Infinite State Model Checking by Abstract Interpretation and Program Specialisation

We illustrate the use of logic programming techniques for finite model checking of CTL formulae. We present a technique for infinite state model checking of safety properties based upon logic program specialisation and analysis techniques. The power of the approach is illustrated on several examples. For that, the efficient tools logen and ecce are used. We discuss how this approach has to be extended to handle more complicated infinite state systems and to handle arbitrary CTL formulae.

[1]  C. R. Ramakrishnan,et al.  Fully Local and Efficient Evaluation of Alternating Fixed Points (Extended Abstract) , 1998, TACAS.

[2]  Edmund M. Clarke,et al.  Design and Synthesis of Synchronization Skeletons Using Branching-Time Temporal Logic , 1981, Logic of Programs.

[3]  C. R. Ramakrishnan,et al.  Efficient Model Checking Using Tabled Resolution , 1997, CAV.

[4]  Michael Leuschel,et al.  Program Specialisation and Abstract Interpretation Reconciled , 1998, IJCSLP.

[5]  Laurent Fribourg,et al.  Reachability Analysis of (Timed) Petri Nets Using Real Arithmetic , 1999, CONCUR.

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

[7]  M. Sørensen,et al.  Conjunctive Partial Deduction: Foundations, Control, Algorithms, and Experiments , 1999, J. Log. Program..

[8]  Michael Leuschel,et al.  Efficiently Generating Efficient Generating Extensions in Prolog , 1996, Dagstuhl Seminar on Partial Evaluation.

[9]  Peter Henderson,et al.  Questions and Answers About Ten Formal Methods , 1999 .

[10]  John W. Lloyd,et al.  Partial Evaluation in Logic Programming , 1991, J. Log. Program..

[11]  Paul Pettersson,et al.  Tools and Algorithms for the Construction and Analysis of Systems: 28th International Conference, TACAS 2022, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022, Munich, Germany, April 2–7, 2022, Proceedings, Part II , 1998, TACAS.

[12]  Pierre Wolper,et al.  Verifying Systems with Infinite but Regular State Spaces , 1998, CAV.

[13]  Michael Leuschel,et al.  Ecient Specialisation in Prolog Using a Hand-Written Compiler Generator , 1999 .

[14]  Konstantinos Sagonas,et al.  XSB as an efficient deductive database engine , 1994, SIGMOD '94.

[15]  Robert Glück,et al.  An Algorithm of Generalization in Positive Supercompilation , 1995, ILPS.

[16]  Michael Leuschel,et al.  Improving Homeomorphic Embedding for Online Termination , 1998, LOPSTR.

[17]  Andreas Podelski,et al.  Set-Based Analysis of Reactive Infinite-State Systems , 1998, TACAS.

[18]  Javier Esparza,et al.  More infinite results , 2001, INFINITY.

[19]  Danny De Schreye,et al.  Controlling generalization and polyvariance in partial deduction of normal logic programs , 1998, TOPL.

[20]  Matthew B. Dwyer,et al.  Staging Static Analyses Using Abstraction-Based Program Specialization , 1998, PLILP/ALP.

[21]  Faron Moller,et al.  Infinite Results , 1996, CONCUR.

[22]  J. Kruskal Well-quasi-ordering, the Tree Theorem, and Vazsonyi’s conjecture , 1960 .

[23]  Pierre Wolper,et al.  Relative liveness and behavior abstraction (extended abstract) , 1997, PODC '97.

[24]  Pierre Wolper,et al.  Relative Liveness and Behavior Abstraction , 1997 .

[25]  Michael J. Maher,et al.  Unification Revisited , 1988, Foundations of Deductive Databases and Logic Programming..

[26]  Graham Higman,et al.  Ordering by Divisibility in Abstract Algebras , 1952 .

[27]  Danny De Schreye,et al.  Logic Program Specialisation: How To Be More Specific , 1996, PLILP.

[28]  John M. Rushby Mechanized Formal Methods: Where Next? , 1999, World Congress on Formal Methods.

[29]  Javier Esparza,et al.  Decidability of model checking for infinite-state concurrent systems , 1997, Acta Informatica.

[30]  Edmund M. Clarke,et al.  Formal Methods: State of the Art and Future Directions Working Group Members , 1996 .

[31]  Robert Glück,et al.  Abstraction-Based Partial Deduction for Solving Inverse Problems - A Transformational Approach to Software Verification , 1999, Ershov Memorial Conference.

[32]  Yassine Lakhnech,et al.  Computing Abstractions of Infinite State Systems Compositionally and Automatically , 1998, CAV.

[33]  Ernst-Rüdiger Olderog,et al.  Verification of Sequential and Concurrent Programs , 1997, Graduate Texts in Computer Science.

[34]  Michael Leuschel,et al.  On the Power of Homeomorphic Embedding for Online Termination , 1998, SAS.

[35]  Thomas A. Henzinger,et al.  HYTECH: The Cornell HYbrid TECHnology Tool , 1994, Hybrid Systems.

[36]  Randal E. Bryant,et al.  Symbolic Boolean manipulation with ordered binary-decision diagrams , 1992, CSUR.

[37]  Maurizio Gabbrielli,et al.  The s-Semantics Approach: Theory and Applications , 1994, J. Log. Program..