A new decomposition method for multilevel circuit design

Bochmann, D.; Dresig, F.; Steinbach, Bernd

doi:10.1109/edac.1991.206428

Cited by 28 publications

(21 citation statements)

References 3 publications

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“…A seed variable partition makes (4) unsatisfiable where partition X A and X B each take at least one variable. This scheme also applies to the proposed new model (6). It can be shown that the existence of non-trivial OR bi-decomposition can be checked with at most C 2 n = (n − 1) + · · · + 1 = n(n−1) 2 different seed partitions [11].…”

Section: Plain Mus-based Bi-decompositionmentioning

confidence: 99%

“…The Craig Interpolation serves to derive f A and f B in OR bi-decomposition [11]. Formula (5) is suggested to replace the use of formula (6).…”

Section: Example 2 (Plain-mus Based or Bi-decomposition)mentioning

confidence: 99%

“…Bi-decomposition [6][7][8][9][10][11][12] is a special form (with m=2) of Boolean function decomposition, and it is arguably the most widely used form of Boolean function decomposition. It consists of decomposing Boolean function f (X) into the form of f (X) = h(f A (X A , X C ), f B (X B , X C )), under variable partition X = {X A |X B |X C }.…”

Section: Introductionmentioning

confidence: 99%

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Improvements to Satisfiability-Based Boolean Function Bi-Decomposition

Chen

Marques-Silva

2012

VLSI-SoC: Advanced Research for Systems on Chip

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Abstract. Boolean function bi-decomposition is pervasive in logic synthesis. Bi-decomposition entails the decomposition of a Boolean function into two other functions connected by a simple two-input gate. Existing solutions are based on Binary Decision Diagrams (BDDs) and, more recently, on Boolean Satisfiability (SAT). Recent work exploited the identification of Minimally Unsatisfiable Subformulas (MUSes) for computing the sets of variables to use in Boolean function bi-decomposition. This paper develops new techniques for improving the use of MUSes in function bi-decomposition. The first technique exploits structural properties of the function being decomposed, whereas the second technique exploits group-oriented MUSes. Experimental results obtained on representative benchmarks from logic synthesis demonstrate significant improvements both in performance and in the quality of decompositions.

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Section: Plain Mus-based Bi-decompositionmentioning

confidence: 99%

“…The Craig Interpolation serves to derive f A and f B in OR bi-decomposition [11]. Formula (5) is suggested to replace the use of formula (6).…”

Section: Example 2 (Plain-mus Based or Bi-decomposition)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Improvements to Satisfiability-Based Boolean Function Bi-Decomposition

Chen

Marques-Silva

2012

VLSI-SoC: Advanced Research for Systems on Chip

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“…The bi-decomposition [1,3] ensures the simplification in each decomposition step because it restricts to subfunctions of the decomposition which depend on less variables than the given function. The known bi-decomposition approach even detects existing subfunctions which depend on the smallest number of variables.…”

Section: Introductionmentioning

confidence: 99%

Simpler Functions for Decompositions

Steinbach

2015

Progress in Systems Engineering

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Abstract. This paper deals with the synthesis of combinatorial circuits by decomposition. The main idea of each decomposition method is that a complicate Boolean function is split into two or more simpler subfunctions. In this way the trivial function f = xi can be achieved after a certain number of decomposition steps and terminates the decomposition procedure. The two subfunctions of a bi-decomposition are simpler than the given function because the number of independent variables is reduced at least by one. However, for completeness, the weak bi-decomposition is needed, in which only one of the two subfunctions depends on less variables than the given function. The main aim of this paper is to answer the question whether further subfunctions for a bi-decomposition exist which depend on the same number of variables as the given function to decompose, but are simpler regarding a certain measure and allow us to determine simple circuit structures.

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“…Logic decomposition is a logic transformation that has been extensively used in multi-level minimization [1][2][3][4]. Mostly, this transformation has been used aiming at reducing the area of Boolean networks, since common factors from different functions can be shared during the decomposition.…”

Section: Introductionmentioning

confidence: 99%

Timing-driven N-way decomposition

Bañeres

Cortadella

Kishinevsky

2009

Proceedings of the 19th ACM Great Lakes Symposium on VLSI

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Logic decomposition has been extensively used to optimize the worst-case delay and the area in the technology independent phase. Bi-decomposition is one of the state-of-art techniques to reduce the depth of the netlist due to the affordable computational cost. We present a novel n-way decomposition technique that improves bi-decomposition. The problem of decomposition is formulated as a Boolean relation which captures a larger set of possible solutions compared to bi-decomposition. The solution obtained from the Boolean relation improves the delay with near-zero cost in area. As it is shown on the experimental results, a considerable improvement is achieved on large netlists and even larger depending on which technology mapper is used.

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A new decomposition method for multilevel circuit design

Cited by 28 publications

References 3 publications

Improvements to Satisfiability-Based Boolean Function Bi-Decomposition

Improvements to Satisfiability-Based Boolean Function Bi-Decomposition

Simpler Functions for Decompositions

Timing-driven N-way decomposition

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