Results 1  10
of
87
Improvements To Propositional Satisfiability Search Algorithms
, 1995
"... ... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400variable 3SAT problems in about 2 hours on the average. In general, it can solve hard nvariable ..."
Abstract

Cited by 160 (0 self)
 Add to MetaCart
... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400variable 3SAT problems in about 2 hours on the average. In general, it can solve hard nvariable random 3SAT problems with search trees of size O(2 n=18:7 ). In addition to justifying these claims, this dissertation describes the most significant achievements of other researchers in this area, and discusses all of the widely known general techniques for speeding up SAT search algorithms. It should be useful to anyone interested in NPcomplete problems or combinatorial optimization in general, and it should be particularly useful to researchers in either Artificial Intelligence or Operations Research.
Practical reasoning for very expressive description logics
 Journal of the Interest Group in Pure and Applied Logics 8
, 2000
"... Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm t ..."
Abstract

Cited by 157 (21 self)
 Add to MetaCart
Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm that decides satisfiability of the DL ALC extended with transitive and inverse roles and functional restrictions with respect to general concept inclusion axioms and role hierarchies; early experiments indicate that this algorithm is wellsuited for implementation. Additionally, we show that ALC extended with just transitive and inverse roles is still in PSpace. We investigate the limits of decidability for this family of DLs, showing that relaxing the constraints placed on the kinds of roles used in number restrictions leads to the undecidability of all inference problems. Finally, we describe a number of optimisation techniques that are crucial in obtaining implementations of the decision procedures, which, despite the hight worstcase complexity of the problem, exhibit good performance with reallife problems. 1
The Quest for Efficient Boolean Satisfiability Solvers
, 2002
"... has seen much interest in not just the theoretical computer science community, but also in areas where practical solutions to this problem enable significant practical applications. Since the first development of the basic search based algorithm proposed by Davis, Putnam, Logemann and Loveland (DPLL ..."
Abstract

Cited by 125 (2 self)
 Add to MetaCart
has seen much interest in not just the theoretical computer science community, but also in areas where practical solutions to this problem enable significant practical applications. Since the first development of the basic search based algorithm proposed by Davis, Putnam, Logemann and Loveland (DPLL) about forty years ago, this area has seen active research effort with many interesting contributions that have culminated in stateoftheart SAT solvers today being able to handle problem instances with thousands, and in same cases even millions, of variables. In this paper we examine some of the main ideas along this passage that have led to our current capabilities. Given the depth of the literature in this field, it is impossible to do this in any comprehensive way; rather we focus on techniques with consistent demonstrated efficiency in available solvers. For the most part, we focus on techniques within the basic DPLL search framework, but also briefly describe other approaches and look at some possible future research directions. 1.
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 124 (3 self)
 Add to MetaCart
. 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...
Finding Hard Instances of the Satisfiability Problem: A Survey
, 1997
"... . Finding sets of hard instances of propositional satisfiability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case ..."
Abstract

Cited by 113 (1 self)
 Add to MetaCart
. Finding sets of hard instances of propositional satisfiability is of interest for understanding the complexity of SAT, and for experimentally evaluating SAT algorithms. In discussing this we consider the performance of the most popular SAT algorithms on random problems, the theory of average case complexity, the threshold phenomenon, known lower bounds for certain classes of algorithms, and the problem of generating hard instances with solutions.
A DavisPutnam Based Enumeration Algorithm for Linear PseudoBoolean Optimization
, 1995
"... The DavisPutnam enumeration method (DP) has recently become one of the fastest known methods for solving the clausal satisfiability problem of propositional calculus. We present a generalization of the DPprocedure for solving the satisfiability problem of a set of linear pseudoBoolean (or 01) ..."
Abstract

Cited by 102 (1 self)
 Add to MetaCart
The DavisPutnam enumeration method (DP) has recently become one of the fastest known methods for solving the clausal satisfiability problem of propositional calculus. We present a generalization of the DPprocedure for solving the satisfiability problem of a set of linear pseudoBoolean (or 01) inequalities. We extend the method to solve linear 01 optimization problems, i.e. optimize a linear pseudoBoolean objective function w.r.t. a set of linear pseudoBoolean inequalities. The algorithm compares well with traditional linear programming based methods on a variety of standard 01 integer programming benchmarks. Keywords 01 Integer Programming; Propositional Calculus; Enumeration Contents 1 Introduction 1 2 Preliminaries 1 3 The Classical DavisPutnam Procedure 3 4 DavisPutnam for Linear PseudoBoolean Inequalities 5 5 Optimizing with PseudoBoolean DavisPutnam 7 6 Implementation 8 7 Heuristics 10 8 Computational Results 10 9 Conclusion 12 1 Introduction The DavisPutn...
Tractable Reasoning via Approximation
 Artificial Intelligence
, 1995
"... Problems in logic are wellknown to be hard to solve in the worst case. Two different strategies for dealing with this aspect are known from the literature: language restriction and theory approximation. In this paper we are concerned with the second strategy. Our main goal is to define a semantical ..."
Abstract

Cited by 94 (0 self)
 Add to MetaCart
Problems in logic are wellknown to be hard to solve in the worst case. Two different strategies for dealing with this aspect are known from the literature: language restriction and theory approximation. In this paper we are concerned with the second strategy. Our main goal is to define a semantically wellfounded logic for approximate reasoning, which is justifiable from the intuitive point of view, and to provide fast algorithms for dealing with it even when using expressive languages. We also want our logic to be useful to perform approximate reasoning in different contexts. We define a method for the approximation of decision reasoning problems based on multivalued logics. Our work expands and generalizes in several directions ideas presented by other researchers. The major features of our technique are: 1) approximate answers give semantically clear information about the problem at hand; 2) approximate answers are easier to compute than answers to the original problem; 3) approxim...
A twophase exact algorithm for MAXSAT and weighted MAXSAT problems
 Journal of Combinatorial Optimization
, 1997
"... We describe a two phase algorithm for MAXSAT and weighted MAX SAT problems. In the first phase, we use the GSAT heuristic to find a good solution to the problem. In the second phase, we use an enumeration procedure based on the DavisPutnamLoveland algorithm, to find a provably optimal soluti ..."
Abstract

Cited by 79 (4 self)
 Add to MetaCart
We describe a two phase algorithm for MAXSAT and weighted MAX SAT problems. In the first phase, we use the GSAT heuristic to find a good solution to the problem. In the second phase, we use an enumeration procedure based on the DavisPutnamLoveland algorithm, to find a provably optimal solution. The first heuristic stage improves the performance of the algorithm by obtaining an upper bound on the minimum number of unsatisfied clauses that can be used in pruning branches of the search tree. We compare our algorithm with an integer programming branch and cut algorithm. Our implementation of the two phase algorithm is faster Research partially supported by ONR Grant number N000149410391. y Mathematics Department, New Mexico Tech, Socorro, NM 87801. z Department of Mathematical Sciences, Clemson University, Clemson, SC 29634 than the integer programming approach on many problems. However, the integer programming approach is more effective than the two phase algorithm o...
Lazy Satisfiability Modulo Theories
 Journal on Satisfiability, Boolean Modeling and Computation
, 2007
"... Satisfiability Modulo Theories (SMT) is the problem of deciding the satisfiability of a firstorder formula with respect to some decidable firstorder theory T (SMT (T)). These problems are typically not handled adequately by standard automated theorem provers. SMT is being recognized as increasingl ..."
Abstract

Cited by 79 (33 self)
 Add to MetaCart
Satisfiability Modulo Theories (SMT) is the problem of deciding the satisfiability of a firstorder formula with respect to some decidable firstorder theory T (SMT (T)). These problems are typically not handled adequately by standard automated theorem provers. SMT is being recognized as increasingly important due to its applications in many domains in different communities, in particular in formal verification. An amount of papers with novel and very efficient techniques for SMT has been published in the last years, and some very efficient SMT tools are now available. Typical SMT (T) problems require testing the satisfiability of formulas which are Boolean combinations of atomic propositions and atomic expressions in T, so that heavy Boolean reasoning must be efficiently combined with expressive theoryspecific reasoning. The dominating approach to SMT (T), called lazy approach, is based on the integration of a SAT solver and of a decision procedure able to handle sets of atomic constraints in T (Tsolver), handling respectively the Boolean and the theoryspecific components of reasoning. Unfortunately, neither the problem of building an efficient SMT solver, nor even that of acquiring a comprehensive background knowledge in lazy SMT, is of simple solution. In this paper we present an extensive survey of SMT, with particular focus on the lazy approach. We survey, classify and analyze from a theoryindependent perspective the most effective techniques and optimizations which are of interest for lazy SMT and which have been proposed in various communities; we discuss their relative benefits and drawbacks; we provide some guidelines about their choice and usage; we also analyze the features for SAT solvers and Tsolvers which make them more suitable for an integration. The ultimate goals of this paper are to become a source of a common background knowledge and terminology for students and researchers in different areas, to provide a reference guide for developers of SMT tools, and to stimulate the crossfertilization of techniques and ideas among different communities.
Branching Rules for Satisfiability
 Journal of Automated Reasoning
, 1995
"... Recent experience suggests that branching algorithms are among the most attractive for solving propositional satisfiability problems. A key factor in their success is the rule they use to decide on which variable to branch next. We attempt to explain and improve the performance of branching rules wi ..."
Abstract

Cited by 78 (2 self)
 Add to MetaCart
Recent experience suggests that branching algorithms are among the most attractive for solving propositional satisfiability problems. A key factor in their success is the rule they use to decide on which variable to branch next. We attempt to explain and improve the performance of branching rules with an empirical modelbuilding approach. One model is based on the rationale given for the JeroslowWang rule, variations of which have performed well in recent work. The model is refuted by carefully designed computational experiments. A second model explains the success of the JeroslowWang rule, makes other predictions confirmed by experiment, and leads to the design of branching rules that are clearly superior to JeroslowWang. Recent computational studies [2, 7, 13, 21] suggest that branching algorithms are among the most attractive for solving the propositional satisfiability problem. An important factor in their successperhaps the dominant factoris the branching rule they use [...