Efficient encoding schemes for symbolic analysis of Petri nets

Petri nets are a graph-based formalism appropriate to model concurrent systems such as asynchronous circuits or network protocols. Symbolic techniques based on Binary Decision Diagrams (BDDs) have emerged as one of the strategies to overcome the state explosion problem in the analysis of systems modeled by Petri nets. The existing techniques for state encoding use a variable-per-place strategy that leads to encoding schemes with very low density. This drawback has been partially mitigated by using Zero-Suppressed BDDs, that provide a typical reduction of BDD sizes by a factor of two. This work presents novel encoding schemes for Petri nets. By using algebraic techniques to analyze the topology of the net, sets of places "structurally related" can be derived and encoded by only using a logarithmic number of Boolean variables. Such an approach allows one to drastically decrease the number of variables for state encoding and reduce memory and CPU requirements significantly.

[1]  Michel Hack,et al.  ANALYSIS OF PRODUCTION SCHEMATA BY PETRI NETS , 1972 .

[2]  Alexandre Yakovlev,et al.  Checking signal transition graph implementability by symbolic BDD traversal , 1995, Proceedings the European Design and Test Conference. ED&TC 1995.

[3]  Jörg Desel,et al.  Free choice Petri nets , 1995 .

[4]  Edmund M. Clarke,et al.  Symbolic model checking for sequential circuit verification , 1993, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

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

[6]  Luciano Lavagno,et al.  Logic synthesis techniques for embedded control code optimization , 1997 .

[7]  Luciano Lavagno,et al.  Coupling Asynchrony and Interrupts: Place Chart Nets , 1997, ICATPN.

[8]  Luciano Lavagno,et al.  Synthesizing Petri nets from state-based models , 1995, ICCAD.

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

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

[11]  E. McCluskey.  Minimization of Boolean functions , 1956 .

[12]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[13]  Gérard Roucairol,et al.  Linear Algebra in Net Theory , 1979, Advanced Course: Net Theory and Applications.

[14]  Kurt Lautenbach.  Linear Algebraic Techniques for Place/Transition Nets , 1986, Advances in Petri Nets.

[15]  K. Hamaguchi.  Design verification of asynchronous sequential circuits using symbolic model checking , 1992 .

[16]  Tomohiro Yoneda,et al.  BDDs vs. Zero-Suppressed BDDs: for CTL Symbolic Model Checking of Petri Nets , 1996, FMCAD.

[17]  Randal E. Bryant,et al.  Efficient implementation of a BDD package , 1991, DAC '90.