Multiple Preprocessing for Systematic SAT Solvers

2009

Beside impressive progresses made by SAT solvers over the last ten years, only few works tried to understand why Conflict Directed Clause Learning algorithms (CDCL) are so strong and efficient on most industrial applications. We report in this work a key observation of CDCL solvers behavior on this family of benchmarks and explain it by an unsuspected side effect of their particular Clause Learning scheme. This new paradigm allows us to solve an important, still open, question: How to designing a fast, static, accurate, and predictive measure of new learnt clauses pertinence. Our paper is followed by empirical evidences that show how our new learning scheme improves state-of-the art results by an order of magnitude on both SAT and UNSAT industrial problems.

2002

Recent work on microprocessor testing and verification has begun to consider the possible applicability of general-purpose satisfiability tools to this domain. In this paper, we will discuss some of the likely upcoming representational enhancements to these solvers, and the extent to which these representational improvements are likely to impact work in MTV.

Lecture Notes in Computer Science, 2012

Satisfiability (SAT) is considered as one of the most important core technologies in formal verification and related areas. Even though there is steady progress in improving practical SAT solving, there are limits on scalability of SAT solvers. We address this issue and present a new approach, called cube-and-conquer, targeted at reducing solving time on hard instances. This two-phase approach partitions a problem into many thousands (or millions) of cubes using lookahead techniques. Afterwards, a conflict-driven solver tackles the problem, using the cubes to guide the search. On several hard competition benchmarks, our hybrid approach outperforms both lookahead and conflict-driven solvers. Moreover, because cube-and-conquer is natural to parallelize, it is a competitive alternative for solving SAT problems in parallel.

Algorithms

Boolean structural measures were introduced to explain the high performance of conflict-driven clause-learning (CDCL) SAT solvers on industrial SAT instances. Those considered in this study include measures related to backbones and backdoors: backbone size, backbone frequency, and backdoor size. A key area of research is to improve the performance of CDCL SAT solvers by exploiting these measures. For the purpose of guiding the CDCL SAT solver for branching on backbone and backdoor variables, this study proposes low-overhead heuristics for computing these variables. Through these heuristics, a set of modifications to the Variable State Independent Decaying Sum (VSIDS) decision heuristic is suggested to exploit backbones and backdoors and potentially improve the performance of CDCL SAT solvers. In total, fifteen variants of two competitive base solvers, MapleLCMDistChronoBT-DL-v3 and LSTech, were developed. Empirical evaluation was conducted on 32 industrial families from 2002–2021 SA...

2008

Abstract Due to the widespread demands for efficient SAT solvers in Electronic Design Automation applications, methods to boost the performance of the SAT solver are highly desired. We propose a Hybrid Solution to boost SAT solver performance in this paper, via an integration of local and DPLL-based search approaches. A local search is used to identify a subset of clauses from the original formula to be passed to a DPLL SAT solver incrementally until all the clauses have been passed.

2007

Abstract Due to the widespread demands for efficient SAT solvers in electronic design automation applications, methods to boost the performance of the SAT solver are highly desired. The paper proposed a hybrid solution to boost SAT solver performance in this paper, via an integration of local and DPLL-based search approaches. A local search is used to identify a subset of clauses to be passed to a DPLL SAT solver through an incremental interface.

Design, Automation and Test in Europe

A sequential SAT solver Satori [1] was recently proposed as an alternative to combinational SAT in verification applications. This paper describes the design of Seq-SAT-an efficient sequential SAT solver with improved search strategies over Satori. The major improvements include (1) a new and better heuristic for minimizing the set of assignments to state variables, (2) a new priority-based search strategy and a flexible sequential search framework which integrates different search strategies, and (3) a decision variable selection heuristic more suitable for solving the sequential problems. We present experimental results to demonstrate that our sequential SAT solver can achieve orders-of-magnitude speedup over Satori. We plan to release the source code of Seq-SAT along with this paper.

2017

Clause Learning is one of the most important components of a conflict driven clause learning (CDCL) SAT solver that is effective on industrial instances. Since the number of learned clauses is proved to be exponential in the worse case, it is necessary to identify the most relevant clauses to maintain and delete the irrelevant ones. As reported in the literature, several learned clauses deletion strategies have been proposed. However the diversity in both the number of clauses to be removed at each step of reduction and the results obtained with each strategy increase the difficulty to determine which criterion is better. Thus, the problem to select which learned clauses are to be removed during the search step remains very challenging. In this paper, we propose a novel approach to identify the most relevant learned clauses without favoring or excluding any of the proposed measures, but by adopting the notion of dominance relationship among those measures. Our approach bypasses the ...

Journal on Satisfiability, Boolean Modeling and Computation

Due to the widespread demands for efficient SAT solvers in Electronic Design Automation applications, methods to boost the performance of the SAT solver are highly desired. We propose a Hybrid Solution to boost SAT solver performance in this paper, via an integration of local and DPLL-based search approaches. A local search is used to identify a subset of clauses from the original formula to be passed to a DPLL SAT solver incrementally until all the clauses have been passed. In addition, the solution obtained by the DPLL solver on the subset of clauses is fed back to the local search solver to jump over any locally optimal points. The proposed solution is highly portable to the existing SAT solvers. For satisfiable instances, up to an order of magnitude speedup was obtained via the proposed hybrid solver. For unsatisfiable instances, the speedup was smaller due to the overhead.

2000

The paper compares two popular strategies for solving propositional satisfiability, backtracking search and resolution, and analyzes the complexity of a directional resolution algorithm (DR) as a function of the "width" (w * ) of the problem's graph. Our empirical evaluation confirms theoretical prediction, showing that on low-w * problems DR is very efficient, greatly outperforming the backtracking-based Davis-Putnam-Logemann-Loveland procedure (DP). We also emphasize the knowledge-compilation properties of DR and extend it to a tree-clustering algorithm that facilitates query answering. Finally, we propose two hybrid algorithms that combine the advantages of both DR and DP. These algorithms use control parameters that bound the complexity of resolution and allow time/space trade-offs that can be adjusted to the problem structure and to the user's computational resources. Empirical studies demonstrate the advantages of such hybrid schemes.