A new viewpoint on two-level logic minimization

Coudert, Olivier; Madre, Jean Christophe; Fraisse, Henri

doi:10.1145/157485.165071

Cited by 40 publications

(15 citation statements)

References 11 publications

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“…Previous work showed how to compute implicitly the primes of a Boolean function and how to reduce implicitly the unate table of the Quine-McCluskey procedure to its cyclic core ( [4,8]). Exact solutions to problems too hard for ESPRESSO were found.…”

Section: Introductionmentioning

confidence: 99%

A fully implicit algorithm for exact state minimization

Kam

Villa

Brayton

et al. 1994

Proceedings of the 31st Annual Conference on Design Automation Conference - DAC '94

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State minimization of incompletely specified machines is an important step of FSM synthesis. An exact algorithm consists of generation of prime compatibles and solution of a binate covering problem. This paper presents an implicit algorithm for exact state minimization of FSM's. We describe how to do implicit prime computation and implicit binate covering. We show that we can handle sets of compatibles and prime compatibles of cardinality up to 2 1500 . We present the first published algorithm for fully implicit exact binate covering. We show that we can reduce and solve binate tables with up to 10 6 rows and columns. The entire branch-and-bound procedure is carried on implicitly. We indicate also where such examples arise in practice.

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Section: Introductionmentioning

confidence: 99%

A fully implicit algorithm for exact state minimization

Kam

Villa

Brayton

et al. 1994

Proceedings of the 31st Annual Conference on Design Automation Conference - DAC '94

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show abstract

“…This method enables us to implicitly manipulate a huge number of combinations, which have never been practical before. Recently, new two-level logic minimization methods have been developed based on implicit set representation [4]. These techniques are also used to solve general covering problems [5].…”

Section: Introductionmentioning

confidence: 99%

Calculation of unate cube set algebra using zero-suppressed BDDs

Minato

1994

Proceedings of the 31st Annual Conference on Design Automation Conference - DAC '94

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“…Since our new representation method maintains uniqueness, we can immediately check the equivalence between two polynomials after generating 0-sup-BDDs. 4 Algorithms for Arithmetic Operations Polynomials can be manipulated by arithmetic operations, such as addition, subtraction, and multiplication. Based on this knowledge, we rst generate 0-sup-BDDs for trivial formulas which are single variables or constants, and then apply those arithmetic operations to construct more complicated polynomials.…”

Section: Representation Of Coecientsmentioning

confidence: 99%

“…This method enables us to manipulate a huge number of combinations implicitly, which has never been practical before. Based on implicit set representation, new two-level logic minimization methods have been developed [4][5]. These techniques are also used to solve a kind of covering problem [6].…”

Section: Introductionmentioning

confidence: 99%

Implicit manipulation of polynomials using zero-suppressed BDDs

Minato¹

Proceedings the European Design and Test Conference. ED&TC 1995

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We present a new technique that broadens the scope of BDD application. It involves manipulating arithmetic polynomials containing higher-degree variables and integer coecients. Our method c an represent large-scale polynomials compactly and uniquely, and it greatly accelerates computation of polynomials. As the polynomial calculus is a basic model in mathematics, our method is very useful in various areas, including formal verication techniques for VLSI design. As our understanding of BDDs has deepened, the range of applications has broadened. Besides Boolean functions, we are often faced with manipulating sets of combinations in many LSI design problems. By mapping a set of combinations into the Boolean space, it can be represented as a characteristic function using a BDD. This method enables us to manipulate a huge number of combinations implicitly, which has never been practical before. Based on implicit set representation, new two-level logic minimization methods have been developed [4][5]. These techniques are also used to solve a kind of covering problem [6].A zero-suppressed BDD (0-sup-BDD) [7] is a new type of BDD adapted the implicit set representation. It can manipulate sets of combinations more eciently than conventional BDDs, especially when dealing with sparse combinations. We have recently studied cube set algebra for manipulating sets of combinations [8], and proposed ecient algorithms for computing cube set operations based on 0-sup-BDDs. This technique is useful for many practical activities related to LSI design, including multi-level logic synthesis [9] and fault simulation.In this paper, we present a new technique that broadens the scope of BDD application. It involves manipulating arithmetic polynomial formulas containing higher-degree variables and integer coecients. Using 0-sup-BDDs, we can represent large-scale polynomials compactly and uniquely. W e developed ecient algorithms for polynomial calculus based on 0-sup-BDD operations. In this method, we can atten arithmetic expressions into canonical forms of polynomials with millions of terms, which have never been represented before. Constructing canonical forms of polynomials immediately leads to equivalence checking of arithmetic expressions. Since polynomial calculus is a basic model in mathematics, our method is expected to be useful for various problems.In this paper, we rst explain 0-sup-BDDs and their operations. We then present a method for representing polynomials with 0-sup-BDDs, and discuss the operation algorithms for polynomial calculus. Finally, w e show implementation of our method and the application for LSI CAD. Eliminate all nodes with the 1-edge pointing to the 0-terminal node. Then connect the edge to the other subgraph directly (Fig. 1).Share all equivalent sub-graphs in the same manner as with conventional BDDs.Notice that, contrary to conventional BDDs, we do not eliminate nodes whose two edges both point to the same node. This reduction rule is asymmetric for the two edges because the nodes remain when their...

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A new viewpoint on two-level logic minimization

Cited by 40 publications

References 11 publications

A fully implicit algorithm for exact state minimization

A fully implicit algorithm for exact state minimization

Calculation of unate cube set algebra using zero-suppressed BDDs

Implicit manipulation of polynomials using zero-suppressed BDDs

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