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Mini: A heuristic approach for logic minimization
 IBM Journal of Research and Development
, 1974
"... Abstract: MINI is a heuristic logic minimization technique for manyvariable problems. It accepts as input a Boolean logic specification expressed as an inputoutput table, thus avoiding a long list of minterms. It seeks a minimal implicant solution, without generating all prime implicants, which ca ..."
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Cited by 51 (0 self)
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Abstract: MINI is a heuristic logic minimization technique for manyvariable problems. It accepts as input a Boolean logic specification expressed as an inputoutput table, thus avoiding a long list of minterms. It seeks a minimal implicant solution, without generating all prime implicants, which can be converted to prime implicants if desired. New and effective subprocesses, such as expanding, reshaping, and removing redundancy from cubes, are iterated until there is no further reduction in the solution. The process is general in that it can minimize both conventional logic and logic functions of multivalued variables.
A Continuous Approach to Inductive Inference
 Mathematical Programming
, 1992
"... In this paper we describe an interior point mathematical programming approach to inductive inference. We list several versions of this problem and study in detail the formulation based on hidden Boolean logic. We consider the problem of identifying a hidden Boolean function F : f0; 1g n ! f0; 1g ..."
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Cited by 38 (2 self)
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In this paper we describe an interior point mathematical programming approach to inductive inference. We list several versions of this problem and study in detail the formulation based on hidden Boolean logic. We consider the problem of identifying a hidden Boolean function F : f0; 1g n ! f0; 1g using outputs obtained by applying a limited number of random inputs to the hidden function. Given this inputoutput sample, we give a method to synthesize a Boolean function that describes the sample. We pose the Boolean Function Synthesis Problem as a particular type of Satisfiability Problem. The Satisfiability Problem is translated into an integer programming feasibility problem, that is solved with an interior point algorithm for integer programming. A similar integer programming implementation has been used in a previous study to solve randomly generated instances of the Satisfiability Problem. In this paper we introduce a new variant of this algorithm, where the Riemannian metric used...
CirCUs: A hybrid satisfiability solver
 In International Conference on Theory and Applications of Satisfiability Testing (SAT 2004
, 2004
"... Abstract. CirCUs is a satisfiability solver that works on a combination of an AndInverterGraph (AIG), Conjunctive Normal Form (CNF) clauses, and Binary Decision Diagrams (BDDs). We show how BDDs are used by CirCUs to help in the solution of SAT instances given in CNF. Specifically, the clauses are ..."
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Cited by 12 (3 self)
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Abstract. CirCUs is a satisfiability solver that works on a combination of an AndInverterGraph (AIG), Conjunctive Normal Form (CNF) clauses, and Binary Decision Diagrams (BDDs). We show how BDDs are used by CirCUs to help in the solution of SAT instances given in CNF. Specifically, the clauses are sorted by solving a hypergraph linear arrangement problem. Then they are clustered by an algorithm that strives to avoid explosion in the resulting BDD sizes. If clustering results in a single diagram, the SAT instance is solved directly. Otherwise, search for a satisfying assignment is conducted on the original clauses, enhanced with information extracted from the BDDs. We also describe a new decision variable selection heuristic that is based on recognizing that the variables involved in a conflict clause are often best treated as a related group. We present experimental results that demonstrate CirCUs’s efficiency especially for mediumsize SAT instances that are hard to solve by traditional solvers based on DPLL. 1
An introduction to zerosuppressed binary decision diagrams
 in ‘Proceedings of the 12th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning
, 2001
"... ..."
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...
Worst and Best Irredundant SumofProducts Expressions
 IEEE Trans. Comp
, 2001
"... In an irredundant sumofproducts expression (ISOP), each product is a prime implicant (PI), and no product can be deleted without changing the function. Among the ISOPs for some function f,aworst ISOP (WSOP) is an ISOP with the largest numberofPIs,anda minimum ISOP (MSOP) is one with the smalles ..."
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Cited by 5 (0 self)
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In an irredundant sumofproducts expression (ISOP), each product is a prime implicant (PI), and no product can be deleted without changing the function. Among the ISOPs for some function f,aworst ISOP (WSOP) is an ISOP with the largest numberofPIs,anda minimum ISOP (MSOP) is one with the smallest number. We show a class of functions for which the MinatoMorreale ISOP algorithm produces WSOPs. Since the ratio of the size of the WSOP to the size of the MSOP is arbitrarily large when n, the number of variables, is unbounded, the MinatoMorreale algorithm can produce results that are very far from minimum. We present a class of multipleoutput functions whose WSOP size is also much larger than its MSOP size. For a set of benchmark functions, we show the distribution of ISOPs to the number of PIs. Among this set are functions where the MSOPs have almost as many PIs as do the WSOPs. These functions are known to be easy to minimize. Also, there are benchmark functions where the fraction of ISOPs that are MSOPs is small and MSOPs havemany fewer PIs than the WSOPs. Such functions are known to be hard to minimize. For one class of functions, we show that the fraction of ISOPs that are WSOPs approaches0asn approaches infinity, suggesting that such functions are hard to minimize. Index terms: Logic minimization, complete sumofproducts expressions, irredundant sumof products, multipleoutput functions, heuristic minimization, prime implicants, symmetric functions, minimum sumofproducts expressions, worst sumofproducts expressions, graph enumeration, minimally strongly connected digraphs. I
Delay Optimization Using SOP Balancing
"... Reducing delay of a digital circuit is an important topic in logic synthesis for standard cells and LUTbased FPGAs. This paper presents a simple, fast, and very efficient synthesis algorithm to improve the delay after technology mapping. The algorithm scales to large designs and is implemented in a ..."
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Cited by 2 (1 self)
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Reducing delay of a digital circuit is an important topic in logic synthesis for standard cells and LUTbased FPGAs. This paper presents a simple, fast, and very efficient synthesis algorithm to improve the delay after technology mapping. The algorithm scales to large designs and is implemented in a publiclyavailable technology mapper. The code is available online. Experimental results on industrial designs show that the method can improve delay by 30 % with the increase in area 2.4%, or by 41 % with the increase in area by 3.9%, on top of a higheffort synthesis and mapping flow. 1.
Exploring multivalued minimization using binary methods
 in International Workshop on Logic and Synthesis
, 2003
"... A transformation of multivalued input binaryoutput functions, called cosingleton transform (CST), was introduced in [11] to reduce algebraic multivalued (MV) operations to binary. In this paper, we explore its potential for a number of problems related to MV SOP minimization, such as computing I ..."
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Cited by 1 (1 self)
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A transformation of multivalued input binaryoutput functions, called cosingleton transform (CST), was introduced in [11] to reduce algebraic multivalued (MV) operations to binary. In this paper, we explore its potential for a number of problems related to MV SOP minimization, such as computing ISOPs, the set of all primes, and the set of all essential primes. Experimental results show that in some cases these problems can be solved more efficiently than by the traditional MV SOP minimization approaches represented by ESPRESSOMV, but that generally there is no clear methodofchoice. 1
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.