Expand, Enlarge and Check: New algorithms for the coverability problem of WSTS

In this paper, we present a general algorithmic schema called Expand, Enlarge and Check from which new efficient algorithms for the coverability problem of WSTS can be constructed. We show here that our schema allows us to define forward algorithms that decide the coverability problem for several classes of systems for which the Karp and Miller procedure cannot be generalized, and for which no complete forward algorithms were known. Our results have important applications for the verification of parameterized systems and communication protocols.

[1]  Jean-François Raskin,et al.  Petri Nets with Non-blocking Arcs are Difficult to Analyze , 2004, INFINITY.

[2]  James Lyle Peterson,et al.  Petri net theory and the modeling of systems , 1981 .

[3]  Parosh Aziz Abdulla,et al.  Verifying programs with unreliable channels , 1993, [1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science.

[4]  Philippe Schnoebelen,et al.  Well-structured transition systems everywhere! , 2001, Theor. Comput. Sci..

[5]  Ahmed Bouajjani,et al.  Model Checking Lossy Vector Addition Systems , 1999, STACS.

[6]  Parosh Aziz Abdulla,et al.  On-the-Fly Analysis of Systems with Unbounded, Lossy FIFO Channels , 1998, CAV.

[7]  Jean-François Raskin,et al.  Expand, Enlarge and Check... Made Efficient , 2005, CAV.

[8]  Tadao Kasami,et al.  Some Decision Problems Related to the Reachability Problem for Petri Nets , 1976, Theor. Comput. Sci..

[9]  Rüdiger Valk On the Computational Power of Extended Petri Nets , 1978, MFCS.

[10]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[11]  Kedar S. Namjoshi,et al.  On model checking for non-deterministic infinite-state systems , 1998, Proceedings. Thirteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.98CB36226).

[12]  Thomas A. Henzinger,et al.  The theory of hybrid automata , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[13]  Parosh Aziz Abdulla,et al.  General decidability theorems for infinite-state systems , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[14]  Philippe Schnoebelen,et al.  Reset Nets Between Decidability and Undecidability , 1998, ICALP.

[15]  Giorgio Delzanno,et al.  Towards the Automated Verification of Multithreaded Java Programs , 2002, TACAS.

[16]  Richard M. Karp,et al.  Parallel Program Schemata , 1969, J. Comput. Syst. Sci..

[17]  Thomas A. Henzinger,et al.  From Pre-Historic to Post-Modern Symbolic Model Checking , 1998, Formal Methods Syst. Des..

[18]  Marcus Nilsson,et al.  Regular Model Checking , 2000, CAV.

[19]  Neil Immerman,et al.  Number of Quantifiers is Better Than Number of Tape Cells , 1981, J. Comput. Syst. Sci..

[20]  Gianfranco Ciardo,et al.  Petri Nets with Marking-Dependent Ar Cardinality: Properties and Analysis , 1994, Application and Theory of Petri Nets.

[21]  Rajeev Alur,et al.  A Theory of Timed Automata , 1994, Theor. Comput. Sci..

[22]  Parosh Aziz Abdulla,et al.  Symbolic Verification of Lossy Channel Systems: Application to the Bounded Retransmission Protocol , 1999, TACAS.

[23]  Alain Finkel,et al.  Reduction and covering of infinite reachability trees , 1990, Inf. Comput..

[24]  Jean-François Raskin,et al.  Efficient verification of counting abstractions for parametric systems , 2004 .

[25]  Alain Finkel,et al.  Monotonic Extensions of Petri Nets: Forward and Backward Search Revisited , 2002, INFINITY.

[26]  Laure Petrucci,et al.  FAST: Fast Acceleration of Symbolikc Transition Systems , 2003, CAV.

[27]  A. Prasad Sistla,et al.  Reasoning about systems with many processes , 1992, JACM.

[28]  Alain Finkel,et al.  On the verification of broadcast protocols , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).