Monotonic Extensions of Petri Nets: Forward and Backward Search Revisited

In this paper, we revisit the forward and backward approaches to the verification of extensions of infinite state Petri Nets. As contributions, we propose an efficient data structure to represent infinite downward closed sets of markings and to compute symbolically the minimal coverability set of Petri Nets, we identify a subclass of Transfer Nets for which the forward approach generalizes and we propose a general strategy to use both the forward and the backward approach for the efficient verification of general Transfer Nets.

[1]  Marco Ajmone Marsan,et al.  Modelling with Generalized Stochastic Petri Nets , 1995, PERV.

[2]  Alain Finkel,et al.  The Minimal Coverability Graph for Petri Nets , 1991, Applications and Theory of Petri Nets.

[3]  Charles Rackoff,et al.  The Covering and Boundedness Problems for Vector Addition Systems , 1978, Theor. Comput. Sci..

[4]  Jim Handy,et al.  The cache memory book , 1993 .

[5]  David S. Johnson,et al.  A Catalog of Complexity Classes , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

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

[7]  Manuel Silva Suárez,et al.  Linear Algebraic and Linear Programming Techniques for the Analysis of Place or Transition Net Systems , 1996, Petri Nets.

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

[9]  Gianfranco Ciardo,et al.  Storage Alternatives for Large Structured State Spaces , 1997, Computer Performance Evaluation.

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

[11]  Gianni Conte,et al.  Analysis of large GSPN models: a distributed solution tool , 1997, Proceedings of the Seventh International Workshop on Petri Nets and Performance Models.

[12]  Giorgio Delzanno,et al.  Symbolic Representation of Upward-Closed Sets , 2000, TACAS.

[13]  D. Zampuniéris,et al.  Efficient handling of large sets of tuples with sharing trees , 1995, Proceedings DCC '95 Data Compression Conference.

[14]  Philippe Schnoebelen,et al.  Verifying lossy channel systems has nonprimitive recursive complexity , 2002, Inf. Process. Lett..

[15]  Karsten Stahl,et al.  Abstracting WS1S Systems to Verify Parameterized Networks , 2000, TACAS.

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

[17]  Giorgio Delzanno,et al.  Attacking Symbolic State Explosion , 2001, CAV.

[18]  Parosh Aziz Abdulla,et al.  Effective Lossy Queue Languages , 2001, ICALP.

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

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

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

[22]  Giorgio Delzanno,et al.  Covering sharing trees: a compact data structure for parameterized verification , 2004, International Journal on Software Tools for Technology Transfer.

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

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

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