Enumeration algorithms for minimal siphons in Petri nets based on place constraints

The paper addresses the problem of enumerating minimal siphons in an ordinary Petri net. The algorithms developed in this work recursively use a problem partitioning procedure to reduce the original search problem to multiple simpler search subproblems. Each subproblem has specific additional place constraints with respect to the original problem. Some results on algorithm correctness, convergence, and computational complexity are provided, as well as an experimental evaluation of performance. The algorithms can be applied to enumerate minimal, place-minimal siphons, or even siphons that are minimal with respect to given subsets of places.

[1]  K. Lautenback.  Linear algebraic calculation of deadlocks and traps , 1987 .

[2]  Wolfgang Reisig.  Petri Nets: An Introduction , 1985, EATCS Monographs on Theoretical Computer Science.

[3]  MuDer Jeng,et al.  Generating minimal siphons and traps for Petri nets , 1996, 1996 IEEE International Conference on Systems, Man and Cybernetics. Information Intelligence and Systems (Cat. No.96CH35929).

[4]  Manuel Silva Suárez,et al.  A New Technique for Finding a Generating Family of Siphons, Traps and st-Components. Application to Colored Petri Nets , 1991, Applications and Theory of Petri Nets.

[5]  M. Yamauchi,et al.  Finding Minimal Siphons in General Petri Nets , 1996 .

[6]  MuDer Jeng,et al.  Deadlock prevention policy based on Petri nets and siphons , 2001 .

[7]  MengChu Zhou,et al.  Elementary siphons of Petri nets and their application to deadlock prevention in flexible manufacturing systems , 2004, IEEE Trans. Syst. Man Cybern. Part A.

[8]  Roberto Cordone,et al.  Characterization of minimal and basis siphons with predicate logic and binary programming , 2002, Proceedings. IEEE International Symposium on Computer Aided Control System Design.

[9]  Javier Martínez,et al.  A Petri net based deadlock prevention policy for flexible manufacturing systems , 1995, IEEE Trans. Robotics Autom..

[10]  Toshimasa Watanabe,et al.  Extracting siphons containing a specified set of places in a Petri net , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).

[11]  Kamel Barkaoui,et al.  Deadlocks and traps in Petri nets as Horn-satisfiability solutions and some related polynomially solvable problems , 1990, Discret. Appl. Math..

[12]  Kamel Barkaoui,et al.  A Polynomial-Time Graph Algorithm to Decide Liveness of Some Basic Classes of Bounded Petri Nets , 1992, Application and Theory of Petri Nets.

[13]  Masahiro Yamaguchi,et al.  Algorithms for Extracting Minimal Siphons Containing Specified Places in a General Petri Net (Special Section on Concurrent Systems Technology) , 1999 .

[14]  MuDer Jeng,et al.  Petri nets liveness analysis by minimal siphons , 1997, 1997 IEEE 6th International Conference on Emerging Technologies and Factory Automation Proceedings, EFTA '97.

[15]  Panos J. Antsaklis,et al.  Supervisory Control of Discrete Event Systems Using Petri Nets , 1998, The International Series on Discrete Event Dynamic Systems.

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

[17]  Feng Chu,et al.  Deadlock analysis of Petri nets using siphons and mathematical programming , 1997, IEEE Trans. Robotics Autom..

[18]  Erwin R. Boer,et al.  Generating basis siphons and traps of Petri nets using the sign incidence matrix , 1994 .