Computation of Minimal Siphons in Petri Nets by Using Binary Decision Diagrams

Siphons play an important role in the development of deadlock control methods by using Petri nets. The number of siphons increases exponentially with respect to the size of a Petri net. This article presents a symbolic approach to the computation of minimal siphons in Petri nets by using binary decision diagrams (BDD). The siphons of a Petri net can be found via a set of logic conditions. The logic conditions are symbolically modeled by using Boolean algebras. The operations of Boolean algebras are implemented by BDD that are capable of representing large sets of siphons with small shared data structures. The proposed method first uses BDD to compute all siphons of a Petri net and then a binary relation is designed to extract all minimal siphons. Finally, by using a number of examples, the efficiency of the proposed method is verified through different-sized problems.

[1]  ZhiWu Li,et al.  Liveness Enforcing Supervision in Video Streaming Systems using Siphons , 2009, J. Inf. Sci. Eng..

[2]  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.

[3]  Roberto Cordone,et al.  Enumeration algorithms for minimal siphons in Petri nets based on place constraints , 2005, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

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

[5]  MengChu Zhou,et al.  An improved iterative synthesis method for liveness enforcing supervisors of flexible manufacturing systems , 2006 .

[6]  MengChu Zhou,et al.  Liveness Enforcing Supervision of Video Streaming Systems Using Nonsequential Petri Nets , 2009, IEEE Transactions on Multimedia.

[7]  Hyunbo Cho,et al.  A structured approach to deadlock detection, avoidance and resolution in flexible manufacturing systems , 1994 .

[8]  Roberto Cordone,et al.  Combined Siphon and Marking Generation for Deadlock Prevention in Petri Nets , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[9]  H. Andersen.  An Introduction to Binary Decision Diagrams , 1997 .

[10]  Zhiwu Li,et al.  Efficient deadlock prevention policy in automated manufacturing systems using exhausted resources , 2009 .

[11]  ChenYufeng,et al.  Computation of Minimal Siphons in Petri Nets by Using Binary Decision Diagrams , 2013 .

[12]  Roberto Cordone,et al.  Selective Siphon Control for Deadlock Prevention in Petri Nets , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[13]  MengChu Zhou,et al.  Clarifications on the Definitions of Elementary Siphons in Petri Nets , 2006, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[14]  MengChu Zhou,et al.  Deadlock control of concurrent manufacturing processes sharing finite resources , 2008 .

[15]  MuDer Jeng,et al.  A Maximally Permissive Deadlock Prevention Policy for FMS Based on Petri Net Siphon Control and the Theory of Regions , 2008, IEEE Transactions on Automation Science and Engineering.

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

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

[18]  Zhiwu Li,et al.  Modeling and scheduling for manufacturing grid workflows using timed Petri nets , 2009 .

[19]  E. Pastor,et al.  Symbolic Analysis of Bounded Petri Nets , 2001, IEEE Trans. Computers.

[20]  MengChu Zhou,et al.  Control of Elementary and Dependent Siphons in Petri Nets and Their Application , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[21]  X. Xie,et al.  Siphon-Based Deadlock Prevention Policy for Flexible Manufacturing Systems , 2006, IEEE Trans. Syst. Man Cybern. Part A.

[22]  Zhiwu Li,et al.  Smart deadlock prevention policy for flexible manufacturing systems using Petri nets , 2009 .

[23]  Nidhal Rezg,et al.  Design of a live and maximally permissive Petri net controller using the theory of regions , 2003, IEEE Trans. Robotics Autom..

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

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

[26]  MengChu Zhou,et al.  Two-Stage Method for Synthesizing Liveness-Enforcing Supervisors for Flexible Manufacturing Systems Using Petri Nets , 2006, IEEE Transactions on Industrial Informatics.

[27]  Gianfranco Ciardo,et al.  Efficient Reachability Set Generation and Storage Using Decision Diagrams , 1999, ICATPN.

[28]  Zhiwu Li,et al.  Deadlock Resolution in Automated Manufacturing Systems: A Novel Petri Net Approach , 2009 .

[29]  MengChu Zhou,et al.  An Effective Algorithm to Find Elementary Siphons in a Class of Petri Nets , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[30]  Frank M. Brown,et al.  Boolean reasoning - the logic of boolean equations , 1990 .

[31]  Zhiwu Li,et al.  An optimal-elementary-siphons-based iterative deadlock prevention policy for flexible manufacturing systems , 2008 .

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

[33]  ZhiWu Li,et al.  Local and global deadlock prevention policies for resource allocation systems using partially generated reachability graphs , 2009, Comput. Ind. Eng..