This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
An Equivalence Theorem for Labeled Marked Graphs
August 1994 (vol. 5 no. 8)
pp. 886-891

Petri nets and their languages are a useful model of systems exhibiting concurrentbehavior. The sequential language associated with a given Petri net S consists of allpossible firing sequences of S, where each element of a firing sequence is a singletransition. The concurrent language associated with S consists of all possible concurrentfiring sequences of S, where each element of a concurrent firing sequence is a set oftransitions. The sequential language and the concurrent language associated with S aredenoted by (L)(S) and (/spl pi/)(S), respectively. In this paper, we consider an importantspecial ease of Petri nets, called labeled marked graphs. The main result derived in thispaper states that if /spl Gammasub 1/ and /spl Gammasub 2/ are two structurallydeterministic labeled marked graphs, then (L)(/spl Gammasub 1/)=L(/spl Gammasub 2/)/spl rlhar2spl pi/(/spl Gammasub 1/)=/spl pi/(/spl Gammasub 2/).

[1] J. L. Peterson,Petri Net Theory and the Modeling of Systems. Englewood Cliffs, NJ: Prentice-Hall, 1981.
[2] J. L. Peterson, "Petri nets,"ACM Comput. Surveys, vol. 9, no. 3, pp. 223-252, Sept. 1977.
[3] J. L. Baer, "Techniques to exploit parallelism," inParallel Processing Systems. D. J. Evans, Ed. Cambridge, U.K.: Cambridge University Press, 1984, pp. 76-99.
[4] E. Best and R. Devillers, "Sequential and concurrent behavior in Petri net theory,"Theoretical Comput. Sci., vol. 55, pp. 87-136, 1987.
[5] G. Rozenberg and R. Verraedt, "Subset languages of Petri nets I: The relationship to string languages and normal forms,"Theoretical Comput. Sci., vol. 26, pp. 301-326, 1983.
[6] M. Yoeli, "Specification and verification of asynchronous circuits using marked graphs," inConcurrency and Nets: Advances in Petri Nets, K. Voss, H. J. Genrich, and G. Rozenberg, Eds. New York: Springer-Verlag, 1987, pp. 605-622.
[7] F. Commoner, A. W. Holt, S. Even, and A. Pnueli, "Marked directed graphs,"J. Comput. Syst. Sci., vol. 5, pp. 511-523, 1971.
[8] Y. Malka and S. Rajsbaum, "Analysis of distributed algorithms based on recurrence relations,"Proc. 5th Workshop on Distributed Algorithms on Graphs (WDAG-5), 1991, pp.
[9] S. Rajsbaum, "Stochastic marked graphs,"Proc. 4th Int. Workshop on Petri Nets and Performance Models (PNPM91), 1991, pp.
[10] C. V. Ramamoorthy and G. S. Ho, "Performance evaluation of asynchronous concurrent systems using Petri nets,"IEEE Trans. Software Eng., vol. 6, pp. 440-449, May 1989.
[11] M. Yoeli and T. Etzion, "Behavioral equivalence of concurrent systems," inApplications and Theory of Petri Nets, A. Pagoni and G. Rozenberg, Eds.Informatik Fachberichte 66, pp. 292-305, 1983.
[12] C. L. Seitz, "System timing," inIntroduction to VLSI Systems, C. Mead and L. Conway, Eds. Reading, MA: Addison-Wesley, 1980, pp. 218-262.

Index Terms:
Index TermsPetri nets; formal languages; multiprocessing systems; equivalence theorem; labeledmarked graphs; Petri nets; structural determinism; sequential language; firing sequences;transitions; concurrent language
Citation:
Y. Wolfstahl, M. Yoeli, "An Equivalence Theorem for Labeled Marked Graphs," IEEE Transactions on Parallel and Distributed Systems, vol. 5, no. 8, pp. 886-891, Aug. 1994, doi:10.1109/71.298217
Usage of this product signifies your acceptance of the Terms of Use.