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Liveness and home states in equal conflict systems

  • Enrique Teruel
  • Manuel Silva
Full Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 691)

Abstract

Structure theory is a branch of net theory devoted to investigate the relationship between the structure and the behaviour of net models. Many of its powerful results have been derived for some subclasses of ordinary (i.e. all weights one) Place/Transition net systems. Nevertheless, weights may be very convenient to properly model systems with bulk services and arrivals. They can be implemented by means of ordinary subnets, but then the original structure of the net becomes too complex, even in the simplest cases, to be amenable of some interesting structural analysis techniques.

We present here some results regarding the structure theory of a subclass of (weighted) Place/Transition systems that naturally generalizes the ordinary subclass of Free Choice systems: Equal Conflict systems. We concentrate on a couple of important results concerning the relationship between the structure (in particular, represented by the state equation) and the behaviour. Actually, we show that liveness of bounded Equal Conflict systems can be decided verifying that there is no solution to a linear system of inequalities in the integer domain, and that live and bounded Equal Conflict systems have home states.

Keywords

Place/Transition Net Systems Structure Theory Equal Conflict Systems 

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References

  1. [BCDE 90]
    E. Best, L. Cherkasova, J. Desel, J. Esparza. Characterisation of Home States in Free Choice Systems. Technical Report 9/90, Institut für Informatik, Universität Hildesheim.Google Scholar
  2. [Best 87]
    E. Best. Structure Theory of Petri Nets: the Free Choice Hiatus. In APN 86, LNCS 254:168–205. Springer-Verlag.Google Scholar
  3. [BV 84]
    E. Best, K. Voss. Free Choice Systems Have Home States. Acta Informatica 21:89–100.Google Scholar
  4. [Colom 89]
    J.M. Colom. Análisis Estructural de Redes de Petri. Programación Lineal y Geometría Convexa. PhD Thesis, Dpto. Ing. Eléctrica e Informática, Universidad de Zaragoza.Google Scholar
  5. [CS 91]
    J.M. Colom, M. Silva. Improving the Linearly Based Characterization of P/T Nets. In APN 90, LNCS 483:113–145. Springer-Verlag.Google Scholar
  6. [ES 91]
    J. Esparza, M. Silva. On the Analysis and Synthesis of Free Choice Systems. In APN 90, LNCS 483:243–286. Springer-Verlag.Google Scholar
  7. [Hack 72]
    M.H.T. Hack. Analysis of Production Schemata by Petri Nets. M.S.Thesis, Project MAC TR-94, MIT, Cambridge, Massachusetts. (Corrections in Computation Structures Note 17, 1974.)Google Scholar
  8. [Murata 89]
    T. Murata. Petri Nets: Properties, Analysis and Applications. In Procs. IEEE 77,4:541–580. Google Scholar
  9. [NW 88]
    G.L. Nemhauser, L.A. Wolsey. Integer and Combinatorial Optimization. Wiley.Google Scholar
  10. [Silva 85]
    M. Silva. Las Redes de Petri: en la Aulomática y la Informatica. AC.Google Scholar
  11. [TCCS 92]
    E. Teruel, P. Chrzastowski-Wachtel, J.M. Colom, M. Silva. On Weighted T-systems. In Applications and Theory of Petri Nets 1992, LNCS 616:348–367. Springer-Verlag.Google Scholar
  12. [TCS 92]
    E. Teruel, J.M. Colom, M. Silva. Linear Analysis or Deadlock-Freeness of Petri Net Models. Technical Report GISI-RR-92-29, Dpto. Ing. Eléctrica e Informática, Universidad de Zaragoza. (To appear in Procs. European Control Conference, ECC '93.)Google Scholar
  13. [TV 84]
    P.S. Thiagarajan, K. Voss. A Fresh Look at Free Choice Nets. Information and Control 61,2:85–113.Google Scholar
  14. [Vogler 89]
    W. Vogler. Live and Bounded Free Choice Nets have Home States. Petri Net Newsletter 32:18–21.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Enrique Teruel
    • 1
  • Manuel Silva
    • 1
  1. 1.Departamento de Ingeniería Eléctrica e InformáticaCentro Politécnico Superior de Ingenieros de la Universidad de ZaragozaZaragozaSpain

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