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A New Method to Compute Prime and Essential Prime Implicants of Boolean Functions
 In MIT Conference on Advanced Research in VLSI and Parallel Systems. IEEE Computer Society, 1992. 118 [CM93a] [CM93b] [Cod99
, 1993
"... Computing the prime implicants and the essential prime implicants of Boolean functions is a problem that has applications in several areas of computer science, for instance it is critical in circuit synthesis and optimization, but also in automated reasoning. In this paper we propose a new method t ..."
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Cited by 15 (4 self)
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Computing the prime implicants and the essential prime implicants of Boolean functions is a problem that has applications in several areas of computer science, for instance it is critical in circuit synthesis and optimization, but also in automated reasoning. In this paper we propose a new method to compute implicitly the sets of prime implicants and of essential prime implicants of incompletely specified Boolean functions. This method allows us to handle functions that have sets of prime implicants and of essential prime implicants several orders of magnitude larger than those of the functions that could be handled by existing methods. The key idea that makes these computations possible is to manipulate sets of prime and of essential prime implicants denoted by their metaproducts, which are characteristic functions. These functions are represented with binary decision diagrams that are a very compact canonical graph representation of Boolean functions and that support very efficiently all the operations needed here. 1
Multiplevalued logic minimization for PLA synthesis
, 1986
"... Multiplevalued logic minimization is an important technique for reducing the area required by a Programmable Logic Array (PLA). This report describes both heuristic and exact algorithms for solving the multiplevalued logic minimization probleb. These algorithms have been implemented in a C program ..."
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Cited by 15 (0 self)
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Multiplevalued logic minimization is an important technique for reducing the area required by a Programmable Logic Array (PLA). This report describes both heuristic and exact algorithms for solving the multiplevalued logic minimization probleb. These algorithms have been implemented in a C program called EspressoMV. I
AOXMINMV: A Heuristic Algorithm for ANDORXOR Minimization
 Proc. 4th International Workshop on the Applications of the ReedMuller Expansion in Circuit Design
, 1999
"... Threelevel logic is shown to have a potential for reduction of the area over twolevel implementations, as well as for a gain in speed over multilevel implementations. In this paper we present an heuristic algorithm, AOXMINMV, targeting a threelevel logic expression which is an XOR of two sumof ..."
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Cited by 12 (4 self)
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Threelevel logic is shown to have a potential for reduction of the area over twolevel implementations, as well as for a gain in speed over multilevel implementations. In this paper we present an heuristic algorithm, AOXMINMV, targeting a threelevel logic expression which is an XOR of two sumofproducts. For some practical functions, such an ANDORXOR expression may have up to 27 times less productterms compared to the classical sumofproducts form. Several algorithms for finding minimal ANDORXOR expressions were presented, but they all are timeconsuming for large functions. The algorithm presented here solves this problem by (1) introducing an estimation metric, checking whether the input function is likely to have a compact ANDORXOR expression; (2) employing a new strategy for decomposing the input function into two sumofproducts; (3) treating the output part of a multipleoutput function as a single multiplevalued variable. The experimental results show that these modification yield a faster and more efficient algorithm. Furthermore, it gives a solution to a more general problem of minimization of multiplevalued input binaryvalued output logic functions. 1
Compact SOP Representations for MultipleOutput Functions  An Encoding Method using MultipleValued Logic 
, 2001
"... This paper shows a method to represent a multipleoutput function: Encoded characteristic function for nonzero outputs (ECFN). The ECFN uses (n + u) binary variables to represent an ninput moutput function, where u = dlog 2 me. The size of the sumofproducts expressions (SOPs) depends on the enc ..."
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Cited by 9 (8 self)
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This paper shows a method to represent a multipleoutput function: Encoded characteristic function for nonzero outputs (ECFN). The ECFN uses (n + u) binary variables to represent an ninput moutput function, where u = dlog 2 me. The size of the sumofproducts expressions (SOPs) depends on the encoding method of the outputs. For some class of functions, the optimal encoding produces SOPs with O(n) products, while the worst encoding produces SOPs with O(2 n ) products. We formulate encoding problem and show a heuristic optimization method. Experimental results using standard benchmark functions show the usefulness of the method. Index term: Multipleoutput function, encoding problem, multiplevalued logic, TDM, SOP, characteristic function. 1.
Implicit Prime Cover Computation: An Overview
, 1993
"... A set of products is a prime cover of a Boolean function f if it is made of prime implicants of f , and if the sum of its products covers f . Finding a prime cover, an irredundant prime cover, or a minimal prime cover of a function f is a problem that arises in several fields of computer science, f ..."
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Cited by 9 (0 self)
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A set of products is a prime cover of a Boolean function f if it is made of prime implicants of f , and if the sum of its products covers f . Finding a prime cover, an irredundant prime cover, or a minimal prime cover of a function f is a problem that arises in several fields of computer science, for instance in logic synthesis, automated reasoning, realiability analysis, and some optimization problems. This paper shows how the three prime cover computation problems mentioned above can be efficiently solved using implicit manipulations of sets of products. 1 Introduction Computing a prime cover, an irredundant prime cover, or a minimal prime cover of a Boolean function has several applications in computer science. In logic synthesis, an irredundant prime cover, or better, a minimal prime cover, provides the user with an efficient 2level logic implementation of a single or multi output Boolean function [2, 24, 14]. In reliability analysis, prime covers are a way for either exhaustive...
Fast Heuristic and Exact Algorithms for TwoLevel HazardFree Logic Minimization
, 1998
"... None of the available minimizers for twolevel hazardfree logic minimization can synthesize very large circuits. This limitation has forced researchers to resort to manual and automated circuit partitioning techniques. This paper ..."
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None of the available minimizers for twolevel hazardfree logic minimization can synthesize very large circuits. This limitation has forced researchers to resort to manual and automated circuit partitioning techniques. This paper
Worst and best irredundant sumofproducts expressions
 IEEE Trans. On Comp
, 2001
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Asynchronous Control Circuits
, 2002
"... 2002 cfl2002 Michael Theobald All Rights Reserved ..."
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Implicit and Incremental Computation of Primes and Essential Primes of Boolean functions
 In Proceedings of the 29th ACM/IEEE Design Automation Conference
, 1991
"... Recently introduced implicit set manipulation techniques have made it possible to formally verify finite state machines with state graphs too large to be built. This paper shows that these techniques can also be used with success to compute and manipulate implicitly extremely large sets of prime and ..."
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Recently introduced implicit set manipulation techniques have made it possible to formally verify finite state machines with state graphs too large to be built. This paper shows that these techniques can also be used with success to compute and manipulate implicitly extremely large sets of prime and of essential prime implicants of incompletely specified Boolean functions. These sets are denoted by metaproducts that are represented with binary decision diagrams. This paper describes two procedures. One is based on the standard BDD operators, and the other, more efficient, takes advantage of the structural properties of BDDs and of metaproducts to handle a larger class of functions than the former one. 1 Introduction We have recently introduced a technique [ 4 ] for verifying finite state machines that can deal with machines with state graphs too large to be built. The key concepts that make this verification possible are to denote subsets of f0; 1g @ with their characteristic func...
New Qualitative Analysis Strategies in Metaprime
"... This paper proposes original algorithms, now integrated in Metaprime, to generate efficiently prime covers, irredundant prime covers, and minimal prime covers of noncoherent fault trees. Experiments show that these algorithms are robust and provide reliability engineers with efficient strategies for ..."
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This paper proposes original algorithms, now integrated in Metaprime, to generate efficiently prime covers, irredundant prime covers, and minimal prime covers of noncoherent fault trees. Experiments show that these algorithms are robust and provide reliability engineers with efficient strategies for the analysis of complex noncoherent multiplefault trees.