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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… (More)

argo-lib is a C++ library that provides support for using decision procedures and for schemes for combining and augmenting decision procedures. This platform follows the smt-lib initiative which aims at establishing a library of benchmarks for satisfiability modulo theories. The platform can be easily integrated into other systems. It also enables… (More)

Execution of most of the modern DPLL-based SAT solvers is guided by a number of heuristics. Decisions made during the search process are usually driven by some fixed heuristic policies. Despite the outstanding progress in SAT solving in recent years, there is still an appealing lack of techniques for selecting policies appropriate for solving specific input… (More)

We present a formalization and a formal total correctness proof of a MiniSAT-like SAT solver within the system Isabelle/HOL. The solver is based on the DPLL procedure and employs most state-of-the art SAT solving techniques, including the conflict-guided backjumping, clause learning, and the two-watched unit propagation scheme. A shallow embedding into… (More)

We describe a system URBiVA for specifying and solving a range of problems by uniformly reducing them to bit-vector arithmetic (bva). A problem description is given in a C-like specification language and this high-level specification is transformed to a bva formula by symbolic execution. The formula is passed to a bva solver and, if it is satisfi-able, its… (More)

The DPLL procedure for the SAT problem is one of the fundamental algorithms in computer science, with many applications in a range of domains, including software and hardware verification. Most of the modern SAT solvers are based on this procedure, extending it with different heuristics. In this paper we present a formal proof that the DPLL procedure is… (More)

We describe our ongoing project of formalization of algebraic methods for geometry theorem proving (Wu's method and the Gröbner bases method), their implementation and integration in educational tools. The project includes formal verification of the algebraic methods within Isabelle/HOL proof assistant and development of a new, open-source Java… (More)

The Frankl's conjecture, formulated in 1979. and still open, states that in every family of sets closed for unions there is an element contained in at least half of the sets. FC-families are families for which it is proved that every union-closed family containing them satisfies the Frankl's condition (e.g., in every union-closed family that contains a… (More)

We present a formalization of modern SAT solvers and their properties in a form of abstract state transition systems. SAT solving procedures are described as transition relations over states that represent the values of the solver's global variables. Several different SAT solvers are formalized, including both the classical DPLL procedure and its… (More)