A Rule-Based System for Optimizing Combinational Logic

Geus, Aart J. de; Cohen, William A.

doi:10.1109/mdt.1985.294719

Cited by 77 publications

(9 citation statements)

References 5 publications

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“…The first multi-level synthesis system was the ffiM Logic Synthesis System [6], [7]. Other systems are: Yorktown Silicon Compiler [8], SOCRATES [9], and MIS [10].…”

Section: Kronecker and Pseudo Kronecker Product Of Twomentioning

confidence: 99%

“…In addition, rule based systems [7], [9] have been found to be effective in the design of large systems.…”

Section: Kronecker and Pseudo Kronecker Product Of Twomentioning

confidence: 99%

“…9 The sum of all spectral coefficients of the S spectrum for any completely specified two-dimensional map is ± 2 n • IV.IO The sum of all spectral coefficients of the S spectrum for any incompletely specified two-dimensional map is not ± 2 n • IV.II The maximal (minimal) value of any individual spectral coefficient of spectrum S is ± 2 n • This happens when the binary function represented in a given twodimensional map is equal to either a standard trivial function Uj (sign +) or to its complement (sign -). In either case, all the remaining spectral coefficients have zero values because of the orthogonality of the transform matrix T.…”

Section: Iva Basic Properties Of Hadamard-walsh Spectra S and R For Tmentioning

confidence: 99%

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Spectral Methods for Boolean and Multiple-Valued Input Logic Functions

Falkowski¹

2000

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Spectral techniques in digital logic design have been known for more than thirty years. They have been used for Boolean function classification, disjoint decomposition, parallel and serial linear decomposition, spectral translation synthesis (extraction of 2 linear pre-and post-filters), multiplexer synthesis, prime implicant extraction by spectral summation, threshold logic synthesis, estimation of logic complexity, testing, and state assignment.This dissertation resolves many important issues concerning the efficient application of spectral methods used in the computer-aided design of digital circuits. The main obstacles in these applications were, up to now, memory requirements for computer systems and lack of the possibility of calculating spectra direcdy from Boolean equations.By using the algorithms presented here these obstacles have been overcome. Moreover, the methods presented in this dissertation can be regarded as representatives of a whole family of methods and the approach presented can 1Y: easily adapted to other orthogonal transforms used in digital logic design. Algorithms are shown for Adding, Arithmetic, and Reed-Muller transforms. However, the main focus of this dissertation is on the efficient computer calculation of Rademacher-Walsh spectra of Boolean functions, since this particular ordering of Walsh transforms is most frequendy used in digital logic design.A theory has been developed to calculate the Rademacher-Walsh transform from a cube array specification of incompletely specified Boolean functions. The importance of representing Boolean functions as arrays of disjoint ON-and DC-cubes has been pointed out, and an efficient new algorithm to generate disjoint cubes from non-disjoint ones has been designed. The transform algorithm makes use of the properties of an array of disjoint cubes and allows the determination of the spectral coefficients in an independent way. By such an approach each spectral coefficient can be calculated separately or all the coefficients can be calculated in parallel. These advantages are absent in the existing methods. The possibility of calculating only some coefficients is very important since there are many spectral methods in digital logic design for which the values of only a few selected coefficients are needed.Most of the current methods used in the spectral domain deal only with completely specified Boolean functions. On the other hand, all of the algorithms introduced here are valid, not only for completely specified Boolean functions, but for functions with don't cares. Don't care minterms are simply represented in the form of disjoint cubes.The links between spectral and classical methods used for designing digital cir- A new algorithm is shown that converts the disjoint cube representation of Boolean functions into fixed-polarity Generalized Reed-Muller Expansions (GRME).Since the known fast algorithm that generates the GR..\1E, based on the factorization of 4 the Reed-Muller transform matrix, always starts from the truth table (mintenns) of a Boole...

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“…The first multi-level synthesis system was the ffiM Logic Synthesis System [6], [7]. Other systems are: Yorktown Silicon Compiler [8], SOCRATES [9], and MIS [10].…”

Section: Kronecker and Pseudo Kronecker Product Of Twomentioning

confidence: 99%

“…In addition, rule based systems [7], [9] have been found to be effective in the design of large systems.…”

Section: Kronecker and Pseudo Kronecker Product Of Twomentioning

confidence: 99%

Section: Iva Basic Properties Of Hadamard-walsh Spectra S and R For Tmentioning

confidence: 99%

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Spectral Methods for Boolean and Multiple-Valued Input Logic Functions

Falkowski¹

2000

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“…Decisions concerning which rules to apply are made by a heuristic search algorithm based on cost estimates of design area and speed. The concept of using rule-based graph transformation optimizations has been used in logic synthesis [23]- [24], bit-serial DSP synthesis [25], and general purpose DSP synthesis [26].…”

Section: Filter Architecture Transformationsmentioning

confidence: 99%

Strategies for design automation of high speed digital filters

Duncan¹,

Kindsfater²,

Liu³

et al. 1995

Journal of VLSI Signal Processing

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Abstract. Optimization techniques for DSP circuits are described based on the design experience with a number of high-speed digital filter chips. These designs show that efficient high speed digital filter designs can be achieved using several optimizations at the architecture, circuit, and layout level. The problems of automating these optimizations in a general DSP synthesis environment are discussed, and possible CAD solutions are proposed.

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“…This practice helps chip designer save on number of transistors, chip area, and helps reduce logic delays and power requirements. It is no surprise therefore that many efforts have been made to develop fully functional, interactive programs for the industry even in the 80s, such as MIS [1] and SOCRATES [2] and the field has only grown ever since with the advent of many companies competing in this domain. In this section, we discuss various logic optimization methods.…”

Section: Introduction and Literature Overviewmentioning

confidence: 99%

A Novel Graphical Technique for Combinational Logic Representation and Optimization

Pandit

Schuller

2017

Complexity

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We present a new technique for defining, analysing, and simplifying digital functions, through hand-calculations, easily demonstrable therefore in the classrooms. It can be extended to represent discrete systems beyond the Boolean logic. The method is graphical in nature and provides complete "implementation-free" description of the logical functions, similar to binary decision diagrams (BDDs) and Karnaugh-maps (K-maps). Transforming a function into the proposed representations (also the inverse) is a very intuitive process, easy enough that a person can hand-calculate these transformations. The algorithmic nature allows for its computing-based implementations. Because the proposed technique effectively transforms a function into a scatter plot, it is possible to represent multiple functions simultaneously. Usability of the method, therefore, is constrained neither by the number of inputs of the function nor by its outputs in theory. This, being a new paradigm, offers a lot of scope for further research. Here, we put forward a few of the strategies invented so far for using the proposed representation for simplifying the logic functions. Finally, we present extensions of the method: one that extends its applicability to multivalued discrete systems beyond Boolean functions and the other that represents the variants in terms of the coordinate system in use.

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A Rule-Based System for Optimizing Combinational Logic

Cited by 77 publications

References 5 publications

Spectral Methods for Boolean and Multiple-Valued Input Logic Functions

Spectral Methods for Boolean and Multiple-Valued Input Logic Functions

Strategies for design automation of high speed digital filters

A Novel Graphical Technique for Combinational Logic Representation and Optimization

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