Acta Informatica

, Volume 52, Issue 1, pp 35–60 | Cite as

Synthesis and reengineering of persistent systems

  • Eike BestEmail author
  • Raymond Devillers
Original Article


In formal verification, a structural object, such as a program or a Petri net, is given, and questions are asked about its behaviour. In system synthesis, conversely, a behavioural object, such as a transition system, is given, and questions are asked about the existence of a structural object realising this behaviour. In system reengineering, one wishes to transform a given system into another one, with similar behaviour and other properties not enjoyed by the original system. This paper addresses synthesis and reengineering problems in the specific framework of finite-state labelled transition systems, place/transition Petri nets, and behaviour isomorphisms. Since algorithms solving these problems are prohibitively time-consuming in general, it is interesting to know whether they can be improved in restricted circumstances, and whether direct correspondences can be found between classes of behavioural and classes of structural objects. This paper is concerned with persistent systems, which occur in hardware design and in various other applications. We shall derive exact conditions for a finite persistent transition system to be isomorphically implementable by a bounded Petri net exhibiting persistence in a structural way, and derive an efficient algorithm to find such a net if one exists. For the class of marked graph Petri nets, this leads to an exact characterisation of their state spaces.



We are grateful to Philippe Darondeau, Hanna Klaudel, and Elisabeth Pelz for discussions. It was Philippe, in particular, who promoted the general idea of trying to characterise the state spaces of classes of Petri nets. The first author would like to thank Université de Rennes, Université d’Évry-val-d’Essonne, Université Paris Est Créteil Val de Marne, and Uniwersytet Mikołaja Kopernika Toruń (project POKL.04.01.01-00-081/10) for supporting research stays. The authors are grateful to two reviewers for their very helpful remarks. We would also like to thank the editors, Rob van Glabbeek, Ursula Goltz and Ernst-Rüdiger Olderog, for inviting us to take part in the celebration of 25 years of Combining Compositionality and Concurrency and to submit a contribution.


  1. 1.
    Badouel, É., Bernardinello, L., Darondeau, P.: The synthesis problem for elementary nets is NP-complete. Theoret. Comput. Sci. 186, 107–134 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Badouel, É., Bernardinello, L., Darondeau, P.: Polynomial algorithms for the synthesis of bounded nets. In: Mosses, P.D., Nielsen, M., Schwartzbach, M.I. (eds.) TAPSOFT 1995, Lecture Notes in Computer Science, vol. 915, pp. 364–378 (1995)Google Scholar
  3. 3.
    Badouel, É., Darondeau, P.: Theory of regions. In: Reisig, W., Rozenberg, G. (eds.) Lectures on Petri Nets I: Basic Model, LNCS vol. 1491, pp. 529–586. Springer (1998)Google Scholar
  4. 4.
    Best, E., Darondeau, P.: A decomposition theorem for finite persistent transition systems. Acta Inform. 46, 237–254 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Best, E., Darondeau, P.: Separability in persistent Petri nets. Fundam. Inform. 112, 1–25 (2011)MathSciNetGoogle Scholar
  6. 6.
    Best, E., Darondeau, P.: Petri net distributability. In: Virbitskaite, I., Voronkov, A. (eds.) PSI’11, Novosibirsk, LNCS vol. 7162, pp. 1–18. Springer (2011)Google Scholar
  7. 7.
    Best, E., Devillers, R.: Persistent Systems with Unique Minimal Cyclic Parikh Vectors. Technical report 02–14, Dep. Informatik, Carl von Ossietzky Universität Oldenburg, 80 pp (February 2014)Google Scholar
  8. 8.
    Best, E., Devillers, R.: A Characterisation of the state spaces of live and bounded marked graphs. In: Dediu, A.-H., et al. (eds.) Proceedings of LATA’14 (8th International Conference on Language and Automata Theory and Applications, Madrid, March 2014), LNCS 8370, pp. 161–172. Springer (2014)Google Scholar
  9. 9.
    Best, E., Devillers, R.: Synthesis of persistent systems. In: Ciardo, G., Kindler, E. (eds.) Proceedings of the 35rd International Conference on Application and Theory of Petri Nets and Concurrency (Tunis, August 2014), LNCS 8489, pp. 111–129. Springer (2014)Google Scholar
  10. 10.
    Best, E., Wimmel, H.: Structure theory of Petri nets. In: Jensen, K., et al. (eds.) Proceedings of the Fifth Advanced Course on Petri Nets, Rostock, 2010. ToPNoC VII, vol. 7480 of LNCS, pp. 162–224. Springer, Berlin, Heidelberg (2013)Google Scholar
  11. 11.
  12. 12.
    Carmona, J., Cortadella, J., Khomenko, V., Yakovlev, A.: Synthesis of asynchronous hardware from petri nets. In: Desel, J., Reisig, W., Rozenberg, G. (eds.) Lectures on Concurrency and Petri Nets. Advances in Petri Nets, LNCS vol. 3098, pp. 345–401. Springer (2003)Google Scholar
  13. 13.
    Commoner, F., Holt, A.W., Even, S., Pnueli, A.: Marked directed graphs. J. Comput. Syst. Sci. 5(5), 511–523 (1971)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Crespi-Reghizzi, S., Mandrioli, D.: A decidability theorem for a class of vector-addition systems. Inf. Process. Lett. 3(3), 78–80 (1975)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Desel, J., Reisig, W.: The synthesis problem of Petri nets. Acta Inform. 33, 297–315 (1996)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Devillers, R.: plain.c, pure.c, frag.c: Specially tailored programs written in C++ (described in [7])Google Scholar
  17. 17.
    Ehrenfeucht, A., Rozenberg, G.: Partial 2-structures, part I: basic notions and the representation problem, and part II: state spaces of concurrent systems. Acta Inform. 27(4), 315–368 (1990)CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Farkas, G.: Über die Theorie der Einfachen Ungleichungen. Journal für die Reine und Angewandte Mathematik 124, 1–27 (1902)Google Scholar
  19. 19.
    Genrich, H.J., Lautenbach, K.: Synchronisationsgraphen. Acta Inform. 2, 143–161 (1973)CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Hack, M.H.T.: Analysis of Production Schemata by Petri Nets. M.S. Thesis, D.E.E. MIT, Cambridge Mass. Project MAC-TR 94 (1972)Google Scholar
  21. 21.
    Júlvez, J., Recalde, L., Silva, M.: Deadlock-freeness analysis of continuous mono-T-semiflow Petri nets. IEEE Trans. Autom. Control 51–9, 1472–1481 (2006)CrossRefGoogle Scholar
  22. 22.
    Keller, R.M.: A fundamental theorem of asynchronous parallel computation. In: Processing of the Parallel, LNCS vol. 24, pp. 102–112. Springer (1975)Google Scholar
  23. 23.
    Kondratyev, A., Cortadella, J., Kishinevsky, M., Pastor, E., Roig, O., Yakovlev, A.: Checking signal transition graph implementability by symbolic BDD traversal. In: Proceedings of the European Design and Test Conference, pp. 325–332. Paris, France (1995)Google Scholar
  24. 24.
    Lamport, L.: Arbiter-free synchronization. Distrib. Comput. 16(2/3), 219–237 (2003)CrossRefGoogle Scholar
  25. 25.
    Landweber, L.H., Robertson, E.L.: Properties of conflict-free and persistent Petri nets. JACM 25(3), 352–364 (1978)CrossRefzbMATHMathSciNetGoogle Scholar
  26. 26.
    Recalde, L., Teruel, E., Silva, M.: Autonomous continuous P/T-systems. In: Donatelli, J.K.S. (ed.) Application and Theory of Petri Nets, LNCS vol. 1639, pp. 107–126. Springer, New York (1999)Google Scholar
  27. 27.
    Schlachter, U., et al.:
  28. 28.
    Teruel, E., Chrza̧stowski-Wachtel, P., Colom, J.M., Silva, M.: On Weighted T-Systems. Application and Theory of Petri Nets. Lecture Notes in Computer Science vol. 616, pp. 348–367 (1992)Google Scholar
  29. 29.
    Teruel, E., Colom, J.M., Silva, M.: Choice-free petri nets: a model for deterministic concurrent systems with bulk services and arrivals. IEEE Trans. Syst. Man Cybern. Part A 27–1, 73–83 (1997)CrossRefGoogle Scholar
  30. 30.
    van Glabbeek, R.J., Goltz, U., Schicke, J.-W.: On causal semantics of petri nets (extended abstract). In: Katoen, J.-P., König, B. (eds.) Proceedings of the International Conference on Concurrency Theory (CONCUR 2011), LNCS vol. 6901, pp. 43–59. Springer (2011)Google Scholar
  31. 31.
    van Glabbeek, R.J., Goltz, U., Schicke-Uffmann, J.-W.: On distributability of Petri nets (extended abstract). In: Birkedal, L. (ed.) Proceedings of the FoSSaCS 2012 (held as part of ETAPS), LNCS vol. 7213, pp. 331–345. Springer (2012)Google Scholar
  32. 32.
    Ville, J.: Sur la théorie générale des jeux où intervient l’habileté des joueurs. In: Borel, E. (ed.) Traité du calcul des probabilités et de ses applications, vol 4, pp. 105–113, Gauthiers-Villars (1938)Google Scholar
  33. 33.
    Yakovlev, A.: Designing control logic for counterflow pipeline processor using Petri nets. Form. Methods Syst. Des. 12(1), 39–71 (1998)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Parallel Systems, Department of Computing ScienceCarl von Ossietzky Universität OldenburgOldenburgGermany
  2. 2.Département d’InformatiqueUniversité Libre de BruxellesBrusselsBelgium

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