A Comparative Study of Symbolic Algorithms for the Computation of Fair Cycles

Detection of fair cycles is an important task of many model checking algorithms. When the transition system is represented symbolically, the standard approach to fair cycle detection is the one of Emerson and Lei. In the last decade variants of this algorithm and an alternative method based on strongly connected component decomposition have been proposed. We present a taxonomy of these techniques and compare representatives of each major class on a collection of real-life examples. Our results indicate that the Emerson-Lei procedure is the fastest, but other algorithms tend to generate shorter counter-examples.

[1]  Kenneth L. McMillan,et al.  Symbolic model checking , 1992 .

[2]  Robert K. Brayton,et al.  Testing Language Containment for omega-Automata Using BDD's , 1995, Inf. Comput..

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

[4]  Tiziano Villa,et al.  VIS: A System for Verification and Synthesis , 1996, CAV.

[5]  R. McNaughton.  Review: J. Richard Buchi, Weak Second-Order Arithmetic and Finite Automata; J. Richard Buchi, On a Decision Method in Restricted second Order Arithmetic , 1963, Journal of Symbolic Logic.

[6]  Peter A. Beerel,et al.  Implicit enumeration of strongly connected components , 1999, 1999 IEEE/ACM International Conference on Computer-Aided Design. Digest of Technical Papers (Cat. No.99CH37051).

[7]  Sandeep K. Shukla,et al.  A New Heuristic for Bad Cycle Detection Using BDDs , 1997, Formal Methods Syst. Des..

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

[9]  Robert K. Brayton,et al.  BDD-Based Debugging Of Design Using Language Containment and Fair CTL , 1993, CAV.

[10]  J. R. Büchi.  On a Decision Method in Restricted Second Order Arithmetic , 1990 .

[11]  Robert P. Kurshan,et al.  Computer-Aided Verification of Coordinating Processes: The Automata-Theoretic Approach , 2014 .

[12]  Edmund M. Clarke,et al.  Efficient generation of counterexamples and witnesses in symbolic model checking , 1995, DAC '95.

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

[14]  Amir Pnueli,et al.  Checking that finite state concurrent programs satisfy their linear specification , 1985, POPL.

[15]  Fabio Somenzi,et al.  An Algorithm for Strongly Connected Component Analysis in n log n Symbolic Steps , 2000, Formal Methods Syst. Des..

[16]  Fabio Somenzi,et al.  Symbolic State Exploration , 2001, SMC@FLoC.

[17]  Amir Pnueli,et al.  Algorithmic Verification of Linear Temporal Logic Specifications , 1998, ICALP.

[18]  L. Kantorovitch.  The method of successive approximation for functional equations , 1939 .

[19]  A. Tarski.  A LATTICE-THEORETICAL FIXPOINT THEOREM AND ITS APPLICATIONS , 1955 .

[20]  Robert E. Tarjan,et al.  Depth-First Search and Linear Graph Algorithms , 1972, SIAM J. Comput..

[21]  Robert K. Brayton,et al.  Efficient omega-Regular Language Containment , 1992, CAV.