This article is concerned with the application of the program extraction technique to a new class of problems: the synthesis of decision procedures for the classical satisfiability problem that are correct by construction. To this end, we formalize a completeness proof for the DPLL proof system and extract a SAT solver from it. When applied to a propositional formula in conjunctive normal form ...

This paper shows that the use of “local symmetry breaking” can dramatically reduce the length of propositional refutations. For each of the three propositional proof systems known as (i) treelike resolution, (ii) resolution, and (iii) k-DNF resolution, we describe families of unsatisfiable formulas in conjunctive normal form (CNF) that are “hard-to-refute”, i.e., require exponentially long refu...

Solving Quantified Boolean Formulas (QBF) has become an important and attractive research area, since several problem classes might be formulated efficiently as QBF instances (e.g. planning, non monotonic reasoning, twoplayer games, model checking, etc). Many QBF solvers has been proposed, most of them perform decision tree search using the DPLL-like techniques. To set free the variable orderin...

Lazy algorithms for Satisfiability Modulo Theories (SMT) combine a generic DPLL-based SAT engine with a theory solver for the given theory T that can decide the T -consistency of conjunctions of ground literals. For many theories of interest, theory solvers need to reason by performing internal case splits. Here we argue that it is more convenient to delegate these case splits to the DPLL engin...

For this assignment, the Walksat and DPLL algorithms were implemented in the OCaml language, using a mostly purely functional style (with the exception of pseudo-random number generation needed by Walksat, which must store its state). The representation of CNF formulas was a very natural one for a functional, list based language. Each literal is represented as a string, boolean tuple. The strin...

We report on a case study of implementing parallel variants of the DavisPutnam-Logemann-Loveland algorithm for solving the SAT problem of propositional formulas in the functional programming language Haskell. We explore several state of the art programming techniques for parallel and concurrent programming in Haskell and provide the corresponding implementations. Based on our experimental resul...

In this article, we present a 4.5–5.1-GHz fractional- $N$ digitally intensive phase-locked loop (DPLL) capable of maintaining its performance in face large supply ripple, thus enabling direct connection to switched-mode dc–dc converte...

This thesis presents NC(T ), an extension of the DPLL(T ) scheme [16, 29] for decision procedures for quantifier-free first-order logics. In DPLL(T ), a general Boolean DPLL engine is instantiated with a theory solver for the theory T . The DPLL engine is responsible for computing Boolean implications and detecting Boolean conflicts, while the theory solver detects implications and conflicts in...

The paper is devoted to lower bounds on the time complexity of DPLL algorithms that solve the satisfiability problem using a splitting strategy. Exponential lower bounds on the running time of DPLL algorithms on unsatisfiable formulas follow from the lower bounds for resolution proofs. Lower bounds on satisfiable instances are also known for some classes of DPLL algorithms; this lower bounds ar...