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In re Alappat, 33 F.3d 1526, 31 U.S.P.Q.2d (BNA) 1545 (Fed. Cir. 1994) (full-text).

Factual Background[]

The invention related to a means for creating a smooth waveform display on a digital oscilloscope. Alappat's claim employed an anti-aliasing technique that eliminated any apparent discontinuity, jaggedness or oscillation in the waveform, thus giving the visual appearance of a smooth continuous waveform. This process improved the oscilloscope similar to a clearer picture on a TV. The screen of an oscilloscope is the front of a cathode-ray tube (CRT), which like a TV tube, has a screen that displays pixels arranged at intersections of vertical columns and horizontal rows, illuminated by directing an electron beam at the pixel on the screen.

Since a CRT contains a finite number of pixels, rapidly rising and falling portions of a waveform can appear discontinuous or jagged due to differences in the elevation of horizontally contiguous pixels included in the waveform. The number of rows of pixels on the screen may limit the vertical resolution of the display. The noticeability and appearance of these effects is aliasing. The invention, a machine known as a “rasterizer,” operates by performing a sequence of steps in accordance with electronically-generated instructions. This operation requires several mathematical calculations performed with the aid of microelectronic circuitry or performed by a digital computer. The structure resides in the configuration under which the device operates and is independent from that configuration.

Initially, the patent examiner rejected Alappat’s claims under 35 U.S.C. §101 as non-statutory subject matter. Alappat appealed to the Board of Patent Appeals and Interferences (Board). The Board found that each clause of Claim 15 recited a mathematical operation and together obtained a numeric value as the product of this claim. The panel held that the question whether the subject matter including a mathematical algorithm is within Section 101 was whether the claims recited “specific apparatus distinct from other apparatus capable of performing the identical mathematical function.” Although claim 15 recited a mathematical algorithm, the claim as a whole was directed to a machine and thus to statutory subject matter under Section 101. In reaching their decision, this panel construed the means clauses in claims 15 pursuant to 35 U.S.C. §112 ¶6 as corresponding to the structures disclosed in the specification of the application. Under a general rule, where a claim recites a "means-for” performing functions, a claimed invention falls within patent law unless the functionally-defined means are so broad that they encompass every “means-for” performing the mathematical functions. Here, the claim fell within patent law.

The examiner then requested reconsideration of this decision, stating that the panel’s decision conflicted with PTO policy. The examiner further requested that an expanded panel carry out such reconsideration. An expanded eight-member panel affirmed the examiner’s decision, ruling contrary to the decision of the original three-member panel. The three members of the original panel dissented.

The panel majority’s decision based part of its decision on interpretation following the PTO that gives means-plus-function clauses in claims their broadest interpretation and does not impute limitations from the specification into the claims. It held that the PTO does not need to apply Section 112 ¶6 in rendering patentability determinations. The majority held that Alappat’s claim was written completely in “means-for” language since the claim read on any and every means for performing the particular function recited. Therefore, this claim represented only a step in that process, whereby each step is a mathematical operation when combined to form a “mathematical algorithm for computing pixel information” not eligible for patent protection.

Furthermore, the examiner during prosecution had explained, “the use of physical elements to provide the ‘number crunching’ was not considered patentable.” The panel found that the specification did not disclose nor did the application claim where the input data should come from or how it should be generated. Thus, the claim was directed towards non-statutory subject matter not within the scope of Section 101. In addition, Appellant’s drafted claim reads on a digital computer “means” to perform the various steps under the program control and should be treated as if drawn to a method.

Alappat appealed the reconsideration panel’s decision on the basis that his claim was a “machine” that qualified as statutory subject matter under 35 U.S.C. §101, thereby deserving protection under patent law.

Appellate Court Proceedings[]

The Federal Circuit Court of Appeals reversed the decision of the Board.

First, the Court held that the Board’s majority had erred because it read the claim at issue, claim 15, broadly as every "means-for" performing the functions of the claim thereby rendering it a process claim rather than an apparatus claim. The court noted that the PTO is not exempt from statutory application of 35 U.S.C. §112 ¶6. The court did not presume that a stored program digital computer is not within the Section 112 ¶6 range of equivalents disclosed in the specification. The claim on its face appeared as a machine or apparatus made up of a combination of known electronic elements. Claim 15 is analyzed under Section 112 ¶6, revealed that each of the means covered at least the structure corresponding to the means.

Upon further review under Section 101, the court expressed that the Board's majority erred in application of this statute to determine patentable subject matter. The recited claims were reviewed to determine whether they satisfied the statutory subject matter requirement. Alappat contended that the rasterizer ("machine") performs the same overall function as rasterizers of prior art, but does so differently thereby being subject of a patentable discovery under Section 101 as a new and useful machine. Because claim 15 is directed towards a machine, a category of subject matter in Section 101, the claim falls under patent law.

Further review of the Board's decision subjects the claim to analysis under the judicially created "mathematical algorithm" exception under Section 101 that applies to apparatus claims. The court concludes that the claimed machine of this claim does not fall within the exception. Under Diehr, a review involves an inquiry as to whether the claimed subject matter as a whole is a disembodied mathematical concept that precludes the patenting of the subject matter. In Diehr, the Supreme Court held that "laws of nature, natural phenomena, and abstract ideas" might not receive patent protection under Section 101.[1] "Mathematical algorithms" fall under the category of abstract ideas that constitute disembodied concepts of truths, which are not "useful" until reduced to some practical application.<re>Id.</ref> A machine, process, or manufacture employing a law of nature, natural phenomena, or abstract idea may be patentable. A close analysis of Diehr, Flook, and Benson, revealed that the Supreme Court did not likely intend to create a broad exclusion, but sought to exclude certain mathematical subject matter that standing alone represented abstract ideas.

In the case at hand, the court noted the Supreme Court at the time was not clear on what subject matter falls in the exclusion from Section 101, more so, what qualifies as a mathematical algorithm, formula, or equation. The Supreme Court in Diehr emphasized that the claim must be analyzed as a whole thereby deserving protection under patent law. Alappat's claim does not fall under the exception when analyzed under Diehr because the claimed invention as a whole is directed to a combination of elements, which form a machine. The way the claim is written does not preempt the use of any apparatus employing a combination of the mathematical calculations recited therein.

The court also concluded that the Board majority erred in its reasoning that the claim is unpatentable because "it reads on a general purpose digital computer ‘means’ to perform the various steps under program control." Thus, the court appeared to hold that a standard computer, when programmed to do a certain function, becomes a "new machine," which new machines constitute patentable subject matter. Under this analysis, the court looks at the software and hardware to see if it operates as a single unit, and whether each time a new piece of software is added to the hardware, a new machine totality is created. In this case, a rasterizer is a computer, and for purposes of Section 101, is an apparatus, not mathematics. This case stands for the proposition that a general-purpose computer or machine may represent patentable subject matter if the software meets all the requirements under Title 35.


In dissent, the Chief Judge for the court disagrees with majority’s conclusion that Alappat’s “rasterizer” constitutes an invention or discovery within Section 101. The dissent focuses on reviewing of sound principles of patent law and understanding Section 101 to determine how it applies to discoveries and inventions in the field of digital electronics, including so-called general-purpose digital computers, because digital electronic devices involve solutions to problems through arithmetic. A set of Supreme Court cases, Benson, Flook, and Diehr are reviewed to understand when an invention or discovery in the field of digital electronic related subject matter is within the scope of the patent law. In the dissent’s view, these cases provide that a solution of a mathematic function is nonstatutory subject matter even if the mathematics are limited to perform in digital electronic circuitry or general purpose digital computer. The focus should be on whether the invention of discovery for a patent is more than just discovery in abstract mathematics. Mere association of digital electronics or computer does not per se bring mathematical operation within patent law.

The dissents main contention is that the statute does not support a simple “structure” test as the majority relied on. The discovery of a mathematical process claimed under some structure on the face of the claim does not deserve a patent. Structure is not a class of subject matter under Section 101 rather that the applicant must have “invented” or “discovered” some practical method or means of producing a beneficial result or effect. Dissent finds the application of the mathematics is not an application of mathematics in a statutory process or product. Rejection is especially important because Alappat’s claim focused on the “process” of the circuit elements and the mathematics performed. The rasterizer is an arrangement of circuit elements defined by mathematical operations that do nothing more than solve the operation that defines those elements.

Under the holding, many of the other requirements in patent law cannot be applied to abstract mathematics. Patent law does not examine abstract mathematics and therefore, no further analysis could be done under 35 U.S.C. Section 102-103. The claimed invention or discovery is not implemented or applied in a structure or process which when considered as a whole represents an invention or discovery of a machine or process that can be analyzed as a whole. This majority’s holding stands for allowing a claim that is directed at allowing a computer to be made patentable. Majority does not clarify how one can distinguish a true apparatus claim from one that is not. Dissent suggests that a determination is made whether a patent would serve the purpose of patent law.

The dissent’s concern was for future implications where a patent would be awarded for digital electronic circuitry that would be considered statutory subject matter if it performs a mathematical operation. This holding might allow patents for mathematical discovery, against the statutory scheme for promotion of useful arts under patent protection.


Concurring opinions of the majority address statutory subject matter with respect to computer-related inventions. Patentability must be viewed in terms of practical applications such that devices that work by way of digital electronics should not be excluded from the patent system because their mechanism of operation can be represented by mathematical equations. Most technologic inventions involve the application of scientific principles and phenomena of nature to specific purposes. Barring such inventions as Alappat’s will eliminate incentives provided by the law.

Furthermore, concurrence review of Section 101’s language reveals that the court should not extend a patent to some new and useful inventions and deny it to others. However, under careful review of statutory conditions for patentability, the majority correctly applied these conditions and principles. Concurrence notes that mathematical algorithms and formulae can represent ideas or mental processes for communicating possible solutions to complex problems. Review of Diehr reveals that inventors may express the inventions in any manner they see fit including algorithms. The inventor can describe the invention in terms of a circuit or even a process. Since software is interchangeable with a hardware circuit, technology recognizes no difference whether an invention is a process. Calling an invention, a process or a machine is inconsequential.

  1. Diehr, 450 U.S. 175, 185.