Results 1  10
of
438
GSAT and Dynamic Backtracking
 Journal of Artificial Intelligence Research
, 1994
"... There has been substantial recent interest in two new families of search techniques. One family consists of nonsystematic methods such as gsat; the other contains systematic approaches that use a polynomial amount of justification information to prune the search space. This paper introduces a new te ..."
Abstract

Cited by 360 (14 self)
 Add to MetaCart
There has been substantial recent interest in two new families of search techniques. One family consists of nonsystematic methods such as gsat; the other contains systematic approaches that use a polynomial amount of justification information to prune the search space. This paper introduces a new technique that combines these two approaches. The algorithm allows substantial freedom of movement in the search space but enough information is retained to ensure the systematicity of the resulting analysis. Bounds are given for the size of the justification database and conditions are presented that guarantee that this database will be polynomial in the size of the problem in question. 1 INTRODUCTION The past few years have seen rapid progress in the development of algorithms for solving constraintsatisfaction problems, or csps. Csps arise naturally in subfields of AI from planning to vision, and examples include propositional theorem proving, map coloring and scheduling problems. The probl...
SATO: an Efficient Propositional Prover
 In Proceedings of the International Conference on Automated Deduction
, 1997
"... r class of SAT instances. For instance, in our study of quasigroup problems, one rule seems better than the others: choose one literal in one of the shortest positive clauses (a positive clause is a clause where all the literals are positive). On the other hand, a proved effective splitting rule is ..."
Abstract

Cited by 194 (6 self)
 Add to MetaCart
r class of SAT instances. For instance, in our study of quasigroup problems, one rule seems better than the others: choose one literal in one of the shortest positive clauses (a positive clause is a clause where all the literals are positive). On the other hand, a proved effective splitting rule is to choose a variable x such that the value f 2 (x) f 2 (:x) is maximal, where f 2 (L) is one plus the number of occurrences of literal L in binary clauses [2, 5]. We tried to combine the above two rules into one as follows: Let 0 ! a 1 and n be the number of shortest nonHorn clauses in the current set. At first, we collect all the variable names appearing in the first da ne shortest positive clauses. Then we choose x in this pool
DPLL(T): Fast Decision Procedures
, 2004
"... The logic of equality with uninterpreted functions (EUF) and its extensions have been widely applied to processor verification, by means of a large variety of progressively more sophisticated (lazy or eager) translations into propositional SAT. Here we propose a new approach, namely a general DP ..."
Abstract

Cited by 118 (14 self)
 Add to MetaCart
The logic of equality with uninterpreted functions (EUF) and its extensions have been widely applied to processor verification, by means of a large variety of progressively more sophisticated (lazy or eager) translations into propositional SAT. Here we propose a new approach, namely a general DPLL(X) engine, whose parameter X can be instantiated with a specialized solver Solver T for a given theory T , thus producing a system DPLL(T ). We describe this DPLL(T ) scheme, the interface between DPLL(X) and Solver T , the architecture of DPLL(X), and our solver for EUF, which includes incremental and backtrackable congruence closure algorithms for dealing with the builtin equality and the integer successor and predecessor symbols. Experiments with a first implementation indicate that our technique already outperforms the previous methods on most benchmarks, and scales up very well.
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 114 (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.
Resolve and Expand
 In Proc. of SATâ€™04
, 2004
"... Abstract. We present a novel expansion based decision procedure for quantified boolean formulas (QBF) in conjunctive normal form (CNF). The basic idea is to resolve existentially quantified variables and eliminate universal variables by expansion. This process is continued until the formula becomes ..."
Abstract

Cited by 105 (15 self)
 Add to MetaCart
Abstract. We present a novel expansion based decision procedure for quantified boolean formulas (QBF) in conjunctive normal form (CNF). The basic idea is to resolve existentially quantified variables and eliminate universal variables by expansion. This process is continued until the formula becomes propositional and can be solved by any SAT solver. On structured problems our implementation quantor is competitive with stateoftheart QBF solvers based on DPLL. It is orders of magnitude faster on certain hard to solve instances. 1
Generating Hard Satisfiability Problems
 Artificial Intelligence
, 1996
"... We report results from largescale experiments in satisfiability testing. As has been observed by others, testing the satisfiability of random formulas often appears surprisingly easy. Here we show that by using the right distribution of instances, and appropriate parameter values, it is possible ..."
Abstract

Cited by 98 (2 self)
 Add to MetaCart
We report results from largescale experiments in satisfiability testing. As has been observed by others, testing the satisfiability of random formulas often appears surprisingly easy. Here we show that by using the right distribution of instances, and appropriate parameter values, it is possible to generate random formulas that are hard, that is, for which satisfiability testing is quite difficult. Our results provide a benchmark for the evaluation of satisfiabilitytesting procedures. In Artificial Intelligence, 81 (19996) 1729. 1 Introduction Many computational tasks of interest to AI, to the extent that they can be precisely characterized at all, can be shown to be NPhard in their most general form. However, there is fundamental disagreement, at least within the AI community, about the implications of this. It is claimed on the one hand that since the performance of algorithms designed to solve NPhard tasks degrades rapidly with small increases in input size, something ...
Picosat essentials
 Journal on Satisfiability, Boolean Modeling and Computation (JSAT
"... In this article we describe and evaluate optimized compact data structures for watching literals. Experiments with our SAT solver PicoSAT show that this lowlevel optimization not only saves memory, but also turns out to speed up the SAT solver considerably. We also discuss how to store proof traces ..."
Abstract

Cited by 79 (9 self)
 Add to MetaCart
In this article we describe and evaluate optimized compact data structures for watching literals. Experiments with our SAT solver PicoSAT show that this lowlevel optimization not only saves memory, but also turns out to speed up the SAT solver considerably. We also discuss how to store proof traces compactly in memory and further unique features of PicoSAT including an aggressive restart schedule. Keywords: SAT solver, watched literals, occurrence lists, proof traces, restarts
The Probabilistic Analysis of a Greedy Satisfiability Algorithm
, 2002
"... Consider the following simple, greedy DavisPutnam algorithm applied to a random 3CNF formula of fixed density (clauses to variables ratio): Arbitrarily select and set to True a literal that appears in as many clauses as possible, irrespective of their size (and irrespective of the number of occu ..."
Abstract

Cited by 72 (5 self)
 Add to MetaCart
Consider the following simple, greedy DavisPutnam algorithm applied to a random 3CNF formula of fixed density (clauses to variables ratio): Arbitrarily select and set to True a literal that appears in as many clauses as possible, irrespective of their size (and irrespective of the number of occurrences of the negation of the literal). Delete these clauses from the formula, and also delete the negation of this literal from any clauses it appears. Repeat. If however unit clauses ever appear, then first repeatedly and in any order set the literals in them to True and delete and shrink clauses accordingly, until no unit clause remains. Also if at any step an empty clause appears, then do not backtrack, but just terminate the algorithm and report failure. A slight modification of this algorithm is probabilistically analyzed in this paper (rigorously). It is proved that for random formulas of n variables and density up to 3.42, it succeeds in producing a satisfying truth assignment with bounded away from zero probability, as n approaches infinity. Therefore the satisfiability threshold is at least 3.42.
New methods for 3SAT decision and worstcase analysis
 THEORETICAL COMPUTER SCIENCE
, 1999
"... We prove the worstcase upper bound 1:5045 n for the time complexity of 3SAT decision, where n is the number of variables in the input formula, introducing new methods for the analysis as well as new algorithmic techniques. We add new 2 and 3clauses, called "blocked clauses", generalizing the e ..."
Abstract

Cited by 66 (12 self)
 Add to MetaCart
We prove the worstcase upper bound 1:5045 n for the time complexity of 3SAT decision, where n is the number of variables in the input formula, introducing new methods for the analysis as well as new algorithmic techniques. We add new 2 and 3clauses, called "blocked clauses", generalizing the extension rule of "Extended Resolution." Our methods for estimating the size of trees lead to a refined measure of formula complexity of 3clausesets and can be applied also to arbitrary trees. Keywords: 3SAT, worstcase upper bounds, analysis of algorithms, Extended Resolution, blocked clauses, generalized autarkness. 1 Introduction In this paper we study the exponential part of time complexity for 3SAT decision and prove the worstcase upper bound 1:5044:: n for n the number of variables in the input formula, using new algorithmic methods as well as new methods for the analysis. These methods also deepen the already existing approaches in a systematically manner. The following results...
A backbonesearch heuristic for efficient solving of hard 3SAT formulae
, 2001
"... Of late, new insight into the study of random kSAT formulae has been gained from the introduction of a concept inspired by models of physics, the `backbone ' of a SAT formula which corresponds to the variables having a fixed truth value in all assignments satisfying the maximum number of claus ..."
Abstract

Cited by 62 (1 self)
 Add to MetaCart
Of late, new insight into the study of random kSAT formulae has been gained from the introduction of a concept inspired by models of physics, the `backbone ' of a SAT formula which corresponds to the variables having a fixed truth value in all assignments satisfying the maximum number of clauses.