Results 1 
7 of
7
A Compressed BreadthFirst Search for Satisfiability
 Proc. 4th Workshop on Algorithm Engineering and Experiments
, 2002
"... Leading algorithms for Boolean satisfiability (SAT) are based on either a depthfirst tree traversal of the search space (the DLL procedure [6]) or resolution (the DP procedure [7]). In this work we introduce a variant of BreadthFirst Search (BFS) based on the ability of ZeroSuppressed Binary De ..."
Abstract

Cited by 17 (3 self)
 Add to MetaCart
Leading algorithms for Boolean satisfiability (SAT) are based on either a depthfirst tree traversal of the search space (the DLL procedure [6]) or resolution (the DP procedure [7]). In this work we introduce a variant of BreadthFirst Search (BFS) based on the ability of ZeroSuppressed Binary Decision Diagrams (ZDDs) to compactly represent sparse or structured collections of subsets.
Resolution Cannot Polynomially Simulate CompressedBFS
 Ann. of Math. and A.I
, 2003
"... Many algorithms for Boolean satisfiability (SAT) work within the framework of resolution as a proof system, and thus on unsatisfiable instances they can be viewed as attempting to find proofs by resolution. However it has been known since the 1980s that every resolution proof of the pigeonhole princ ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Many algorithms for Boolean satisfiability (SAT) work within the framework of resolution as a proof system, and thus on unsatisfiable instances they can be viewed as attempting to find proofs by resolution. However it has been known since the 1980s that every resolution proof of the pigeonhole principle (PHP n ), suitably encoded as a CNF instance, includes exponentially many steps [1]. Therefore SAT solvers based upon the DLL procedure [2] or the DP procedure [3] must take exponential time. Polynomialsized proofs of the pigeonhole principle exist for different proof systems, but generalpurpose SAT solvers often remain confined to resolution. This result is in correlation with empirical evidence. Previously, we introduced...
Simple yet efficient improvements of SAT based bounded model checking
 In: FMCAD. Volume 3312 of LNCS
, 2004
"... Abstract. In this paper, we show how proper benchmarking, which matches daytoday use of formal methods, allows us to assess direct improvements for SAT use for formal methods. Proper uses of our benchmark allowed us to prove that previous results on tuning SAT solver for Bounded Model Checking (BM ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Abstract. In this paper, we show how proper benchmarking, which matches daytoday use of formal methods, allows us to assess direct improvements for SAT use for formal methods. Proper uses of our benchmark allowed us to prove that previous results on tuning SAT solver for Bounded Model Checking (BMC) were overly optimistic and that a simpler algorithm was in fact more efficient. 1
www.elsevier.com/locate/entcs Reducing Symmetries to Generate Easier SAT Instances 1
"... Finding countermodels is an effective way of disproving false conjectures. In firstorder predicate logic, model finding is an undecidable problem. But if a finite model exists, it can be found by exhaustive search. The finite model generation problem in the firstorder logic can also be translated ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Finding countermodels is an effective way of disproving false conjectures. In firstorder predicate logic, model finding is an undecidable problem. But if a finite model exists, it can be found by exhaustive search. The finite model generation problem in the firstorder logic can also be translated to the satisfiability problem in the propositional logic. But a direct translation may not be very efficient. This paper discusses how to take the symmetries into account so as to make the resulting problem easier. A static method for adding constraints is presented, which can be thought of as an approximation of the least number heuristic (LNH). Also described is a dynamic method, which asks a model searcher like SEM to generate a set of partial models, and then gives each partial model to a propositional prover. The two methods are analyzed, and compared with each other.
Improving firstorder model searching by propositional reasoning and lemma learning
 Proc. 7th Int’l Conf. on Theory and Applications of Satisfiability Testing
, 2004
"... Abstract. The finite model generation problem in the firstorder logic is a generalization of the propositional satisfiability (SAT) problem. An essential algorithm for solving the problem is backtracking search. In this paper, we show how to improve such a search procedure by lemma learning. For ef ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Abstract. The finite model generation problem in the firstorder logic is a generalization of the propositional satisfiability (SAT) problem. An essential algorithm for solving the problem is backtracking search. In this paper, we show how to improve such a search procedure by lemma learning. For efficiency reasons, we represent the lemmas by propositional formulas and use a SAT solver to perform the necessary reasoning. We have extended the firstorder model generator SEM, combining it with the SAT solver SATO. Experimental results show that the search time may be reduced significantly on many problems. 1
NiVER: Non Increasing Variable Elimination Resolution for Preprocessing SAT instances
 In Proc. 7th International Conference on Theory and Applications of Satisfiability Testing (SAT
, 2004
"... The original algorithm for the SAT problem, Variable Elimination Resolution (VER/DP) has exponential space complexity. To tackle that, the backtracking based DPLL procedure [2] is used in SAT solvers. We present a combination of both of the techniques. We use NiVER, a special case of VER, to elimina ..."
Abstract
 Add to MetaCart
The original algorithm for the SAT problem, Variable Elimination Resolution (VER/DP) has exponential space complexity. To tackle that, the backtracking based DPLL procedure [2] is used in SAT solvers. We present a combination of both of the techniques. We use NiVER, a special case of VER, to eliminate some variables in a preprocessing step and then solve the simplified problem using a DPLL SAT solver. NiVER is a strictly formula size not increasing resolution based preprocessor. Best worstcase upper bounds for general SAT solving (arbitrary clause length) in terms of N (Number of variables), K (Number of clauses) and L (Literal count) are 2 , respectively [14]. In the experiments, NiVER resulted in upto 74% decrease in N , 58% decrease in K and 46% decrease in L. In many real life instances, we observed that most of the resolvents for several variables are tautologies. There will be no increase in space due to VER on them. Hence, despite its simplicity, NiVER does result in easier instances. In most of the cases, NiVER takes less than one second for preprocessing. In case NiVER removable variables are not present, due to very low overhead, the cost of NiVER is insignificant. We also study the e#ect of combining NiVER with HyPre [3], a preprocessor based on hyper binary resolution. Based on experimental results, we classify the SAT instances into 4 classes. NiVER consistently performs well in all those classes and hence can be incorporated into all general purpose SAT solvers.
Exact Minimum Logic Factoring via Quantified Boolean Satisfiability
"... Abstract — This paper presents an exact method which finds the minimum factored form of an incompletely specified Boolean function. The problem is formulated as a Quantified Boolean Formula (QBF) and is solved by generalpurpose QBF solver. We also propose a novel graph structure, called an XB (eXc ..."
Abstract
 Add to MetaCart
Abstract — This paper presents an exact method which finds the minimum factored form of an incompletely specified Boolean function. The problem is formulated as a Quantified Boolean Formula (QBF) and is solved by generalpurpose QBF solver. We also propose a novel graph structure, called an XB (eXchanger Binary) tree, which implicitly enumerates binary trees. Using this graph structure, the factoring problem is compactly transformed into a QBF and hence the size of solvable problems is extended. Experimental results show that the proposed method successfully finds the exact minimum solutions to the problems with up to 12 literals in ten minutes. I.