SAT Solver Design

This paper proposes a new algorithm for solving the Boolean satisfiability (SAT) problem. On the basis of this algorithm a software/reconfigurable hardware SAT solver was designed, implemented and compared to a similar realization of the Davis-Putnam-like method. The satisfier suggested uses an application-specific approach, thus an instance- specific hardware compilation is completely avoided.

We propose a novel preprocessing technique that helps to significantly simplify a CNF instance, such that the resulting formula is easier for any SAT-solver to solve. The core of this simplification centers on a suite of lemmas and theorems derived from nontrivial Boolean reasoning. These theorems help us to deduce powerful unary and binary clauses which aid in the identification of necessary assignments, equivalent signals, complementary signals and other implication relationships among the CNF variables. The nontrivial clauses, when added to the original CNF database, subsequently simplify the CNF formula. We illustrate through experimental results that the CNF formula simplification obtained using our tool outperforms the simplification obtained using the recent preprocessors namely Hypre [F. Bacchus et al., (2003)] and NIVER [S. Subbarayan et al. (2004)]. Also, considerable savings in computation time are obtained when the simplified CNF formula is given to the SAT-solver for processing.

We first introduce Abstract DPLL, a rule-based formulation of the Davis--Putnam--Logemann--Loveland (DPLL) procedure for propositional satisfiability. This abstract framework allows one to cleanly express practical DPLL algorithms and to formally reason about them in a simple way. Its properties, such as soundness, completeness or termination, immediately carry over to the modern DPLL implementations with features such as backjumping or clause

We explore the automatic generation of test data that respect constraints expressed in the Object-Role Modeling (ORM) language. ORM is a popular conceptual modeling language, primarily targeting database applications, with significant uses in practice. The general problem of even checking whether an ORM diagram is satisfiable is quite hard: restricted forms are easily NP-hard and the problem is undecidable for some expressive formulations of ORM. Brute-force mapping to input for constraint and SAT solvers does not scale: state-of-the-art solvers fail to find data to satisfy uniqueness and mandatory constraints in realistic time even for small examples. We instead define a restricted subset of ORM that allows efficient reasoning yet contains most constraints overwhelmingly used in practice. We show that the problem of deciding whether these constraints are consistent (i.e., whether we can generate appropriate test data) is solvable in polynomial time, and we produce a highly efficien...

In this paper, we explore the links between measures of in- consistency for a belief base and the minimal inconsistent subsets of that belief base. The minimal inconsistent subsets can be considered as the relevant part of the base to take into account to evaluate the amount of inconsistency. We define a very natural inconsistency value from these minimal incon- sistent sets. Then we show that the inconsistency value we obtain is a particular Shapley Inconsistency Value, and we provide a complete axiomatization of this value in terms of five simple and intuitive axioms. Defining this Shapley In- consistency Value using the notion of minimal inconsistent subsets allows us to look forward to a viable implementation of this value using SAT solvers.

In order to facilitate automated reasoning about large Boolean combinations of non- linear arithmetic constraints involving transcendental functions, we provide a tight inte- gration of recent SAT solving techniques with interval-based arithmetic constraint solv- ing. Our approach deviates substantially from lazy theorem proving approaches in that it directly controls arithmetic constraint propagation from the SAT solver rather than del- egating

The calculation of Hamiltonian Circuits is an NP-complete task. This paper uses slightly modified complete sets of Hamiltonian circuits for the classification of documents. The known solution method is based on a SAT-instance with a huge number of clauses which is flattening the knowledge about the problem. We suggest an even more compact model of Boolean equations that preserves the

Boolean Satisfiability (SAT) solvers are now routinely used in the verification of large industrial problems. However, their application in safety-critical domains such as the railways, avionics, and automotive industries requires some form of assurance for the results, as the solvers can (and sometimes do) have bugs. Unfortunately, the complexity of modern, highly optimized SAT solvers renders impractical the development of direct formal proofs of their correctness. This paper presents an alternative approach where an untrusted, industrial-strength, SAT solver is plugged into a trusted, formally certified, SAT proof checker to provide industrial-strength certified SAT solving. The key novelties and characteristics of our approach are (i) that the checker is automatically extracted from the formal development, (ii), that the combined system can be used as a standalone executable program independent of any supporting theorem prover, and (iii) that the checker certifies any SAT solver respecting the agreed format for satisfiability and unsatisfiability claims. The core of the system is a certified checker for unsatisfiability claims that is formally designed and verified in Coq. We present its formal design and outline the correctness proofs. The actual standalone checker is automatically extracted from the the Coq development. An evaluation of the certified checker on a representative set of industrial benchmarks from the SAT Race Competition shows that, albeit it is slower than uncertified SAT checkers, it is significantly faster than certified checkers implemented on top of an interactive theorem prover.

We present a preprocessing algorithm for SAT, based on the HypBinRes inference rule, and show that it does not improve the performance of a DPLL-based SAT solver with conflict recording. We also present evidence that the ineffectiveness of the preprocessing algorithm is the result of interaction with the branching heuristic used by the solver.