Finite Instantiations for Integer Difference Logic

The last few years have seen the advent of a new breed of decision procedures for various fragments of first-order logic based on propositional abstraction. A lazy satisfiability checker for a given fragment of first-order logic invokes a theory-specific decision procedure (a theory solver) on (partial) satisfying assignments for the abstraction. If the assignment is found to be consistent in the given theory, then a model for the original formula has been found. Otherwise, a refinement of the propositional abstraction is extracted from the proof of inconsistency and the search is resumed. We describe a theory solver for integer difference logic that is effective when the formula to be decided contains equality and disequality (negated equality) constraints so that the decision problem partakes of the nature of the pigeonhole problem. We propose a reduction of the problem to propositional satisfiability by computing bounds on a sufficient subset of solutions, and present experimental evidence for the efficiency of this approach

[1]  Amir Pnueli,et al.  Range Allocation for Separation Logic , 2004, CAV.

[2]  Joël Ouaknine,et al.  Abstraction-Based Satisfiability Solving of Presburger Arithmetic , 2004, CAV.

[3]  Fabio Somenzi,et al.  Efficient Conflict Analysis for Finding All Satisfying Assignments of a Boolean Circuit , 2005, TACAS.

[4]  K. Cheng,et al.  SATORI-a fast sequential SAT engine for circuits , 2003, ICCAD-2003. International Conference on Computer Aided Design (IEEE Cat. No.03CH37486).

[5]  Sharad Malik,et al.  Chaff: engineering an efficient SAT solver , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[6]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[7]  Albert Oliveras,et al.  DPLL(T) with Exhaustive Theory Propagation and Its Application to Difference Logic , 2005, CAV.

[8]  Chao Wang,et al.  Deciding Separation Logic Formulae by SAT and Incremental Negative Cycle Elimination , 2005, LPAR.

[9]  Amir Pnueli,et al.  The Small Model Property: How Small Can It Be? , 2002, Inf. Comput..

[10]  Marco Bozzano,et al.  Efficient Satisfiability Modulo Theories via Delayed Theory Combination , 2005, CAV.

[11]  Shuvendu K. Lahiri,et al.  An Efficient Nelson-Oppen Decision Procedure for Difference Constraints over Rationals , 2005, PDPAR@CAV.

[12]  Cesare Tinelli,et al.  DPLL( T): Fast Decision Procedures , 2004, CAV.

[13]  Joao Marques-Silva,et al.  GRASP-A new search algorithm for satisfiability , 1996, Proceedings of International Conference on Computer Aided Design.

[14]  David L. Dill,et al.  Checking Satisfiability of First-Order Formulas by Incremental Translation to SAT , 2002, CAV.

[15]  Amir Pnueli,et al.  The small model property: how small can it be? , 2002 .

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

[17]  Xinming Ou,et al.  Theorem Proving Using Lazy Proof Explication , 2003, CAV.

[18]  L. D. Moura.  Lemmas on Demand for Satisfiability Solvers , 2002 .

[19]  Sanjit A. Seshia,et al.  The UCLID Decision Procedure , 2004, CAV.

[20]  Marco Bozzano,et al.  An Incremental and Layered Procedure for the Satisfiability of Linear Arithmetic Logic , 2005, TACAS.

[21]  Donald W. Loveland,et al.  A machine program for theorem-proving , 2011, CACM.

[22]  Fabio Somenzi,et al.  Prime clauses for fast enumeration of satisfying assignments to Boolean circuits , 2005, Proceedings. 42nd Design Automation Conference, 2005..