Improvements to Hybrid Incremental SAT Algorithms

Abstract

Abstract. Boolean Satisfiability (SAT) solvers have been successfully applied to a wide range of practical applications, including hardware model checking, software model finding, equivalence checking, and planning, among many others. SAT solvers are also the building block of more sophisticated decision procedures, including Satisfiability Modulo Theory (SMT) solvers. The large number of applications of SAT yields ever more challenging problem instances, and motivate the development of more efficient algorithms. Recent work studied hybrid approaches for SAT, which involves integrating incomplete and complete SAT solvers. This paper proposes a number of improvements to hybrid SAT solvers. Experimental results demonstrate that the proposed optimizations are effective. The resulting algorithms in general perform better and, more importantly, are significantly more robust.

A survey of the satisfiability-problems solving algorithms

“…[The stochastic local search algorithms evolved out of the Selman and Kautz's 1992 greedy SAT (GSAT) algorithm (Selman et al, 1992)] (Pham et al, 2007). Local search is a meta-heuristic for solving computationally hard optimisation problems (Letombe and Marques-Silva, 2008). On some large satisfiable problems, local search finds a solution much more quickly than complete algorithms, though it currently compares rather badly with backtracking algorithms on industrial benchmarks (Prestwich and Lynce, 2006).…”

“…It then makes a second restart up to a maximum number of restarts if the solution is not found yet. [Selman et al (1994) have also proposed improvements to GSAT, including WalkSAT, whose main differences to GSAT are the addition of random noise, and the step of selecting variables to be flipped from unsatisfied clauses] (Letombe and Marques-Silva, 2008). WalkSAT restricts the selection of the variable to flip from the unsatisfied clauses while GSAT has no such restriction.…”

“…Several of the current best open source SAT solvers scale up to instances with over a million variables and several million clauses (Kroc et al, 2009). Motivated by significant improvements to SAT solvers over the last decade, SAT has been applied to a large number of areas, including model checking, model finding, planning, bioinformatics, and security, among many others (Letombe and Marques-Silva, 2008). In addition, the SAT problems have an application in network routing [see Aloul et al (2008) and Valavi et al (2005) for more details].…”

Boosting Local Search Thanks to cdcl

“…This process is repeated until the next restart (line 24). As long as a model is not found or the unsatisfiability of the formula is not proven the solver restarts the previous process with a new initial complete interpretation (lines [25][26].…”

“…The hybrid solver HBISAT [10] and its extended and improved version hinotos [26] belong to this category. In both approaches, a local search is used to identify a subset of clauses to be passed to a DPLL SAT solver through an incremental interface.…”