Efficient Reachability Set Generation and Storage Using Decision Diagrams

We present a new technique for the generation and storage of the reachability set of a Petri net. Our approach is inspired by previous work on Binary and Multi-valued Decision Diagrams but exploits a concept of locality for the effect of a transition's firing to vastly improve algorithmic performance. The result is a data structure and a set of manipulation routines that can be used to generate and store enormous sets extremely efficiently in terms of both memory and execution time.

[1]  G. Ciardo,et al.  ON THE USE OF KRONECKER OPERATORS FOR THE SOLUTION OF GENERALIZED STOCHASTIC PETRI NETS , 1996 .

[2]  Robert K. Brayton,et al.  Algorithms for discrete function manipulation , 1990, 1990 IEEE International Conference on Computer-Aided Design. Digest of Technical Papers.

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

[4]  Graham Horton,et al.  State space construction and steady-state solution of GSPNs on a shared-memory multiprocessor , 1997, Proceedings of the Seventh International Workshop on Petri Nets and Performance Models.

[5]  Jordi Cortadella,et al.  Efficient encoding schemes for symbolic analysis of Petri nets , 1998, Proceedings Design, Automation and Test in Europe.

[6]  C. Y. Lee.  Representation of switching circuits by binary-decision programs , 1959 .

[7]  Timothy Kam.  State minimization of finite state machines using implicit techniques , 1996 .

[8]  Jordi Cortadella,et al.  Structural Methods to Improve the Symbolic Analysis of Petri Nets , 1999, ICATPN.

[9]  P. Buchholz,et al.  Complexity of Kronecker Operations on Sparse Matrices with Applications to the Solution of Markov Models , 1997 .

[10]  Jordi Cortadella,et al.  Petri Net Analysis Using Boolean Manipulation , 1994, Application and Theory of Petri Nets.

[11]  Robert Valette,et al.  Application and Theory of Petri Nets 1997 , 1997, Lecture Notes in Computer Science.

[12]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[13]  Peter Kemper.  Reachability Analysis Based on Structured Representations , 1996, Application and Theory of Petri Nets.

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

[15]  Susanna Donatelli,et al.  Superposed Generalized Stochastic Petri Nets: Definition and Efficient Solution , 1994, Application and Theory of Petri Nets.

[16]  Peter Kemper.  Numerical Analysis of Superposed GSPNs , 1996, IEEE Trans. Software Eng..

[17]  Wolfgang Reisig,et al.  Application and Theory of Petri Nets 1996 , 1996, Lecture Notes in Computer Science.

[18]  Peter Buchholz,et al.  Hierarchical structuring of superposed GSPNs , 1997, Proceedings of the Seventh International Workshop on Petri Nets and Performance Models.

[19]  Jordi Cortadella,et al.  Verification of Asynchronous Circuits by BDD-based Model Checking of Petri Nets , 1995, Application and Theory of Petri Nets.

[20]  Gianfranco Ciardo,et al.  SMART: simulation and Markovian analyzer for reliability and timing , 1996, Proceedings of IEEE International Computer Performance and Dependability Symposium.

[21]  Giorgio De Michelis,et al.  Application and Theory of Petri Nets 1995 , 1995 .

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