A Direct Algorithm for Multi-valued Bounded Model Checking

Multi-valued Model Checking is an extension of classical, two-valued model checking with multi-valued logic. Multi-valuedness has been proved useful in expressing additional information such as incompleteness, uncertainty, and many others, but with the cost of time and space complexity. This paper addresses this problem, and proposes a new algorithm for Multi-valued Model Checking. While Chechik et al. have extended BDD-based Symbolic Model Checking algorithm to the multi-valued case, our algorithm extends Bounded Model Checking (BMC), which can generate a counterexample of minimum length efficiently (if any). A notable feature of our algorithm is that it directly generates conjunctive normal forms, and never reduces multi-valued formulas into many slices of two-valued formulas. To achieve this feature, we extend the BMC algorithm to the multi-valued case and also devise a new translation of multi-valued propositional formulas. Finally, we show experimental results and compare the performance of our algorithm with that of a reduction-based algorithm.

[1]  David S. Johnson,et al.  Cliques, Coloring, and Satisfiability , 1996 .

[2]  Marsha Chechik,et al.  Implementing a Multi-valued Symbolic Model Checker , 2001, TACAS.

[3]  Melvin Fitting,et al.  Many-valued modal logics , 1991, Fundam. Informaticae.

[4]  Marsha Chechik,et al.  Data structures for symbolic multi-valued model-checking , 2006, Formal Methods Syst. Des..

[5]  Marsha Chechik,et al.  Multi-valued symbolic model-checking , 2003, TSEM.

[6]  Armin Biere,et al.  Symbolic Model Checking without BDDs , 1999, TACAS.

[7]  M. Trick,et al.  Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, Workshop, October 11-13, 1993 , 1996 .

[8]  E. Clarke,et al.  Symbolic model checking using SAT procedures instead of BDDs , 1999, Proceedings 1999 Design Automation Conference (Cat. No. 99CH36361).

[9]  Marsha Chechik,et al.  Efficient Multiple-Valued Model-Checking Using Lattice Representations , 2001, CONCUR.

[10]  David A. Plaisted,et al.  A Structure-Preserving Clause Form Translation , 1986, J. Symb. Comput..

[11]  Marsha Chechik,et al.  A framework for multi-valued reasoning over inconsistent viewpoints , 2001, Proceedings of the 23rd International Conference on Software Engineering. ICSE 2001.

[12]  Rajeev Alur,et al.  A Temporal Logic of Nested Calls and Returns , 2004, TACAS.

[13]  R. Milner,et al.  Bigraphical Reactive Systems , 2001, CONCUR.

[14]  Stephan Merz,et al.  Model Checking , 2000 .