We prove that the graph tautology principles of Alekhnovich, Johannsen, Pitassi and Urquhart have polynomial size pool resolution refutations that use only input lemmas as learned clauses and without degenerate resolution inferences. These graph tautology principles can be refuted by polynomial size DPLL proofs with clause learning, even when restricted to greedy, unit-propagating DPLL search.

A technique for obtaining chaotic response from a stable first order conventional digital phase locked loop (DPLL) driven by another stable first order conventional DPLL has been reported in this paper. The dynamics of the driven system has been characterized using the dynamical measures of Lyapunov exponent and Correlation dimension. It is found that the resultant chaos is low dimensional, whi...

Current parallel SAT solvers suffer from a non-deterministic behavior. This is the consequence of their architectures which rely on weak synchronizing in an attempt to maximize performance. This behavior is a clear downside for practitioners, who are used to both runtime and solution reproducibility. In this paper, we propose the first Deterministic Parallel DPLL engine. Our experimental result...

Satisfiability Modulo Theories (SMT) solvers have proven highly scalable, efficient and suitable for integrated theory reasoning. The most efficient SMT solvers rely on refutationally incomplete methods for incorporating quantifier reasoning. We describe a calculus and a system that tightly integrates Superposition and DPLL(T). In the calculus, all non-unit ground clauses are delegated to the D...

We present an investigation of the use of GPGPU techniques to parallelize the execution of a satisfiability solver, based on the traditional DPLL procedure—which, in spite of its simplicity, still represents the core of the most competitive solvers. The investigation tackles some interesting problems, including the use of a predominantly data-parallel architecture, like NVIDIA’s CUDA platform, ...

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...

I am interested in combining and parallelizing multiple search techniques. For my class project, I am combining portfolio-based DPLL SAT solving with Hyperresolution. Specifically, I am building on top of a system started by Erik Zawadzki and myself; I am incorporating our highly parallel DPLL+Resolution code into the relatively untried portfolio-based parallel solver called ManySAT [7], which ...

We show that the trace of an exhaustive DPLL search can be viewed as a compilation of the propositional theory. With different constraints imposed or lifted on the DPLL algorithm, this compilation will belong to the language of d-DNNF, FBDD, and OBDD, respectively. These languages are decreasingly succinct, yet increasingly tractable, supporting such polynomial-time queries as model counting an...

State-of-the-art satisfiability modulo theory solvers use a combination of the Davis-PutnamLogemann-Loveland (DPLL) procedure for performing Boolean search and an integration of theory solvers for identifying theory conflicts. Theory conflicts are presented as clauses over the propositional vocabulary that prune the DPLL search. This combination is often highly effective, as propositional reaso...