A Method Based on Depth-first Search to Compute All Minimal Siphons

Minimal siphons play an important role in the development of deadlock control policies for discrete event system modeled by Petri net. A new algorithm based on depth-first search of problem decomposition process is proposed to compute all minimal siphons in an ordinary Petri net. The algorithm can reduce the number of problems in the problem list. The proposed algorithm can solve the problem of high requirement for computer memory in computing all minimal siphons and decrease the memory consumption because the computer memory size is closely related to the number of problems in the problem list. Some examples are used to illustrate the superiority of the proposed algorithm.

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

[2]  Jun Lu,et al.  A Pervasive Computing Model of Internet of Things based on Computing Area Network , 2012, J. Comput..

[3]  Roberto Cordone,et al.  Some results on the computation of minimal siphons in Petri nets , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[4]  Yen-Liang Pan.  An Efficient Deadlock Prevention Policy for Flexible Manufacturing Systems Using the Theory of Regions and Selective Siphon Method , 2012 .

[5]  MengChu Zhou,et al.  Optimal Petri-Net-Based Polynomial-Complexity Deadlock-Avoidance Policies for Automated Manufacturing Systems , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[6]  Yue Li,et al.  A Literature Review of Deadlock Prevention Policy Based on Petri Nets for Automated Manufacturing Systems , 2012 .

[7]  Jonghun Park,et al.  On the “Counter-Example” in the Article “Max $^{\prime}$-Controlled Siphons for Liveness of $S^{3}PGR^{2}$” Regarding the Results in “Deadlock Avoidance in Sequential Resource Allocation Systems With Multiple Resource Acquisitions and Flexible Routings” , 2001, IEEE Transactions on Automatic Control.

[8]  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.

[9]  MengChu Zhou,et al.  Supervisor Design to Enforce Production Ratio and Absence of Deadlock in Automated Manufacturing Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[10]  MengChu Zhou,et al.  On Siphon Computation for Deadlock Control in a Class of Petri Nets , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[11]  Yi-Sheng Huang,et al.  A siphon-based deadlock prevention policy for flexible manufacturing systems , 2005, 2005 IEEE International Conference on Systems, Man and Cybernetics.

[12]  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.

[13]  Guangcai Cui,et al.  Intelligent PID Controller on Soft Computing , 2012, J. Comput..

[14]  Dong Wang,et al.  A Fast Convergence Deadlock Control Strategy of Petri Nets Based on MIP Algorithm , 2012 .

[15]  MengChu Zhou,et al.  Deadlock Prevention Based on Structure Reuse of Petri Net Supervisors for Flexible Manufacturing Systems , 2012, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[16]  MengChu Zhou,et al.  Deadlock Prevention for a Class of Petri Nets With Uncontrollable and Unobservable Transitions , 2012, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[17]  Wei Qiu,et al.  Research on Real-Time Software Development Approach , 2012, J. Softw..

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

[19]  Rongming Zhu.  A deadlock prevention approach for flexible manufacturing systems with uncontrollable transitions in their Petri net models , 2012 .

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

[21]  Zhiwu Li,et al.  Petri Net Based Deadlock Prevention Approach for Flexible Manufacturing Systems , 2011 .

[22]  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.

[23]  MengChu Zhou,et al.  A Method to Compute Strict Minimal Siphons in a Class of Petri Nets Based on Loop Resource Subsets , 2012, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[24]  Lei Peng,et al.  A Novel Differential Evolution with Uniform Design for Continuous Global Optimization , 2012, J. Comput..