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

Boolean Satisfiability in Electronic Design Automation

Boolean Satisfiability (SAT) is often used as the underlying model for a significant and increasing number of applications in Electronic Design Automation (EDA) as well as in many other fields of Computer Science and Engineering. In recent years, new and efficient algorithms for SAT have been developed, allowing much larger problem instances to be solved. SAT “packages” are currently expected to have an impact on EDA applications similar to that of BDD packages since their introduction more than a decade ago. This tutorial paper is aimed at introducing the EDA professional to the Boolean satisfiability problem. Specifically, we highlight the use of SAT models to formulate a number of EDA problems in such diverse areas as test pattern generation, circuit delay computation, logic optimization, combinational equivalence checking, bounded model checking and functional test vector generation, among others. In addition, we provide an overview of the algorithmic techniques commonly used for solving SAT, including those that have seen widespread use in specific EDA applications. We categorize these algorithmic techniques, indicating which have been shown to be best suited for which tasks

Efficient satisfiability solver

The past few decades saw great improvements in the performance of satisfiability (SAT) solvers. In this thesis, we discuss the state-of-the-art techniques used in building an efficient SAT solver. Modern SAT solvers are mainly constituted by the following components: decision heuristics, Boolean constraint propagation, conflict analysis, restart, clause deletion and preprocessing. Various algorithms and implementations in each component will be discussed and analyzed. Then we propose a new backtracking strategy, partial backtracking, which can be easily implemented in SAT solvers. It is essentially an extension of the backtracking strategy used in most SAT solvers. With partial backtracking, the solver consecutively amends the variable assignments instead of discarding them completely so that it does not backtrack as many levels as the classic strategy does after analyzing a conflict. We implemented this strategy in our solver Nigma and the experiments show that the solver benefits from this adjustment

Accelerating SAT solving with best-first-search

Solvers for Boolean satisfiability (SAT), like other algorithms for NP-complete problems, tend to have a heavy-tailed runtime distribution. Successful SAT solvers make use of frequent restarts to mitigate this problem by abandoning unfruitful parts of the search space after some time. Although frequent restarting works fairly well, it is a quite simplistic technique that does not do anything explicitly to make the next try better than the previous one. In this paper, we suggest a more sophisticated method: using a best-first-search approach to quickly move between different parts of the search space. This way, the search can always focus on the most promising region. We investigate empirically how the performance of frequent restarts, best-first-search, and a combination of the two compare to each other. Our findings indicate that the combined method works best, improving 36-43\% on the performance of frequent restarts on the used set of benchmark problems