Formalization and Implementation of Modern SAT Solvers

Abstract

Most, if not all, state-of-the-art complete SAT solvers are complex variations of the DPLL procedure described in the early 1960's. Published descriptions of these modern algorithms and related data structures are given either as high-level (rule-based) transition systems or, informally, as (pseudo) programming language code. The former, although often accompanied with (informal) correctness proofs, are usually very abstract and do not specify many details crucial for efficient implementation. The latter usually do not involve any correctness argument and the given code is often hard to understand and modify. This paper aims at bridging this gap: we present SAT solving algorithms that are formally proved correct, but at the same time they contain information required for efficient implementation. We use a tutorial, top-down, approach and develop a SAT solver, starting from a simple design that is subsequently extended, step-by-step, with the requisite series of features. Heuristic parts of the solver are abstracted away, since they usually do not affect solver correctness (although they are very important for efficiency). All algorithms are given in pseudo-code. The code is accompanied with correctness conditions, given in Hoare logic style. Correctness proofs are formalized within the Isabelle theorem proving system and are available in the extended version of this paper. The given pseudo-code served as a basis for our SAT solver argo-sat.

Instance-Based Selection of Policies for SAT Solvers

“…The proposed methodology can be applied to any DPLL-based SAT solver, provided it supports multiple policies. In our experiments, the ArgoSAT solver 2 was used since it implements a large number of policies and since its modular architecture allows easy modification of existing and implementation of new policies [Mar09]. The overall methodology consists of two phases.…”

“…In the rest of the paper, we shall assume that the reader is familiar with the modern SAT solving techniques. More on these topics can be found, for example, in [NOT06,KG07,Mar08,GKSS07]. Although modern SAT solvers share common underlying algorithms and implementation techniques, their operation is guided by a number of heuristic policies that have to be selected in order to obtain deterministic solving strategies.…”

Simple algorithm portfolio for SAT

“…ArgoSmArT is a system developed for instance-based selection of policies for a single SAT solver (Nikolić et al, 2009). As a suitable underlying SAT solver it uses a modular solver ArgoSAT (Marić, 2009). ArgoSmArT uses a training set of SAT instances divided manually in classes of instances of similar origin (e.g., as in the SAT Competition corpus).…”

Unsatisfiability Proofs for Parallel SAT Solver Portfolios with Clause Sharing and Inprocessing

“…For sequential SAT solvers, several formalizations exist, which model different parts of SAT solvers [1,8,24,26,35,39]. Here, we model a sequential SAT solver as a pair (M, F ), where M is a finite set of melted literals, and F is the working formula.…”

“…One approach for improving the reliability of SAT solvers is to mechanically verify them, as done in [35]. However, mechanically-verified SAT solvers are currently significantly slower than state-of-the-art solvers, written in C and C++, such as CryptoMiniSAT , Lingeling, Glucose, and Riss.…”