Proving ∀ μ-Calculus Properties with SAT-Based Model Checking

In this paper, we present a complete bounded model checking algorithm for the universal fragment of μ-calculus. The new algorithm checks the completeness of bounded proof of each property on the fly and does not depend on prior knowledge of the completeness thresholds. The key is to combine both local and bounded model checking techniques and use SAT solvers to perform local model checking on finite Kripke structures. Our proof-theoretic approach works for any property in the specification logic and is more general than previous work on specific properties. We report experimental results to compare our algorithm with the conventional BDD-based algorithm.

[1]  Kenneth L. McMillan,et al.  Interpolation and SAT-Based Model Checking , 2003, CAV.

[2]  Edmund M. Clarke,et al.  Using Branching Time Temporal Logic to Synthesize Synchronization Skeletons , 1982, Sci. Comput. Program..

[3]  D. Kozen.  Results on the Propositional µ-Calculus , 1982 .

[4]  Pierre Wolper,et al.  An Automata-Theoretic Approach to Automatic Program Verification (Preliminary Report) , 1986, LICS.

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

[6]  Anna Philippou,et al.  Tools and Algorithms for the Construction and Analysis of Systems , 2018, Lecture Notes in Computer Science.

[7]  Edmund M. Clarke,et al.  Another Look at LTL Model Checking , 1994, CAV.

[8]  Tobias Schüle,et al.  Global vs. local model checking: a comparison of verification techniques for infinite state systems , 2004, Proceedings of the Second International Conference on Software Engineering and Formal Methods, 2004. SEFM 2004..

[9]  G. Winskel,et al.  A Compositional Proof System for the Modal mu-Calculus , 1994 .

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

[11]  Joël Ouaknine,et al.  Completeness and Complexity of Bounded Model Checking , 2004, VMCAI.

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

[13]  Fabio Somenzi,et al.  Proving More Properties with Bounded Model Checking , 2004, CAV.

[14]  Chin-Laung Lei,et al.  Modalities for Model Checking: Branching Time Logic Strikes Back , 1987, Sci. Comput. Program..

[15]  Harald Ruess,et al.  Bounded Model Checking and Induction: From Refutation to Verification (Extended Abstract, Category A) , 2003, CAV.

[16]  Mary Sheeran,et al.  Checking Safety Properties Using Induction and a SAT-Solver , 2000, FMCAD.

[17]  Edmund M. Clarke,et al.  Symbolic Model Checking: 10^20 States and Beyond , 1990, Inf. Comput..

[18]  Viktor Schuppan,et al.  Efficient reduction of finite state model checking to reachability analysis , 2004, International Journal on Software Tools for Technology Transfer.

[19]  Rance Cleaveland,et al.  Tableau-based model checking in the propositional mu-calculus , 1990, Acta Informatica.

[20]  Chin-Laung Lei,et al.  Efficient Model Checking in Fragments of the Propositional Mu-Calculus (Extended Abstract) , 1986, LICS.

[21]  David Walker,et al.  Local Model Checking in the Modal mu-Calculus , 1991, Theor. Comput. Sci..