Efficient data structures for backtrack search SAT solvers

The implementation of efficient Propositional Satisfiability (SAT) solvers entails the utilization of highly efficient data structures, as illustrated by most of the recent state-of-the-art SAT solvers. However, it is in general hard to compare existing data structures, since different solvers are often characterized by fairly different algorithmic organizations and techniques, and by different search strategies and heuristics. This paper aims the evaluation of data structures for backtrack search SAT solvers, under a common unbiased SAT framework. In addition, advantages and drawbacks of each existing data structure are identified. Finally, new data structures are proposed, that are competitive with the most efficient data structures currently available, and that may be preferable for the next generation SAT solvers

On Using Unsatisfiability for Solving Maximum Satisfiability

Maximum Satisfiability (MaxSAT) is a well-known optimization pro- blem, with several practical applications. The most widely known MAXS AT algorithms are ineffective at solving hard problems instances from practical application domains. Recent work proposed using efficient Boolean Satisfiability (SAT) solvers for solving the MaxSAT problem, based on identifying and eliminating unsatisfiable subformulas. However, these algorithms do not scale in practice. This paper analyzes existing MaxSAT algorithms based on unsatisfiable subformula identification. Moreover, the paper proposes a number of key optimizations to these MaxSAT algorithms and a new alternative algorithm. The proposed optimizations and the new algorithm provide significant performance improvements on MaxSAT instances from practical applications. Moreover, the efficiency of the new generation of unsatisfiability-based MaxSAT solvers becomes effectively indexed to the ability of modern SAT solvers to proving unsatisfiability and identifying unsatisfiable subformulas

Conflict Analysis in Search Algorithms for Satisfiability

This paper introduces GRASP (Generic search Algorithm jr the Satisfiabili{y Problem), a new search algorithm jr Propositional Satisfiabili{y (SAT). GRASP incorporates several search-pruning techniques, some of which are specific to SAT, whereas others find equivalent in other fields of Artificial Intelligence. GRASP is premised on the inevitabili{y of conflicts during search and its most distinguishingjature is the augmentation of basic backtracking search with a powerful conflict analysis procedure. Analyzing conflicts to determine their causes enables GRASP to backtrack non-chronologically to earlier levels in the search tree, potentially pruning large portions of the search space. In addition, by 'gecording" the causes of conflicts, GRASP can recognize and preempt the occurrence of similar conflicts later on in the search. Finally, straigh&rward bookkeeping of the causali {y chains leading up to conflicts allows GRASP to identij) assignments that are necessary jr a solution to be jund. Experimental results obtained jom a large number of benchmarks indicate that application of the proposed conflict analysis techniques to SAT algorithms can be extremely efctive jr a large number of representative classes of SAT instances

Dynamic Search-Space Pruning Techniques in Path Sensitization

Abstract — A powerful combinational path sensitization engine is required for the efficient implementation of tools for test pattern generation, timing analysis, and delay fault testing. Path sensitization can be posed as a search, in the n-dimensional Boolean space, for a consistent assignment of logic values to the circuit nodes which also satisfies a given condition. In this paper we propose and demonstrate the effectiveness of several new techniques for search-space pruning for test pattern generation. In particular, we present linear-time algorithms for dynamically identifying unique sensitization points and for dynamically maintaining reduced head line sets. In addition, we present two powerful mechanisms that drastically reduce the number of backtracks: failure-driven assertions and dependency-directed backtracking. Both mechanisms can be viewed as a form of learning while searching and have analogs in other application domains. These search pruning methods have been implemented in a generic path sensitization engine called LEAP. A test pattern generator, TG-LEAP, that uses this engine was also developed. We present experimental results that compare the effectiveness of our proposed search pruning strategies to those of PODEM, FAN, and SOCRATES. In particular, we show that LEAP is very efficient in identifying undetectable faults and in generating tests for difficult faults. I