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

In re Schrader
United States Court of Appeals for the Federal Circuit
22 F.3d 290 (1994)

Before Newman, Mayer, and Plager, Circuit Judges. Plager, Circuit Judge.

Schrader appeals the decision of the PTO appeals board affirming the rejection of all claims pending in U.S. Pat. App. Ser. No. 07/367,668 (the `668 application) for lack of statutory subject matter under 35 U.S.C. § 101. Finding no reversible error in the board's decision, we affirm.


Schrader's application is directed to a method for competitively bidding on a plurality of related items, such as contiguous tracts of land or the like. After the items have been offered to bidders, bids on one, some, or all of the items are received and entered into a "record." Then, the combination of winning bids is determined by assembling a "completion" from all the entered bids. As explained in the specification, a completion is the particular combination of bids which "would complete a sale of all of the items being offered at the highest offered total price." (In some instances, the completion is formed from those bids that minimize the price of the items bid upon. For example, in a competitive bid for a defense contract, where multiple contractors are bidding to provide services at one or more military bases, the completion is formed from those bids that minimize the contract price, and thus the cost to the government.) The items are then sold (or purchased) in accordance with the "completion."

For example, in an auction involving two contiguous tracts of land, tracts 1 and 2, the following bids might be received and recorded: Bid 1—$100,000 for tract 1 by bidder A; Bid 2—$200,000 for tract 2 by bidder B; and Bid 3—$250,000 for both tracts 1 and 2 by bidder C. The combination of bids that maximizes the revenue to the seller, and thus the combination of bids that forms the "completion," would be bids 1 and 2. [Ed. Note: 100,000 + 200,000 = 300,000 > 250,000.]

Schrader claims that his method constitutes a novel way of conducting auctions. According to Schrader, the type of bids that are normally offered at auctions is dictated solely by the way in which the auctioneer organizes or groups the items to be sold. Through his method, claims Schrader, bids on any combination of the items being auctioned off are offered at the discretion of the bidder. The purported benefit is greater sales revenue or profit to the seller. This is illustrated by the previous example, in which bids were offered on each of the individual tracts as well as on both tracts together. As a result, the seller attained total sales revenue of $300,000. If the seller had only been offered bids on the combined tracts, i.e., Bid 3, the seller would have derived $250,000 in revenue.

Claim 1 is representative:

1. A method of competitively bidding on a plurality of items comprising the steps of:

identifying a plurality of related items in a record;

offering said plurality of items to a plurality of potential bidders;

receiving bids from said bidders for both individual ones of said items and a plurality of groups of said items, each of said groups including one or more of said items, said items and groups being any number of all of said individual ones and all of the possible combinations of said items;

entering said bids in said record;

indexing each of said bids to one of said individual ones or said groups of said items; and

assembling a completion of all said bids on said items and groups, said completion identifying a bid for all of said items at a prevailing total price, identifying in said record all of said bids corresponding to said prevailing total price.

The examiner rejected the claims for lack of statutory subject matter under 35 U.S.C. § 101. Schrader appealed to the board. The board sustained the rejection apparently on three different grounds:

First, "[t]he claimed subject matter is, in our opinion, directed to subject matter that falls within a judicially determined exception to a process set forth in § 101. The claimed process involves only information exchange and data processing and does not involve a process of transforming or reducing an article to a different state or thing. . . .

Second, the claimed method "involves a mathematical algorithm or mathematical calculation steps, as the method includes a procedure for solving a given type of mathematical problem. . . . [T]he mathematical computations of the summation of the possible bidding combinations is at the heart of the invention."

Third, the claimed subject matter is a method of doing business, unpatentable under § 101.


Schrader argues that the board incorrectly applied the Freeman-Walter-Abele test. According to that test:

It is first determined whether a mathematical algorithm is recited directly or indirectly in the claim. If so, it is next determined whether the claimed invention as a whole is no more than the algorithm itself; that is, whether the claim is directed to a mathematical algorithm that is not applied to or limited by physical elements or process steps. Such claims are nonstatutory. However, when the mathematical algorithm is applied to one or more elements of an otherwise statutory process claim, . . . the requirements of 101 are met.

Schrader's first point is that there is no mathematical algorithm implicit in the claim.5 We disagree. Benson defines a "mathematical algorithm" for purposes of § 101 as a "procedure for solving a given type of mathematical problem. . . ." The claim language "assembling a completion" is such a procedure because it describes the solving of a mathematical problem: determining the optimal combination of bids. This process is within or similar to a class of well-known mathematical optimization procedures commonly applied to business problems called linear programming. (Defined in Webster's New International Dictionary to mean "a theory of maximization of linear functions of a large number of variables subject to constraints used esp. in the administrative and economic planning of industrial and military operations." Linear programming is a known procedure for solving business problems involving profit maximization. See 12 McGraw Hill Encyclopedia of Science & Technology at 385–387 (6th ed. 1987)). Thus, a mathematical algorithm is implicit in the claim.

  5     The definition of "algorithm" is not universally agreed. One working definition is that "[a]n algorithm is an unambiguous specification of a conditional sequence of steps or operations for solving a class of problems." Allen Newell, Response: The Models Are Broken, The Models Are Broken, 47 U. Pitt. L. Rev. 1023, 1024 (1986). The same author notes that the label "mathematical algorithm" is a source of confusion: "The first confusion is using involvement with numbers as the hallmark for distinguishing mathematics from nonmathematics, as an aid to determining what is an algorithm. . . . [M]athematics deals with both nonnumerical things and numerical things. . . . [T]here are both numerical and nonnumerical algorithms. . . . Therefore, any attempt to find a helpful or cutting distinction between mathematics and nonmathematics, as between numerical or nonnumerical, is doomed." Id.

Schrader's next point is that, even if a mathematical algorithm is implicit in the claim, the claim recites or implies sufficient physical activity to meet the second prong of the Freeman-Walter-Abele test. Thus, he argues the method physically regroups raw bids into new groupings and ultimately "completions," physically transforms bid data into completion data or display data, and makes physical changes to a "display." In the specification, Schrader says that the claim envisages an auction environment in which "all of the bidders are assembled in one large room with a display in front of the room" or with the bidders "assembled in several rooms either adjacent or in different cities interconnected by a closed-circuit television system or the like using large screen displays."

We find this argument unpersuasive. The word "display" is nowhere mentioned in the claim. Moreover, there is nothing physical about bids per se. Thus, the grouping or regrouping of bids cannot constitute a physical change, effect, or result. Also, the terms "bid data," "completion data," or "display data" are nowhere mentioned in the claim and there is no basis to read them into the claim. Therefore, we do not find in the claim any kind of data transformation. Finally, the notion of bidders assembled in a single location in front of a display, or in several locations interconnected by closed-circuit television through a large-screen display is not recited in the claim. The only physical effect or result which is required by the claim is the entering of bids in a "record," a step that can be accomplished simply by writing the bids on a piece of paper or a chalkboard. For purposes of § 101, such activity is indistinguishable from the data gathering steps which we said in Grams were insufficient to impart patentability to a claim involving the solving of a mathematical algorithm.

Moreover, the step of entering data into a "record" is implicit in any application of a mathematical algorithm. The recitation of such a step in a claim involving the solving of a mathematical algorithm merely makes explicit what had been implicit. A conclusion that such activity is sufficient to impart patentability to a claim involving the solving of a mathematical algorithm would exalt form over substance. A similar point was recognized in Flook, in which the Court concluded that the recitation of insignificant post-solution activity in a claim involving the solving of a mathematical algorithm could not impart patentability to the claim.

Schrader's claims are thus not patentable.

Arrhythmia is not to the contrary. The claims in Arrhythmia involved the manipulation of electrical signals and data representative of human cardiac activity; it was held that they recited patentable subject matter. For purposes of § 101, the claims were indistinguishable from the claims involving the manipulation of data representing CAT scan images held patentable in Abele or the claims involving the manipulation of signals representative of reflected seismic energy held patentable in Taner.

These claims all involved the transformation or conversion of subject matter representative of or constituting physical activity or objects. In Arrhythmia, it was electrocardiograph signals representative of human cardiac activity; in Abele, it was X-ray attenuation data representative of CAT scan images of physical objects; and in Taner, it was seismic reflection signals representative of discontinuities below the earth's surface. Schrader's claims, except for incidental changes to a "record," do not reflect any transformation or conversion of subject matter representative of or constituting physical activity or objects.

The requirement that in a process claim compliance with § 101 requires some kind of transformation or reduction of subject matter is not in violation of the Supreme Court's admonition in Diehr that "courts ‘should not read into the patent laws limitations and conditions which the legislature has not expressed.'" When Congress approved the addition of the term "process" to the categories of patentable subject matter in 1952, it incorporated the definition of "process" that had evolved in the courts.11 As of 1952, that term included a requirement that there be a transformation or reduction of subject matter. We first see the requirement reflected in an early case, Cochrane v. Deener, 94 U.S. 780, 787-788 (1877), in which the Court stated: "A process is . . . an act, or a series of acts, performed upon the subject matter to be transformed and reduced to a different state or thing." We also see it reflected, imperfectly, in Benson, in which the Court stated: "Transformation and reduction of an article `to a different state or thing' is the clue to the patentability of a process claim. . . .

  11.     The legislative history shows Congress approved the substitution of the term "process" for the term "art" used in all previous patent statutes, because it had a more "readily grasped" meaning that had evolved in the courts. There is a presumption that when a statute uses a term of art, such as "process," Congress intended it to have its established meaning. See McDermott Int'l, Inc. v. Wilander, 498 U.S. 337, 342 (1991); Barber v. Gonzales, 347 U.S. 637, 641 (1954).

Finally, we see it cited with approval in Diehr. This basic requirement preceded and remains a part of the requirements incorporated in the 1952 Act. See Astoria Fed. Sav. & Loan Ass'n v. Solimino, 501 U.S. 104, 106-08 (1991) (presumption that well–established common law principles are left unchanged by statutory enactment).


Accordingly, we conclude the board properly rejected the claims for lack of statutory subject matter. (As noted, the board affirmed the rejection of Schrader's claims on three alternative grounds. The dissent suggests other grounds on which the rejection might have been based. Since we are obligated to decide the case on the grounds invoked by the board, we cannot reach the issues suggested by the dissent, and, in view of our disposition of the appeal on the mathematical algorithm ground, we need not address the other grounds offered by the board.) The decision of the board is affirmed.

Pauline Newman, Circuit Judge, dissenting.

I respectfully disagree with my colleagues on this panel, for I do not view this subject matter as nonstatutory.

Schrader is claiming a method whereby parcels of real property or other things are sold at auction by a procedure of bidding and determining optimum prices that, according to Schrader's brief, is usefully but not necessarily performed with the aid of a computer. Although Schrader's claimed process requires computational steps, the fact that mathematical procedures are performed does not preclude patentability. It is necessary to ascertain whether the claim as a whole defines statutory subject matter, whether or not mathematical procedures are invoked along the way.

Even if the Schrader claims are viewed as encompassing a mathematical algorithm, it is applied in a statutory process as set forth in 35 U.S.C. § 101, in this case a process of conducting an auction of multiple lots of separable elements. Although one may debate whether the claimed process is a "method of doing business," as the board found, I can not agree that the claimed invention is no more than a mathematical algorithm.

A process does not become nonstatutory because of the nature of the subject matter to which it is applied, or the nature of the product produced. The nation has benefitted from the adaptability of the patent system to new technologies. The majority now imposes fresh uncertainty on the sorts of inventions that will meet the majority's requirements. All mathematical algorithms transform data, and thus serve as a process to convert initial conditions or inputs into solutions or outputs, through transformation of information. Data representing bid prices for parcels of land do not differ, in § 101 substance, from data representing electrocardiogram signals (see Arrhythmia) or parameters in a process for curing rubber (see Diehr). All of these processes are employed in technologically useful arts. (The majority implies that it is more desirable, from the viewpoint of social policy, to withhold the patent incentive from innovative activity such as that here illustrated.)

In the continuum wherein the jurisprudence relating to computer- implemented inventions has evolved, judge-made law has retreated from specifying how a mathematical algorithm must interact in the claimed invention in order to constitute statutory subject matter, and advanced toward the test of whether the overall process is for a technologically useful art.

Schrader's claimed process requires the performance of specified steps and procedures, including calculations, to achieve a technologically useful result; it is not a mathematical abstraction. As stated in Diehr, subject matter does not become nonstatutory "simply because it uses a mathematical formula" in an otherwise statutory process. Thus I respectfully dissent from the panel majority's view that Schrader's claims do not comply with § 101.

[A portion of Judge Newman's dissent addresses the patentability of methods of doing business. It is omitted here, but is included in chap. 8D.]


1. What did Schrader invent? What the Federal Circuit's two-plot example (tracts 1 and 2) fails to demonstrate is critical to the importance of Schrader's advance. The management of bidding becomes exponentially more complicated as the number of items under bid increases. One can determine in one's head what bid combination provides maximum revenue for two items, as in the court's example, but as the number of items gets larger it becomes impossible to do so. By the same token, doing this kind of competitive auction bidding in real time becomes increasingly infeasible as the number of items increases. The bidders cannot tell what bid they must raise in order to prevail or how much to raise it. The calculations become too difficult to perform at auction speed.

For example, if four items a, b, c, and d are involved, and if we represent the possible combination bids by corresponding capital letters, we have the following possible item combinations or sets:

In general, for n items there are 2n - 1 possible combinations of items on which a bidder might bid. Even the four–item example used here is probably too complex for carrying on an auction in real time without computer assistance, since each of 15 possible combinations may need to be considered in resolving each successive bid.

Schrader's contribution is a method of making it possible to carry on auction bidding of this type in real time. In other words, Schrader made it possible to carry on a multi–item auction the same way that one carries on an ordinary single-item auction.

2. More about what Schrader invented. As the applicants said in their specification, they contemplated carrying out the auction with bidders grouped in different locations, possibly different cities. The bidders would view a large TV display unit on which bids would be displayed. The bids would be processed in a central computer ("processor"), so that the displays could show what combinations for single items or combinations of items were prevailing at any given point. That would give each bidder the opportunity to submit a higher bid for a particular item or combination of items, so as to become prevailing bidder in place of the previously prevailing bidder.

The accompanying diagram does not come from the patent application. It is intended to illustrate Schrader's procedure, from a systems viewpoint, to facilitate your understanding what Schrader had developed and sought unsuccessfully to patent. In this diagram, multiple bidders in two cities enter bids by means of bid entry devices. These may be keyboards, touch-screens, or other conventional input devices. The bids (i.e., bid signals) are then transmitted to the processor via telecommunications links (for example, telephone lines). The processor processes the bids to determine which combinations prevail at a given time.

The patent application did not describe details of Schrader's actual program. But based on discussions with his counsel, it may be concluded that a simple brute force method was used. Such a method could operate on these lines:

While this method is awkward, it proceeds rapidly enough since the computer is a fast calculator.

After each new bid is evaluated, the processor sends image signals to the display units, so that the displays show the then-prevailing bids. Preferably, this information is presented on the screens in a manner that facilitates bidders' comprehension of what kind of bid raises are needed to exceed the previously prevailing bids. For example, the user interface program highlights in contrasting color the prevailing combination bids.

3. Compare the foregoing description of Schrader's system with the language of claim 1. What major differences, if any, do you perceive? What effect, if any, might that have had on the ruling?

4. Consider the following alternative version of an apparatus claim to replace claim 1. (The corresponding method claim is left as an exercise.)

1. An apparatus for electronically processing competitive, auction bids from bidders for items and sets of items subject to bid at a given time and for electronically displaying said competitive, auction bids in real time to actual or potential bidders, said apparatus comprising:

    at least one bid entry device, said device comprising a means for entering bid information from a bidder and for generating an electronic bid signal representative of said bid information, said bid signal being representative of a bid for an item or a bid for a set of items;

    coupled to said bid entry device, at least one first telecommunications link for transmitting said bid signal from said bid entry device;

    at least one display unit for displaying to actual or potential bidders electronically generated images representative of selected bid signals; and

    coupled to said first telecommunications link and coupled to said second telecommunications link, an electronic processor comprising:

      a bid processor for electronically processing each said bid signal received from said first telecommunications link and for selecting a currently prevailing set of bid signals from said bid signals;

      an image generator for electronically generating image signals representative of said currently prevailing set of bid signals; and

      a means for transmitting said image signals via said second telecommunications link to each said display unit for display thereon in real time of images representative of said currently prevailing set of bid signals.

Does this claim relate differently to the case law and Schrader's method than Schrader's actual claim 1? If so, how? Comment on the italicized phrases.

5. Schrader may suggest that whether a computerized method of doing something that involves crunching numbers without using any dedicated apparatus (rather, just a general-purpose digital computer) is statutory subject matter depends on how one writes the claims. If you make a great deal of noise in the claim about transforming signals representative of whatever "physical" the method concerns, and you also put in some references to the conventional and perhaps obvious kinds of apparatus (perhaps a display, keyboard, some telephone wires) that one always uses with things of this sort, voilá — patentable subject matter. But if you fail to do that, you just have a nonstatutory method or an abstract idea.

As for form vs. substance, form is discernible; it is objective. We not only know it when we see it (pace, Stewart, J.; see Jacobellis v. Ohio, 376 U.S. 184, 197 (1964)), but we can even describe and define it with particularity. Substance, as always, is elusive.

6. The nutshell. As of April 13, 1994, the date of the Schrader decision, the law on when an algorithm-related method or apparatus claim is directed to statutory subject matter appeared to have reached an equilibrium:

To be directed to statutory subject matter, the claim should contain some kind of apparatus limitations so that use of the algorithm is “monopolized” only when the use occurs with particular specialized apparatus, rather than just a programmed general-purpose digital computer or microprocessor. The special apparatus may be placed before the algorithm comes into play, as in the case of a CAT scanner input, or a seismic transducer input, whose signals are processed in accordance with the algorithm. (Perhaps an analog-to-digital converter front end will also suffice.) The special apparatus may be placed behind the algorithm, as in the case of an automatic rubber mold opener that opens in accordance with calculations performed using the algorithm. If there is no special hardware at the front end or the back end, it may be satisfactory if “the specific piece of apparatus” is thrust into the middle of the operation of the algorithm, as in the case of a look-up ROM storing data used by the algorithm.

Further, it may be satisfactory simply to process signals representative of a physical parameter, a so-called physical object or activity. The signal might be representative of a temperature reading from a heated rubber mold. The signal might be representative of reflected energy from an underground explosion.

If the claim has none of these things, and simply describes a procedure with data going in and data coming out, the claim lacks "structure" and is directed to nonstatutory subject matter. (Do you see anything different about this form of the machine or transformation test from Flook?)

Now, you know how to draft algorithm-related claims, and opine for clients on their scope and validity. At last, some predictability and thus security of business expectation! The rule may not be simple, but it is manageable. If not a bright line, at least it is a bright zig-zag.

But Schrader marked the Last Hurrah. This decision marked the high-water point for the version of the machine-or-transformation test that evolved in the 1990s. As you read the following case-law, ask yourself why.

Prefatory Notes on In re Alappat (Fed. Cir. 1994)

Watershed or Damp Squibb?

1. The Alappat decision of the Federal Circuit en banc is the only decision of that court showing the views of most members of the court in regard to the same given fact situation involving a computer-related invention. The Alappat decision thus had the possibility of providing a definitive treatise on the extent to which computer-related technology is statutory subject matter. For a number of reasons, however, Alappat did not do so.

Three members of the then eleven-member court refused to opine on the merits, because they believed that the court had no jurisdiction over the appeal. Two judges dissented on the merits. Another judge (Michel) believed that the court lacked jurisdiction but nonetheless voted with the majority on the merits, providing an absolute majority of the eleven-member court (six) to dispose of the case by reversal and remand to the PTO. The issue splintering the court on jurisdiction was the extent to which the appellate board within the PTO was subject to the Commissioner's control. Specifically, could the Commissioner appoint a new appeals board panel to determine a case and issue a final agency order, if he was dissatisfied with the original panel's determination. (A majority of the Federal Circuit held that he could. In effect, the Commissioner’s, not the Board’s, was the last word within the Office on how to interpret substantive law, unless and until the courts ruled otherwise.)

On the merits (statutory subject matter), the court's interpretation of the claim on review as having at least implied apparatus limitations may have obscured the precedential impact of the decision. The following is two commentators' contemporaneous evaluation of Alappat's impact (verb tenses changed, however, to reflect what happened later):

In re Alappat, the Federal Circuit's long–awaited en banc decision on patentability of algorithms, once decided would turn out to be a watershed or a damp squibb, depending on how subsequent Federal Circuit panels would interpret it. Several immediately earlier and later panel decisions by the same court suggested that as many different “spins” could be placed on Alappat as there were different panels. One polar interpretation of Alappat was that henceforth—after the watershed—patents will routinely be allowed on algorithms, as such, so long as the claims are “limited” to use of the algorithm in programmed computer equipment. At the other pole—the damp squibb end of the continuum—the Alappat decision could be regarded simply as addressing a particular set of claims and a particular specification that, when considered as a whole, implied significant limitations into the claims. The effect of these limitations was that the patent covered use of the algorithm only in a subsystem of a specific mechanical apparatus. Given the very different, and equally plausible, possible readings of the Alappat decision, it generated much more uncertainty than it resolved, at least until enough different Federal Circuit panels put a definitive spin on it.

Richard H. Stern and Edward P. Heller III, In re Alappat: The Gordian Knot Retwisted, 2 Balt. Int. Prop. L.J. 187 (1994) (with alterations). In retrospect, Alappat could be viewed as standing at the point when the judges of the Federal Circuit wearied and lost interest in struggling over patent-eligibility and, at least for the time, adopted the view urged in Judge Rader’s “Gordian Knot” opinion.

Alappat's Invention

2. Alappat (and two others, for convenience referred to here collectively as “Alappat”) invented a system for use in improving the appearance of oscilloscope screen displays. The system determines the intensity of illumination of “pixels” on the screen display of a digital oscilloscope to improve the appearance of waveform displays. The screen of an oscilloscope is typically a TV tube (cathode-ray tube or CRT) whose face comprises a rectangular array of pixels. Each pixel is a spot that is illuminated when an electron beam is directed to the spot by circuitry in the oscilloscope. The intensity of illumination may be controlled by varying the amount of energy being delivered to the spot. Although not described in the specification, conventional means are well known for varying the amount of energy delivered to the location of a pixel, and accordingly for varying the intensity of its illumination.

A digital oscilloscope ordinarily samples a continuous waveform and displays individual, discrete observation points on its screen. This may cause a displayed waveform of a curve, such as the S–shaped curve shown at right, to have a jagged, discontinuous appearance. Furthermore, the presence of noise in an input signal may cause points to jump up and down on the screen between vertically adjacent pixels. This effect is called “aliasing”; the term “jaggies” is also used sometimes to describe the staircase–like appearance of what should be a smooth line or curve on the screen.

The invention counteracts these undesired effects by providing variable illumination intensity information for each pixel so that the pixels closest to the trajectory of the observation points are brighter and those farther away are dimmer. This procedure (“anti–aliasing”) improves the appearance of the display by providing a continuous-appearing and non-jumping waveform. The figures at left and right, respectively, show a very enlarged portion of a curve on a screen, first with jaggies and second with the jaggies suppressed by anti-aliasing.

Alappat did not invent the ideas of anti-aliasing or selectively controlling pixel illumination to provide an anti-aliased screen display; the record contains examples of prior art. Rather, Alappat's invention is a particular scheme or system for determining the illumination intensity to be assigned to given pixels.

Alappat's disclosure is illustrated in the figure at left, taken from the patent application (Fig. 5A of the specification). Successive observation points 54 and 52 are shown at the lower left and upper right. With no anti-aliasing system, successive observation points 54 and 52 appear on the screen of the oscilloscope as separate, unconnected spots. The system gives the display the appearance, instead, of line 48 (a so-called "vector"). Each box in the figure represents a pixel in the vicinity of observation points 54 and 52. Numbers at the sides of boxes represent weighting factors from 0 to 15. A box with 0 in it represents a pixel with no illumination; a box with 15 represents a pixel with maximum illumination intensity.

Alappat's system for assigning illumination intensity values to pixels works as follows, using pixel 55 of the figure (shaded box) as an example. First, a vertical distance is determined which is the difference between the Y coordinates of observation points (and pixels) 52 and 54. The patent application (specification) refers to this difference as Δi = |yi - yi+1|; element (a) of claim 15 is a means for determining this difference. In the figure, Δyi = 7 units, where one unit is the center-to-center distance of adjacent pixels.

Second, the elevation of pixel 55 above pixel 54 is determined. This is the difference between the Y coordinates of the centers of those pixels. The patent application refers to this difference as Δyi = |yi - sj|; element (b) of claim 15 is a means for determining this difference. In the figure, Δyi j = 2 units.

Third, Δyi and Δyi j are "normalized." This corresponds to element (c) of claim 15. The idiosyncratic lexicography of Alappat's patent application explains "normalization" as multiplying a number to get larger values to work with; this procedure also provides ready access to the most significant digits of the number. Such normalization can be effected by using a "barrel-shifter" (shift register) to shift the number to the left. For a number in binary format, that means multiplying it by 2, 4, 8, 16, etc.; this is like adding zeros at the end of a number in decimal format, to multiply it by 10, 100, 1000, etc.

Fourth, illumination intensity is determined from the numbers obtained by the preceding operations. The algorithm for this procedure in its simplest form is given in the patent application in terms of the following formula:

I′(i, j) = [1 - (Δyi j / Δyi )] 15

For pixel 55 of the figure, I′ = [1 - (2/7)]15 = (5/7)15 = 10.71 ≈ 11. Accordingly, pixel 55 should be given 11/15 of maximum illumination under Alappat's scheme. (Compare this to the process of interpolating to get the values of logarithms that you learned in high school algebra.)

The procedure is carried out for each pixel in the vicinity of the observation point and vectors from point to point. The numbers shown in light–face type in each of the cells of the figure are those calculated by using the foregoing formula. The numbers represent the relative brightness to be assigned to those pixels to decrease the aliasing effect.

The procedure is carried out for each pixel in the vicinity of the observation point and vectors from point to point. The numbers shown in light–face type in each of the cells of the figure are those calculated by using the foregoing formula. The numbers represent the relative brightness to be assigned to those pixels to decrease the aliasing effect.

Claim 15 calls the foregoing calculation in element (d) “a predetermined function of the normalized vertical distance and elevation.” The patent application also describes more complicated forms of the algorithm of element (d), which are for use with other waveshapes. The patent application does not provide details of how the parameters derived for illumination intensity are actually used to control illumination of the screen. Presumably, this is done in a conventional manner. (For example, making the current in the coil surrounding the neck of the CRT proportional to I′.)

The Controversy Over “Means–for” Versus “Structural” Claiming

3. Much of the controversy here is about interpreting a claim in which every element is a "means for" performing some function (for example, means for adding two parameters), without any specific statement in the claim of how the function is to be implemented in hardware. 35 U.S.C. § 112 ¶ 6 specifically authorizes presentation of claims in this format and states that they are to be interpreted as covering both those structures (i.e., that hardware) for accomplishing the function that the specification describes and the equivalents of such structures.

This claims-drafting expedient is often useful when it does not matter to an inventor how a particular function is accomplished. For example, a "defloximator" invention may work equally well when element A is nailed to element B, or screwed, glued, welded, or soldered to it. How A is fastened to B simply does not matter, so long as there is some means for fastening the two elements, because that is not what this invention is about; the fact of fastening is merely incidental to the invention. The “heart,” “gist,” or “essence” of the invention is something else. But see Aro Mfg. Co. v. Convertible Top Replacement Co., 365 U.S. 336 (1961) (holding that, for infringement purposes, there is no "heart," "gist," or "essence" of an invention, and all claimed elements must be present for infringement to be found). A problem arises with means-for claiming when one tries to determine the scope of the claim. Does a defendant infringe the means-for-fastening patent claim on the defloximator by making a device in which A relaxably sticks to B by means of a switch-controlled electromagnet? What if the claims drafter does not recite the fastening means as a separately named element but instead just describes element B as "a B element fastened to said A element"?

For many years before Alappat, the PTO took the position that such all-means claims should be interpreted during pre-issuance, ex parte prosecution of a patent application before the PTO as covering all possible means for performing the function recited after the words "means for," unless the applicant could persuade the PTO otherwise. That is, when the examiner cited as anticipating prior art a reference using particular hardware as the recited means in a related context, the applicant could try to persuade the examiner that the means of the reference was not equivalent to the means mentioned in the applicant's specification. If the applicant was persuasive, the PTO would withdraw the rejection. If the applicant was unpersuasive or refused to address equivalency, the rejection would stand and the PTO would not issue the patent as claimed. (The applicant could amend, expressly providing a narrower scope.)

According to the PTO, the statement in § 112 ¶ 6 that a means–for claim should be interpreted to cover the structures that the specification describes and their equivalents applies only to claim interpretation after patent issuance and during patent litigation; some CCPA precedent appeared to support this view. In several cases preceding Alappat, however, such as Iwahashi, Federal Circuit panels had stated that § 112 ¶ 6 applied equally to courts interpreting claims in infringement litigation and to the PTO during patent prosecution. The PTO's response, reflected in the Alappat decision, among others, was that a Federal Circuit panel decision could not overrule an en banc CCPA decision.

After this running skirmish had continued for some years, the Federal Circuit set Alappat and another case, In re Donaldson, 16 F.3d 1189 (Fed. Cir. 1994), for argument together en banc. In both cases, the applicants had not rebutted the PTO's interpretation of claims as covering essentially any means for performing recited functions. Thus, Alappat had a means for "normalizing" a certain parameter, which meant multiplying it by a power of 2 until it fell into a certain range. Alappat's specification described use of a barrel shifter to accomplish the multiplication, but the PTO interpreted the claim to cover any means for doing this. Another element of Alappat's claim was taking the absolute value of the difference between two parameters, and the specification described accomplishing this by using an arithmetic logic unit "configured" to perform this function. Again, the PTO interpreted the claim to cover any means for doing this. (Alappat agreed that the means used made no difference. The rasterizer could be an appropriately programmed microprocessor chip.)

The Federal Circuit handed down its Donaldson opinion earlier than Alappat. In Donaldson the Federal Circuit unanimously directed the PTO to read the specifications of patent applications and to determine in each case what the equivalent means were, just as courts must do in patent infringement litigation. The treatment of this issue is therefore cursory in Alappat, but the issue is important to the outcome.

The Federal Circuit's Alappat opinion did not satisfactorily resolve the question of the scope of such a claim in respect of a programmed general-purpose digital computer. Clearly, a programmed general-purpose digital computer was equivalent to and therefore within the scope of the aspect of the claim involving a "configured" arithmetic logic unit. But was a programmed general-purpose digital computer equivalent to the barrel shifter, too? Ask yourself, when you read the majority opinion and the dissent of Judge Archer, whether all of the elements of the claim involved in Alappat can be provided by a programmed general-purpose digital computer (or, equivalently, a programmed microprocessor chip). By the same token, would an accused infringer be liable to the patentee for using or selling a device with no barrel shifter and using no hardware but a programmed general-purpose digital computer (or microprocessor chip)?

In re Alappat
United States Court of Appeals for the Federal Circuit
33 F.3d 1526 (Fed. Cir. 1994)(en banc)

Rich, Circuit Judge.

Our conclusion is that the appealed decision should be reversed because the appealed claims are directed to a “machine” which is one of the categories named in 35 U.S.C. § 101, as the first panel of the board held.

A. Alappat's Invention

Alappat's invention relates generally to a means for creating a smooth waveform display in a digital oscilloscope. The screen of an oscilloscope is the front of a cathode-ray tube (CRT), which is like a TV picture tube, whose screen, when in operation, presents an array (or raster) of pixels arranged at intersections of vertical columns and horizontal rows, a pixel being a spot on the screen which may be illuminated by directing an electron beam to that spot, as in TV. Each column in the array represents a different time period, and each row represents a different magnitude.

Because a CRT screen 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. In addition, the presence of “noise” in an input signal can cause portions of the waveform to oscillate between contiguous pixel rows when the magnitude of the input signal lies between values represented by the elevations of the two rows. The appearance of these effects is known as aliasing.

To overcome these effects, Alappat's invention employs an anti-aliasing system wherein each vector making up the waveform is represented by modulating the illumination intensity of pixels having center points bounding the trajectory of the vector. The intensity at which each of the pixels is illuminated depends upon the distance of the center point of each pixel from the trajectory of the vector. Pixels lying squarely on the waveform trace receive maximum illumination, whereas pixels lying along an edge of the trace receive illumination decreasing in intensity proportional to the increase in the distance of the center point of the pixel from the vector trajectory. Employing this anti-aliasing technique eliminates any apparent discontinuity, jaggedness, or oscillation in the waveform, thus giving the visual appearance of a smooth continuous waveform. In short, and in lay terms, the invention is an improvement in an oscilloscope comparable to a TV having a clearer picture.

B. The Rejected Claims

Claim 15, the only independent claim in issue, reads:

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, comprising:

(a) means for determining the vertical distance between the endpoints of each of the vectors in the data list;

(b) means for determining the elevation of a row of pixels that is spanned by the vector;

(c) means for normalizing the vertical distance and elevation; and

(d) means for outputting illumination intensity data as a predetermined function of the normalized vertical distance and elevation.

C. The Examiner's Rejection and Board Reviews

The examiner's final rejection was under 35 U.S.C. § 101 “because the claimed invention is nonstatutory subject matter,” and the original three-member board panel reversed this rejection. That board panel held that, although claim 15 recites a mathematical algorithm, the claim as a whole is directed to a machine and thus to statutory subject matter named in § 101. In reaching this decision, the original panel construed the means clauses in claim 15 pursuant to 35 U.S.C. § 112, paragraph six (§ 112 ¶ 6), as corresponding to the respective structures disclosed in the specification of Alappat's application, and equivalents thereof.

In its reconsideration decision, the five-member majority of the expanded, eight-member board panel “modified” the decision of the original panel and affirmed the examiner's § 101 rejection. The majority held that the PTO need not apply § 112 ¶ 6 in rendering patentability determinations, characterizing this court's statements to the contrary in In re Iwahashi “as dicta,” and dismissing this court's discussion of § 112 ¶ 6 in Arrhythmia Research Technology, Inc. v. Corazonix Corp. on the basis that the rules of claim construction in infringement actions differ from the rules for claim interpretation during prosecution in the PTO. The majority stated that, during examination, the PTO gives means–plus–function clauses in claims their broadest interpretation and does not impute limitations from the specification into the claims. See Applicability of the Last Paragraph of 35 U.S.C. § 112 to Patentability Determinations Before the Patent and Trademark Office, 1134 O.G. 633 (1992); Notice Interpreting In Re Iwahashi, 1112 O.G. 16 (1990). Accordingly, the majority held that each of the means recited in claim 15 reads on any and every means for performing the particular function recited.

The board majority further held that, because claim 15 is written completely in “means for” language and because these means clauses are read broadly in the PTO to encompass each and every means for performing the recited functions, claim 15 amounts to nothing more than a process claim wherein each means clause represents only a step in that process. The majority stated that each of the steps in this postulated process claim recites a mathematical operation, which steps combine to form a “mathematical algorithm for computing pixel information,” and that, “when the claim is viewed without the steps of this mathematical algorithm, no other elements or steps are found.” The majority thus concluded that the claim was directed to nonstatutory subject matter.

In its analysis, the board majority further stated:

It is further significant that claim 15, as drafted, reads on a digital computer "means" to perform the various steps under program control. In such a case, it is proper to treat the claim as if drawn to a method. We will not presume that a stored program digital computer is not within the § 112 ¶ 6 range of equivalents of the structure disclosed in the specification. The disclosed ALU, ROM and shift registers are all common elements of stored program digital computers. Even if appellants were willing to admit that a stored program digital computer were not within the range of equivalents, § 112 ¶ 2 requires that this be clearly apparent from the claims based upon limitations recited in the claims.

The board majority also stated that dependent claims 16-19 were not before them for consideration because they had not been argued by Alappat and thus not addressed by the examiner or the original three-member board panel.

D. Analysis

(1) Section 112, Paragraph Six

As recently explained in In re Donaldson, 16 F.3d 1189, 1193, (Fed. Cir. 1994), the PTO is not exempt from following the statutory mandate of § 112 ¶ 6, which reads:

An element in a claim for a combination may be expressed as a means or step for performing a specified function without the recital of structure, material, or acts in support thereof, and such claim shall be construed to cover the corresponding structure, material, or acts described in the specification and equivalents thereof.

The board majority therefore erred as a matter of law in refusing to apply § 112 ¶ 6 in rendering its § 101 patentable subject matter determination.

Given Alappat's disclosure, it was error for the board majority to interpret each of the means clauses in claim 15 so broadly as to “read on any and every means for performing the functions” recited, as it said it was doing, and then to conclude that claim 15 is nothing more than a process claim wherein each means clause represents a step in that process. Contrary to suggestions by the Commissioner, this court's precedents do not support the board's view that the particular apparatus claims at issue in this case may be viewed as nothing more than process claims. The cases relied upon by the Commissioner differ from the instant case. In Abele, Pardo, and Walter, given the apparent lack of any supporting structure in the specification corresponding to the claimed “means” elements, the court reasonably concluded that the claims at issue were in effect nothing more than process claims in the guise of apparatus claims. This is clearly not the case now before us. We further note that Maucorps dealt with a business methodology for deciding how salesmen should best handle respective customers and Meyer involved a “system” for aiding a neurologist in diagnosing patients. Clearly, neither of the alleged “inventions” in those cases falls within any § 101 category.

When independent claim 15 is construed in accordance with § 112 ¶ 6, claim 15 reads as follows, the subject matter in brackets representing the structure which Alappat discloses in his specification as corresponding to the respective means language recited in the claims:

A rasterizer [a "machine"] 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, comprising:

(a) [an arithmetic logic circuit configured to perform an absolute value function, or an equivalent thereof] for determining the vertical distance between the endpoints of each of the vectors in the data list;

(b) [an arithmetic logic circuit configured to perform an absolute value function, or an equivalent thereof] for determining the elevation of a row of pixels that is spanned by the vector;

(c) [a pair of barrel shifters, or equivalents thereof] for normalizing the vertical distance and elevation; and

(d) [a read only memory (ROM) containing illumination intensity data, or an equivalent thereof] for outputting illumination intensity data as a predetermined function of the normalized vertical distance and elevation.

As is evident, claim 15 unquestionably recites a machine, or apparatus, made up of a combination of known electronic circuitry elements.

Despite suggestions by the Commissioner to the contrary, each of dependent claims 16-19 serves to further limit claim 15. Section 112 ¶ 6 requires that each of the means recited in independent claim 15 be construed to cover at least the structure disclosed in the specification corresponding to the “means.” Each of dependent claims 16-19 is in fact limited to one of the structures disclosed in the specification.

(2) Section 101

The reconsideration board majority affirmed the examiner's rejection of claims 15-19 on the basis that these claims are not directed to statutory subject matter as defined in § 101, which reads:

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.

Claim 15, properly construed, claims a machine, namely, 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,” which machine is made up of, at the very least, the specific structures disclosed in Alappat's specification corresponding to the means-plus-function elements (a)-(d) recited in the claim. According to Alappat, the claimed rasterizer performs the same overall function as prior art rasterizers, but does so in a different way, which is represented by the combination of four elements claimed in means-plus-function terminology. Because claim 15 is directed to a “machine,” which is one of the four categories of patentable subject matter enumerated in § 101, claim 15 appears on its face to be directed to § 101 subject matter.

This does not quite end the analysis, however, because the board majority argues that the claimed subject matter falls within a judicially created exception to § 101 which the majority refers to as the “mathematical algorithm” exception. Although the PTO has failed to support the premise that the “mathematical algorithm” exception applies to true apparatus claims, we recognize that our own precedent suggests that this may be the case. See In re Johnson, 589 F.2d 1070, 1077 (CCPA 1978) (“Benson applies equally whether an invention is claimed as an apparatus or process, because the form of the claim is often an exercise in drafting”). Even if the mathematical subject matter exception to § 101 does apply to true apparatus claims, the claimed subject matter in this case does not fall within that exception.


The plain and unambiguous meaning of § 101 is that any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may be patented if it meets the requirements for patentability set forth in Title 35, such as those found in §§ 102, 103, and 112. The use of the expansive term “any” in § 101 represents Congress's intent not to place any restrictions on the subject matter for which a patent may be obtained beyond those specifically recited in § 101 and the other parts of Title 35. Indeed, the Supreme Court has acknowledged that Congress intended § 101 to extend to “anything under the sun that is made by man.” Diamond v. Chakrabarty, 447 U.S. 303, 309 (1980), quoting S. Rep. No. 1979, 82d Cong., 2d Sess. 5 (1952); H.R. Rep. No. 1923, 82d Cong., 2d Sess., 6 (1952). Thus, it is improper to read into § 101 limitations as to the subject matter that may be patented where the legislative history does not indicate that Congress clearly intended such limitations. See Chakrabarty, 447 U.S. at 308, (“We have also cautioned that courts ‘should not read into the patent laws limitations and conditions which the legislature has not expressed’”).

Despite the apparent sweep of § 101, the Supreme Court has held that certain categories of subject matter are not entitled to patent protection. In Diamond v. Diehr (1981), its most recent case addressing § 101, the Supreme Court explained that there are three categories of subject matter for which one may not obtain patent protection, namely “laws of nature, natural phenomena, and abstract ideas.” Of relevance to this case, the Supreme Court also has held that certain mathematical subject matter is not, standing alone, entitled to patent protection. A close analysis of Diehr, Flook, and Benson reveals that the Supreme Court never intended to create an overly broad, fourth category of subject matter excluded from § 101. Rather, at the core of the Court's analysis in each of these cases lies an attempt by the Court to explain a rather straightforward concept, namely, that certain types of mathematical subject matter, standing alone, represent nothing more than abstract ideas until reduced to some type of practical application, and thus that subject matter is not, in and of itself, entitled to patent protection.

Diehr also demands that the focus in any statutory subject matter analysis be on the claim as a whole. Indeed, the Supreme Court stated in Diehr:

[W]hen a claim containing a mathematical formula [, mathematical equation, mathematical algorithm, or the like,] implements or applies that formula [, equation, algorithm, or the like,] in a structure or process which, when considered as a whole, is performing a function which the patent laws were designed to protect (e.g., transforming or reducing an article to a different state or thing), then the claim satisfies the requirements of § 101.

It is thus not necessary to determine whether a claim contains, as merely a part of the whole, any mathematical subject matter which standing alone would not be entitled to patent protection. Indeed, because the dispositive inquiry is whether the claim as a whole is directed to statutory subject matter, it is irrelevant that a claim may contain, as part of the whole, subject matter which would not be patentable by itself. “A claim drawn to subject matter otherwise statutory does not become nonstatutory simply because it uses a mathematical formula, [mathematical equation, mathematical algorithm,] computer program or digital computer.” Diehr.


Given the foregoing, the proper inquiry in dealing with the so called mathematical subject matter exception to § 101 alleged herein is to see whether the claimed subject matter as a whole is a disembodied mathematical concept, whether categorized as a mathematical formula, mathematical equation, mathematical algorithm, or the like, which in essence represents nothing more than a “law of nature,” “natural phenomenon,” or “abstract idea.” If so, Diehr precludes the patenting of that subject matter. That is not the case here.

Although many, or arguably even all, of the means elements recited in claim 15 represent circuitry elements that perform mathematical calculations, which is essentially true of all digital electrical circuits, the claimed invention as a whole is directed to a combination of interrelated elements which combine to form a machine for converting discrete waveform data samples into anti–aliased pixel illumination intensity data to be displayed on a display means. This is not a disembodied mathematical concept which may be characterized as an “abstract idea,” but rather a specific machine to produce a useful, concrete, and tangible result.

The fact that the four claimed means elements function to transform one set of data to another through what may be viewed as a series of mathematical calculations does not alone justify a holding that the claim as a whole is directed to nonstatutory subject matter. See In re Iwahashi. (The board majority's attempts to distinguish Iwahashi on the basis that the claim at issue in that case recited a ROM are unavailing. The Iwahashi court clearly did not find patentable subject matter merely because a ROM was recited in the claim at issue; rather the court held that the claim as whole, directed to the combination of the claimed means elements, including the claimed ROM as one element, was directed to statutory subject matter. It was not the ROM alone that carried the day.)

Indeed, claim 15 as written is not “so abstract and sweeping” that it would “wholly pre-empt” the use of any apparatus employing the combination of mathematical calculations recited therein. See Benson. Rather, claim 15 is limited to the use of a particularly claimed combination of elements performing the particularly claimed combination of calculations to transform, i.e., rasterize, digitized waveforms (data) into anti-aliased, pixel illumination data to produce a smooth waveform.

Furthermore, the claim preamble's recitation that the subject matter for which Alappat seeks patent protection is a rasterizer for creating a smooth waveform is not a mere field-of-use label having no significance. Indeed, the preamble specifically recites that the claimed rasterizer converts waveform data into output illumination data for a display, and the means elements recited in the body of the claim make reference not only to the inputted waveform data recited in the preamble but also to the output illumination data also recited in the preamble. Claim 15 thus defines a combination of elements constituting a machine for producing an anti-aliased waveform.

The reconsideration board majority also erred in its reasoning that claim 15 is unpatentable merely because it “reads on a general purpose digital computer `means' to perform the various steps under program control.” The board majority stated that it would “not presume that a stored program digital computer is not within the § 112 ¶ 6 range of equivalents of the structure disclosed in the specification.” Alappat admits that claim 15 would read on a general purpose computer programmed to carry out the claimed invention, but argues that this alone also does not justify holding claim 15 unpatentable as directed to nonstatutory subject matter. We agree. 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.

Under the board majority's reasoning, a programmed general purpose computer could never be viewed as patentable subject matter under § 101. This reasoning is without basis in the law. The Supreme Court has never held that a programmed computer may never be entitled to patent protection. Indeed, the Benson Court specifically stated that its decision therein did not preclude “a patent for any program servicing a computer.” Consequently, a computer operating pursuant to software may represent patentable subject matter, provided, of course, that the claimed subject matter meets all of the other requirements of Title 35. In any case, a computer, like a rasterizer, is apparatus not mathematics.


For the foregoing reasons, the appealed decision of the board affirming the examiner's rejection is reversed.

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