Results 1  10
of
13
Algorithms for the Satisfiability (SAT) Problem: A Survey
 DIMACS Series in Discrete Mathematics and Theoretical Computer Science
, 1996
"... . The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, compute ..."
Abstract

Cited by 142 (3 self)
 Add to MetaCart
(Show Context)
. The satisfiability (SAT) problem is a core problem in mathematical logic and computing theory. In practice, SAT is fundamental in solving many problems in automated reasoning, computeraided design, computeraided manufacturing, machine vision, database, robotics, integrated circuit design, computer architecture design, and computer network design. Traditional methods treat SAT as a discrete, constrained decision problem. In recent years, many optimization methods, parallel algorithms, and practical techniques have been developed for solving SAT. In this survey, we present a general framework (an algorithm space) that integrates existing SAT algorithms into a unified perspective. We describe sequential and parallel SAT algorithms including variable splitting, resolution, local search, global optimization, mathematical programming, and practical SAT algorithms. We give performance evaluation of some existing SAT algorithms. Finally, we provide a set of practical applications of the sat...
Global Optimization for Satisfiability (SAT) Problem
, 1994
"... The satisfiability (SAT) problem is a fundamental problem in mathematical logic, inference, automated reasoning, VLSI engineering, and computing theory. In this paper, following CNF and DNF local search methods, we introduce the Universal SAT problem model, UniSAT, that transforms the discrete SAT ..."
Abstract

Cited by 20 (3 self)
 Add to MetaCart
The satisfiability (SAT) problem is a fundamental problem in mathematical logic, inference, automated reasoning, VLSI engineering, and computing theory. In this paper, following CNF and DNF local search methods, we introduce the Universal SAT problem model, UniSAT, that transforms the discrete SAT problem on Boolean space f0; 1g m into an unconstrained global optimization problem on real space E m . A direct correspondence between the solution of the SAT problem and the global minimum point of the UniSAT objective function is established. Many existing global optimization algorithms can be used to solve the UniSAT problems. Combined with backtracking /resolution procedures, a global optimization algorithm is able to verify satisfiability as well as unsatisfiability. This approach achieves significant performance improvements for certain classes of conjunctive normal form (CNF ) formulas. It offers a complementary approach to the existing SAT algorithms.
Redundancy Identification using Transitive Closure
 in Proc. Fifth IEEE Asian Test Symp
, 1996
"... ..."
(Show Context)
A FaultIndependent Transitive Closure Algorithm for Redundancy Identification
 IN PROC. OF THE 16 TH INTERNATIONAL CONF. VLSI DESIGN
, 2003
"... We present a faultindependent redundancy identification algorithm. The controllabilities and observabilities are defined as Boolean variables and represented on an implication graph. A major enhancement over previously published results is that we include all direct and partial implications, as we ..."
Abstract

Cited by 8 (5 self)
 Add to MetaCart
We present a faultindependent redundancy identification algorithm. The controllabilities and observabilities are defined as Boolean variables and represented on an implication graph. A major enhancement over previously published results is that we include all direct and partial implications, as well as node fixation. The transitive closure, whose computation now requires a new algorithm, provides many redundant faults in a singlepass analysis. Because of these improvements, we obtain better performance than all previous faultindependent methods at execution speeds that are much faster than any exhaustive ATPG. For example, in the s9234 circuit more than half of the redundant faults are found in just 14 seconds on a Sparc 5. All 34 redundant faults of c6288 are found in one pass. Besides, our single pass procedure can classify faults according to the causes of their redundancy. The weakness of our method, as we illustrate by examples, lies in the lack of a formulation for the observabilities of fanout stems.
A New Transitive Closure Algorithm with Applications to Redundancy Identification
 in Proc. of the 1st International Workshop on Electronic, Design and Test Applications (DELTAâ€™02
, 2002
"... ..."
(Show Context)
Using Contrapositive Law in an Implication Graph to Identify Logic Redundancies
 Proc. 18 th International Conf. VLSI Design
, 2005
"... ..."
(Show Context)
Convergence Properties of Optimization Algorithms for the Satisfiability (SAT) Problem
 IEEE Trans. on Computers
, 1996
"... : The satisfiability (SAT) problem is a basic problem in computing theory. Presently, an active area of research on SAT problem is to design efficient optimization algorithms for finding a solution for a satisfiable CNF formula. A new formulation, the Universal SAT problem model, which transforms t ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
: The satisfiability (SAT) problem is a basic problem in computing theory. Presently, an active area of research on SAT problem is to design efficient optimization algorithms for finding a solution for a satisfiable CNF formula. A new formulation, the Universal SAT problem model, which transforms the SAT problem on Boolean space into an optimization problem on real space has been developed [31, 35, 34, 32]. Many optimization techniques, such as the steepest descent method, Newton's method, and the coordinate descent method, can be used to solve the Universal SAT problem. In this paper, we prove that, when the initial solution is sufficiently close to the optimal solution, the steepest descent method has a linear convergence ratio fi ! 1, Newton's method has a convergence ratio of order two, and the convergence ratio of the steepest descent method is approximately (1 \Gamma fi=m) for the Universal SAT problem with m variables. An algorithm based on the coordinate descent method for the...
Theorems on Redundancy Identification
, 2003
"... There is a class of implicationbased methods that identify logic redundancy from circuit topology and without any primary input assignment. These methods are less complex than automatic test pattern generation (ATPG) but identify only a subset of all redundancies. This paper provides new results to ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
There is a class of implicationbased methods that identify logic redundancy from circuit topology and without any primary input assignment. These methods are less complex than automatic test pattern generation (ATPG) but identify only a subset of all redundancies. This paper provides new results to enlarge this subset. Contributions are a fixedvalue theorem and two theorems on fanout stem unobservability. Our framework is an implication graph of signal controllabilities and observabilities represented as Boolean variables. Besides the conventional implication edges this graph also contains partial implications implemented by AND nodes. An analysis of the transitive closure (TC) of this graph provides many redundancies. Weaknesses of this procedure are in dealing with the effects of xedvalued variables on TC and the lack of observability relations across fanouts. The fixedvalue theorem adds unconditional edges from all variables to the fixed variable and then recomputes TC recursively until no new fixed nodes are found. The stem unobservability theorems determine the observability status of a fanout stem from its dominator set, which either has fixed values or is unobservable. Results are considerably improved from the previously reported implicationbased identi ers. In the c5315 circuit we identify 58 out of 59 redundant faults. All 34 redundant faults of c6288 are identi ed. Besides, our procedure can classify faults according to the causes of their redundancy, namely, unexcitable, unobservable, or undrivable. For the future research, we provide examples of cases where the present method still fails.
Using Contrapositives to Enhance the Implication Graph of Logic Circuits
 in Proc. of the 13 th IEEE North Atalantic Test Workshop
, 2004
"... ..."
(Show Context)