An extension of the Davis-Putnam procedure and its application to preprocessing in SMT

We present a decision procedure for SMT(LRA) that works by eliminating Boolean and rational variables. The algorithm we propose (DPFM) is based on a combination of the Davis-Putnam procedure and the Fourier-Motzkin elimination. We report on preliminary experiments where DPFM is not directly used to solve the formula (as its prohibitive complexity does not make it practical), but it is instead used in a controlled manner as a simplification and preprocessing device.

[1]  Nikolaj Bjørner,et al.  Z3: An Efficient SMT Solver , 2008, TACAS.

[2]  Alexander Schrijver,et al.  Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.

[3]  Marco Bozzano,et al.  MathSAT: Tight Integration of SAT and Mathematical Decision Procedures , 2005, Journal of Automated Reasoning.

[4]  Albert Oliveras,et al.  The Barcelogic SMT Solver , 2008, CAV.

[5]  Armin Biere,et al.  Effective Preprocessing in SAT Through Variable and Clause Elimination , 2005, SAT.

[6]  J. A. Robinson,et al.  The Generalized Resolution Principle , 1983 .

[7]  Kenneth L. McMillan,et al.  Generalizing DPLL to Richer Logics , 2009, CAV.

[8]  Ofer Strichman.  On Solving Presburger and Linear Arithmetic with SAT , 2002, FMCAD.

[9]  Dhiraj K. Pradhan,et al.  NiVER: Non Increasing Variable Elimination Resolution for Preprocessing SAT instances , 2004, SAT.

[10]  William Pugh,et al.  The Omega test: A fast and practical integer programming algorithm for dependence analysis , 1991, Proceedings of the 1991 ACM/IEEE Conference on Supercomputing (Supercomputing '91).

[11]  Bruno Dutertre,et al.  A Fast Linear-Arithmetic Solver for DPLL(T) , 2006, CAV.

[12]  Hilary Putnam,et al.  A Computing Procedure for Quantification Theory , 1960, JACM.

[13]  H. P. Williams.  Logic applied to integer programming and integer programming applied to logic , 1995 .

[14]  J. A. Robinson,et al.  A Machine-Oriented Logic Based on the Resolution Principle , 1965, JACM.

[15]  L. D. Moura,et al.  The YICES SMT Solver , 2006 .

[16]  Ofer Strichman.  Deciding Disjunctive Linear Arithmetic with SAT , 2004, ArXiv.

[17]  Sharad Malik,et al.  Lemma Learning in SMT on Linear Constraints , 2006, SAT.