶ 6. Paragraph 6 of § 112 is not a magical way to expand patent protection into nonstatutory subject matter.

As to equivalency, finding equivalency in a programmed general purpose computer proves the nonstatutory nature of Alappat's purported invention or discovery. Alappat argues that the electrical circuitry of the “rasterizer” is equivalent to a programmed general purpose computer because “powerful, inexpensive microprocessors” are equivalent to “discrete digital components, such as and, or, nand, etc., gates, registers, latches, and the like” are equivalent to “analog components, such as transistors, operational amplifiers, and resistors.” They are all equivalents, in Alappat's view, because they all may achieve the same effect: performing the particular mathematics that is the claimed rasterizer.

To find equivalence based solely on the identity of mathematical function, with absolute disregard for the particular claimed circuitry is to concede that Alappat's claimed circuitry is irrelevant and nonstatutory. Getting back to the music analogy, Alappat is like a composer who claims his song on a compact disc, and then argues that the compact disc is equivalent to a player piano or a music box with the song on a roll or even sheet music because they all represent the same song. The composer is thus clearly asking for (and getting from the majority) a patent for the discovery of a song and a patent covering every physical manifestation of the song.

In any event, even if a programmed general purpose computer is “equivalent” to the rasterizer, it cannot be deemed to be within § 101 by simply reasoning as does the majority that it is a “new machine.” Alappat posits that a “programmed digital computer becomes a special purpose digital computer to perform the function specified by the software. The special purpose computer can be implemented likewise by digital components, or even by analog components.” The majority casually agrees that a “general purpose computer in effect becomes a special purpose computer once it is programmed to perform particular functions from program software.” One cannot, however, just call a programmed computer a “new machine” without going through the § 101 analysis required by the trilogy of Supreme Court decisions. Whether or not subject matter is a “new machine” within § 101 is precisely the same question as whether or not the subject matter satisfies the § 101 analysis I have described.

Thus, a known circuit containing a light bulb, battery, and switch is not a new machine when the switch is opened and closed to recite a new story in Morse code, because the “invent[ion] or discover[y]” is merely a new story, which is nonstatutory subject matter. An old stereo playing a new song on a compact disc is not a new machine because the invention or discovery is merely a new song, which is nonstatutory subject matter. The “perforated rolls [of a player piano] are parts of a machine which, when duly applied and properly operated in connection with the mechanism to which they are adapted, produce musical tones in harmonious combination.” White-Smith Music Publishing Co. v. Apollo Co., 209 U.S. 1, 18 (1908). Yet a player piano playing Chopin's scales does not become a “new machine” when it spins a roll to play Brahms' lullaby. The distinction between the piano before and after different rolls are inserted resides not in the piano's changing quality as a “machine” but only in the changing melodies being played by the one machine. The only invention by the creator of a roll that is new because of its music is the new music. Because the patent law does not examine musical compositions to determine their relation to those that have gone before, the distinction between new and old music can never qualify for patent protection. A programmed general purpose digital computer alleged to be patentable subject matter because of the program presents an independent § 101 inquiry that is not resolved simply by calling the structure a “new machine.”

Finally, a claim formally to a general purpose computer running a certain program cannot be deemed to satisfy § 101 simply because the computer is a physical, tangible device. As the invalidated claims in Flook and Benson demonstrate, and consistent with my earlier discussion, a computer program for use in a physical electronic thing called a computer may nevertheless be held to be nonstatutory subject matter. It is illogical to say that although a claim to a newly discovered mathematical operation to be performed by a computer is merely a nonstatutory discovery of mathematics, a claim to any computer performing that same mathematics is a statutory invention or discovery. Furthermore, the broad statement that a computer using any program is patentable subject matter trivializes the principles and distinctions wrestled with in Benson, Flook, and Diehr, and the case law thereunder.


The majority's holding is dangerous in the following way. First, it reasons that one can obtain a patent for a discovery in mathematics as long as some structure is formally recited on the face of the claim. Under this aspect of the holding, many of the requirements for patentability other than “newness,” such as nonobviousness, make no sense and cannot be meaningfully applied. Thus, mathematical patents will be easier to obtain than other patents. Moreover, the patent law will now engage in the charade wherein claims directed to a particular method of calculating numbers (for use in a computer) are unpatentable, but claims directed to a computer (performing a particular method of calculating numbers) are patentable. (Mercifully, the majority leaves open the possibility that a claim reciting structure on its face can still be rejected under § 101. The majority says that this will happen where the claim reciting structure on its face is merely a “guise” for a claim to a mathematical process. Although the majority finds that Alappat's claim to a rasterizer is clearly not a “guise” for a discovery of a mathematical process, the majority does not describe in detail how one distinguishes in general a “true” apparatus claim from an apparatus claim in “guise.” Presumably, the way this is done is to determine what is the invention or discovery for which the patent applicant seeks an award of patent, and then to determine whether that discovery is the kind the statute was enacted to protect, as this dissenting opinion does.)

Second, the majority accepts the argument that all digital electronic circuitry is statutory subject matter when it performs a mathematical operation, and it is all equivalent when the particular mathematical operation is the same. Under this aspect, the mathematical patents will create an enormous scope of technological exclusivity. The lack of meaningful examination and the breadth of exclusive rights conferred by patents for discoveries of bare mathematical operations are repugnant to Congress's careful statutory scheme for the promotion of the useful arts.

As the player piano playing new music is not the stuff of patent law, neither is the mathematics that is Alappat's “rasterizer.” And the Supreme Court has in its decisions required it so. Alappat's claimed discovery is outside 35 U.S.C. § 101, and for this reason I would affirm the board's rejection. I dissent from the majority's decision on the merits to the contrary.

Pauline Newman, Circuit Judge, concurring.


I join the opinion authored for the court by Judge Rich. I write separately to state additional views on the basic question of this case: that of statutory subject matter. This question has been dominant in the PTO's administration of its responsibilities with respect to computer–related inventions. I explore this subject in the context of the statutory purposes of Title 35, and specifically the issues of 35 U.S.C. § 101 that are raised in this appeal. The board's historical practice of giving § 101 the narrowest possible reading is out of place in a world that has become totally dependent on technology, and in which the laws governing technological innovation have direct consequences for industrial growth. Governmental timidity in the face of scientific and technologic change is not only unnecessary: it is unsupportable.

The boundary between patentable and unpatentable subject matter is not always a bright line. A good example is the function of mathematics in modern technology. Mathematics is not only a set of abstract principles, but a powerful vehicle of applied technology—just as chemistry is both a set of scientific principles and a vehicle of applied technology. The board's underlying error in its Alappat decision arose from failure to distinguish between abstract mathematical principles and their practical applications.


Phenomena of nature and abstract scientific and mathematical principles have always been excluded from the patent system. Some have justified this exclusion simply on the ground of lack of “utility”; some on the ground of lack of “novelty”; and some on the ground that laws of nature, albeit newly discovered, are the heritage of humankind. On whatever theory, the unpatentability of the principle does not defeat patentability of its practical applications. See, e.g., O'Reilly v. Morse.

Most technological inventions involve the application of scientific principles and phenomena of nature to specific purposes. It is these purposes that are the subject matter of 35 U.S.C. § 101, and we need not decide such interesting epistemological questions as whether mathematical formulae exist in nature, or are created by mathematicians in the way that chemical compounds are created by chemists.

The theme underlying the board's rejection of the Alappat claims was that since mathematical steps were involved, and were performable by computer, Alappat was claiming a mathematical algorithm such as was held unpatentable in Benson. However, as is explained by Judge Rich, Alappat is claiming a rasterizer of an oscilloscope and similar devices of applied technology. Alappat's rasterizer is an electronic device for displaying a smooth waveform by selective illumination of pixels. The Alappat rasterizer operates by performing a sequence of steps in accordance with instructions that are generated electronically. This operation requires several mathematical calculations that are performed with the aid of microelectronic circuitry, and can be performed by a digital computer.

The structure resides in the configuration by which the device operates, as Judge Rich has explained, and is independent of how that configuration is provided. The structure may reside in semiconductor chips and hardwired connections, or be permanently embedded in the electronic form designated read-only memory, or removably embedded in the electronic form designated random-access memory. It is not relevant to section 101 whether the structure is hardwired or programmed, machine-readable or manually performed, and indeed the means-plus-function style of claim accommodates these alternatives.

Devices that work by way of digital electronics are not excluded from the patent system simply because their mechanism of operation can be represented by mathematical formulae. The output of an electronic device or circuit may be approximated to any required degree as a mathematical function of its current state and its inputs; some devices, such as the transistor, embody remarkably elementary mathematical functions. Principles of mathematics, like principles of chemistry, are “basic tools of scientific and technological work.” Benson. Such principles are indeed the subject matter of pure science. But they are also the subject matter of applied technology.

Digital electronic devices implement mathematical manipulations of electronic signals, as chemical structures and reactions implement principles of molecular behavior. An apparatus that is configured to perform specific electronic procedures in accordance with instructions that require numerical measurements and mathematical calculations is no less statutory than any other combination of steps and components. A combination of mechanical or chemical components, structured to operate in accordance with the principles of mechanics or chemistry, does not become nonstatutory because those interactions and reactions follow basic scientific principles.

Mathematics is not a monster to be struck down or out of the patent system, but simply another resource whereby technological advance is achieved. Alappat's claim to a rasterizer that is characterized by specified electronic functions and the means of performing them no more preempts the mathematical formulae that are used to direct these functions than did Chakrabarty's bacterium preempt genetic theory.


An inquiring and receptive attitude by the PTO to new technologies finds a mandate in the statute. The text of § 101 has not changed since 1793, other than to change the word “art” to “process.” This simple text served the industrial revolution and the atomic age; surely it can serve modern electronics.

Old law is often adapted to new needs: “If Congress has made a choice of language which fairly brings a given situation within a statute, it is unimportant that the particular application may not have been contemplated by the legislators.” Barr v. United States, 324 U.S. 83, 90 (1945).

Law and public policy intertwine in embracing new fields in the scope of § 101. Patent law has nicely fostered technological advance in the United States, for its principles are particularly suited to a free market system: it requires neither governmental intrusion nor federal funds to provide the incentive for industrial innovation; the innovation incentive is the direct consequence of the patent grant. I know of no major technological advance, no new industry or evolving technology, that has not participated in the patent system.

To bar such inventions as Alappat's rasterizer from access to the patent system is to eliminate the incentive provided by this law, disserving not only technological industry, but the public benefit of improved technology. One must have a powerful reason to exclude technology from the scope of Title 35. Indeed, the importance of the patent incentive in industrial innovation was the principal factor in the formation of the Federal Circuit. It is thus appropriate constructively to apply statute, precedent, and policy to the variety of inventions that the information age has generated, and to remove the cloud on whether these inventions may participate in the benefits and obligations of the patent system.

Rader, Circuit Judge, concurring.

I join Judge Rich's opinion holding that this court has subject matter jurisdiction over this appeal and reversing the reconstituted Board of Patent Appeals and Interferences' decision on the merits. While I fully agree with Judge Rich that Alappat's claimed invention falls squarely within the scope of 35 U.S.C. § 101, I write to clarify that this conclusion does not hinge on whether Alappat's invention is classified as machine or process under section 101.

The dividing line between patentable invention and mere discovery applies equally well to algorithmic inventions. In Diehr, the Court indicated that in special cases, an algorithm is tantamount to a “law of nature” and therefore non-statutory. However, the Court noted that “[t]he term `algorithm' is subject to a variety of definitions.” Only algorithms which merely represent discovered principles are excluded from § 101. The inventions in Benson and Flook involved such algorithms. In Benson, the invention was simply a way to solve a general mathematics problem; in Flook the invention was a way to obtain a number. The Supreme Court only denies patentable subject matter status to algorithms which are, in fact, simply laws of nature.

If a digital circuit or its use would define an invention under section 101, then the same invention described in terms of a mathematical formula, computer program or digital computer should be statutory subject matter as well. Neither Alappat's digital circuit, nor a mathematical algorithm that replaces it in a computer, is a “fundamental law of nature” excluded from the scope of § 101. The limits on patentable subject matter within § 101 do not depend on whether an invention can be expressed as a mathematical relationship or algorithm. Mathematics is simply a form of expression—a language.

Thus, the inventor can describe the invention in terms of a dedicated circuit or a process that emulates that circuit. Indeed, the line of demarcation between a dedicated circuit and a computer algorithm accomplishing the identical task is frequently blurred and is becoming increasingly so as the technology develops. In this field, a software process is often interchangeable with a hardware circuit.

The Board has no justification within the Patent Act to ignore algorithmic processes or machines as “useful Arts” within the scope of § 101. U.S. Const. art. I, § 8. This court should not permit the PTO to administratively emasculate research and development in this area by precluding statutory protection for algorithmic inventions.

The applicants of the instant invention do not seek to patent a mathematical formula. They seek protection for an invention that displays a smooth line on an oscilloscope. Although Alappat's machine or process might employ an equation, it does not preempt that equation. Consequently, whether the invention is called a machine or a process is inconsequential. For these reasons, I agree with this court's reversal of the reconstituted Board's decision.

Further Notes on Alappat

1. The scope of means-for claims is still uncertain. When does § 112 ¶ 6 apply to limit the scope of a claim element to the structures that the specification has described and their equivalents? Clearly, if the magic words “a means for doing so-and-so” are used, § 112 ¶ 6 presumptively applies. Thus, “a means for providing a detent” at least prima facie invokes § 112 ¶ 6; so too does “a detent means.” But what if the claims drafter uses the words, “a detent mechanism” or “detent device”? See Greenberg v. Ethicon Endo–Surgery, Inc., 91 F.3d 1580 (Fed. Cir. 1996).

2. The PTO interpreted the “means for” elements of Alappat's claim 15 to cover all means for performing the recited functions. The Federal Circuit reversed, holding that under § 112 ¶ 6 and Donaldson the means–for elements should be interpreted as covering only the structures for accomplishing the functions that the specification described and equivalent structures. The PTO’s practice may well be questioned when the PTO uses it as a general rule. But was it nevertheless proper in this specific context—that of a number–crunching algorithm?

That is, are the equivalents for the number–crunching structures that this specification described necessarily so broad that the claim covers any and all practical means for performing the functions of this procedure?

a. What are the elements of claim 15?

b. It is well known that any numerical calculation (such as those described above) can be done, as a matter of designer's choice, by either hardware or software. Software means and hardware means for performing mathematical operations are, as a general matter, universal equivalents. A designer chooses one or another means on the basis of engineering trade-offs.

The point is summarized in a well known textbook, A.S. Tanenbaum, Structured Computer Organization 10 (Prentice-Hall, Inc. 1976) (italics in original):

A central theme of this book that will occur over and over again is: hardware and software are logically equivalent.

Any operation performed by software can also be built directly into the hardware, and any instruction executed by the hardware can also be simulated in software. The decision to put certain functions in the hardware and others in the software is made on the basis of such factors as cost, speed, amount of memory required, reliability, and frequency of expected changes. There are no hard and fast rules to the effect that X must go into the hardware and Y must be programmed explicitly.

Moreover, here the board determined, and Alappat conceded, “that claim 15 is broad enough to cover a programmed computer.”)

c. Not only are hardware and software means universally equivalent, but the two also exhaust the entire field of practical means for doing numerical calculations (“number crunching”). There are no further equivalents, except “wetware,” whose use is generally unpatentable and, in any event, is infeasible here. Ordinarily, therefore, an electrical engineer implements a calculation procedure by either hardware or software means; there is no other practical means.

d. Consider, therefore, whether the following legal test is appropriate for means-for claims for number-crunching procedures:

If all of the claimed means are means for adding, subtracting, and doing other mathematical (“number crunching”) operations, the claim is directed to a mathematical algorithm. More generally, the claim is nonstatutory if, but not only if, it (1) is infringed by a general-purpose digital computer programmed to do a numerical calculation, and (2) does not include any other element, such as a hardware “front end” (e.g., a CAT–scanner) for obtaining inputs, or a hardware “back end” (e.g., a device for opening rubber molds) for doing acts with the calculated information.

e. Is it better (on other policy grounds) to have a more general rule used for all means-for claims, and not have a special rule for software cases?

Could a proper decision of the more general issue involve considerations of which the CAFC was not informed in Donaldson and Alappat? For example, does what applies to means for subtracting (in terms of facts and policy) necessarily apply to means for cloning cells or means for oxidizing? Are § 101 policy considerations implicated in mathematics-means cases that are not implicated in cases involving chemical or other means?

3. Another claim construction issue in Alappat was whether claim 15 was tied down to use in an oscilloscope. Judge Archer stated, “Claim 15 is not even limited to the environment of an oscilloscope.” He then suggested that the patentee (Tektronix) might assert claim 15 against manufacture and sale of televisions, laser printers, and other devices—raising the specter of Morse's claim 8 vs. the fax machine.

On the other hand, the last few paragraphs of the majority opinion state that claim 15 does not “wholly preempt” any apparatus that carries out Alappat's smoothing algorithm because the claim is limited to the transformation of digitized waveforms into pixel illumination data for producing a smooth waveform for a display. The reason was that the preamble of claim 15 called for inputs of waveform data and outputs of illumination data. So interpreted, the “rasterizer” of claim 15, whether implemented as a programmed microprocessor or as hard–wired combinatorial logic circuits, is as intertwined with the oscilloscope and its display monitor as the CAT–scanner device in Abele or the rubber mold monitor and opener in Diehr.

Is that a proper interpretation of the claim? The preamble states: “A rasterizer for converting vector list data representing sample magnitudes of an input waveform into anti-aliased pixel illumination intensity data to be displayed on a display means . . . ” What does that mean? It tells what the claimed device is supposed to do. Does it tell us what kind of input it will receive or whether there is an input port adapted to receive any particular thing? Moving on, the last element is “means for outputting illumination intensity data as a predetermined function of the normalized vertical distance and elevation.” That seems to be an output port for delivering the result of a numerical calculation. It does not seem to be a voltage or current or a signal adapted to feed any particular other device, such as a magnetic coil. Is it the kind of device that the case law suggests should be at the back end to satisfy what Schrader tells us to look for? Is this a claim like Flook’s?

Well, let’s suspend disbelief and interpret it as Judge Rich does—as a piece of apparatus generating a signal that controls the intensity of the electron beam of an oscilloscope. The claimed device is intertwined with an oscilloscope monitor. If the opinion stopped there, clearly it would eliminate the basis for the suggestion that the patent was preempting laser printer use of the algorithm, à la Morse’s claim 8. Claim 15 would be limited to the environment of an oscilloscope containing a rasterizer subsystem that passed signals back and forth to the rest of the oscilloscope to control its screen illumination. Alappat would be Abele and Schrader redux.

But the majority opinion does not stop there. It goes on to assert that a general–purpose digital computer newly programmed “to carry out the claimed invention” is a new machine. Moreover, such a new machine “may represent patentable subject matter” if it conforms to the requirements of title 35, the patent code. Finally, “a computer, like a rasterizer, is apparatus not mathematics.”

What does all of this additional commentary mean? How does it interact with the dissent? Is it precedent or obiter dictum? What about the claims in Benson?

a. What is the general–purpose digital computer newly programmed to carry out the claimed invention? First of all, it is a microprocessor chip or microprocessor core of another chip. It is not an IBM mainframe or even a PC; they cost too much for any of the now foreseeable uses (starting with an oscilloscope and moving on to the dissent's candidate systems for possible patent infringement liability). So, it is a microprocessor chip programmed to use the smoothing procedure associated with Alappat's formula I′(i,j) = c [1 - (Δyi j / Δyi )].

What else is it? Must the microprocessor (or other hardware) be intertwined with an oscilloscope à la Abele? Or can the microprocessor be free–standing, intertwined with no further apparatus, like the data–in/data–out system in Schrader? Unless we know that, the court's reference to “carry out the claimed invention” begs the question. What's the “invention”?

b. What does it mean that a programmed general–purpose digital computer may “represent” patentable subject matter? Is it any different to “represent” patentable subject matter than it is to be patentable subject matter? Is there a pea under any of these walnut shells?

c. What further propositions follow from the statement that “a computer, like a rasterizer, is apparatus not mathematics”?

4. Is it fair for Tektronix (Alappat's assignee, the patentee) to be able to sue Hewlett-Packard for making laser printer use of the smoothing procedure of the I′ formula? Does the Alappat patent teach Hewlett–Packard how to make improved laser printers that print diagonal lines without jaggies? Relate the second question to the first one.

5. Suppose that the answer to the second question of not 5 is neither “Yes!” nor “No!” but instead is “Sort of.” What's fair and to what extent? How would Professor Zadeh's fuzzy logic deal with this? Is that viable under U.S. patent law? For a discussion of this point in the context of a historical case example (the application of Professor's Viterbi's approximation algorithm to deep-space communication systems and disk-drive read/write systems), see Richard H. Stern and Edward P. Heller III, In re Alappat: The Gordian Knot Retwisted, 2 Balt. Intel. Prop. L.J. 187, 208–11 (1994). (The authors suggest that what's fair depends on how much is enabled and how difficult and expensive it is to enable.)

6. In his opinion for the majority, Judge Rich says: “We have held that such programming creates a new machine, because a general purpose computer in effect becomes a special purpose computer once it is programmed to perform particular functions pursuant to instructions from program software.” Where have you heard that song before? Didn’t it go to meet its maker after Judge Rich’s dissent in the Johnston case and the Supreme Court’s opinions in Benson and Flook? Has he recanted his dissent? Has he joined the resurrectionists? After the Alappat decision, the piano roll blues became dominant in the Fedceral Circuit for more than a decade. See, e.g., WMS Gaming, Inc. v. International Game Technology, 184 F.3d 1339, 1348 (Fed. Cir. 1999); Aristocrat Technologies Australia Pty Ltd v. International Game Technology, 521 F.3d 1328, 1333 (Fed. Cir. 2008).

7. Several weeks after Alappat, a Federal Circuit panel opinion issued holding method claims 1-4 of a patent application nonstatutory because directed to “the manipulation of basic mathematical constructs,” making them paradigmatically mere abstract ideas. The method was a procedure for structuring data. Claim 5 was directed to a “machine [of unspecified nature — presumably a computer] ... having a memory which contains data representing” the results of carrying out the same non-statutory method for structuring data. The court explained that this claim, in terms, “is for a machine, and is clearly patentable subject matter.” In re Warmerdam, 33 F.3d 1354, 31 U.S.P.Q.2d 1755 (Fed. Cir. 1994).

Is the critical distinction that claim 5 called its subject matter a machine? Suppose I call you a taxi (“You're a taxi!”). Does that make you statutory subject matter qua taxi?

Link to last part of section C of chapter 8

Return to Table of Contents