Advertisement

Priority Rewrite Systems for OSOS Process Languages

  • Irek Ulidowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2761)

Abstract

We propose a procedure for generating a Priority Rewrite System (PRS) for an arbitrary process language in the OSOS format. Rewriting of process terms is sound for bisimulation and head normalising within the produced PRSs. For a subclass of process languages representing finite behaviours the generated PRSs are strongly normalising (terminating), confluent and complete for bisimulation for closed terms modulo associativity and commutativity of the choice operator. We illustrate the usefulness of our procedure with several examples.

Keywords

Process Language Operational Semantic Transition Rule Label Transition System Reduction Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Aceto, L.: Deriving complete inference systems for a class of GSOS languages generating regular behaviours. In: Jonsson, B., Parrow, J. (eds.) CONCUR 1994. LNCS, vol. 836. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  2. 2.
    Aceto, L., Bloom, B., Vaandrager, F.W.: Turning SOS rules into equations. Information and Computation 111, 1–52 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Aceto, L., Fokkink, W., Verhoef, C.: Structured operational semantics. In: Bergstra, J.A., Ponse, A., Smolka, S.A. (eds.) Handbook of Process Algebra, pp. 197–292. Elsevier Science, Amsterdam (2001)CrossRefGoogle Scholar
  4. 4.
    Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, Cambridge (1998)Google Scholar
  5. 5.
    Baeten, J.C.M.: Embedding untimed into timed process algebra: the case for explicit termination. In: Aceto, L., Victor, B. (eds.) EXPRESS 2000. BRICS (2000)Google Scholar
  6. 6.
    Baeten, J.C.M., Bergstra, J.A., Klop, J.W.: Syntax and defining equations for an interrupt mechanism in process algebra. Fundamenta Informaticae XI(2), 127–168 (1986)MathSciNetGoogle Scholar
  7. 7.
    Baeten, J.C.M., Bergstra, J.A., Klop, J.W., Weijland, W.P.: Term-rewriting systems with rule priorities. Theoretical Computer Science 67, 283–301 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Baeten, J.C.M., de Vink, E.P.: Axiomatizing GSOS with termination. In: Alt, H., Ferreira, A. (eds.) STACS 2002. LNCS, vol. 2285, p. 583. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  9. 9.
    Baeten, J.C.M., Weijland, W.P.: Process Algebra. Cambridge Tracts in Theoretical Computer Science, vol. 18. Cambridge University Press, Cambridge (1990)CrossRefGoogle Scholar
  10. 10.
    Bloom, B., Istrail, S., Meyer, A.R.: Bisimulation can’t be traced. Journal of the ACM 42(1), 232–268 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Bosscher, D.J.B.: Term rewriting properties of SOS axiomatisations. In: Proceedings of TACS 1994. LNCS, vol. 1000. Springer, Heidelberg (1994)Google Scholar
  12. 12.
    Cleaveland, R., Sims, S.: The Concurrency Workbench of New Century, http://www.cs.sunysb.edu/~cwb/
  13. 13.
    Hennessy, M., Regan, T.: A process algebra for timed systems. Information and Computation 117, 221–239 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Kennaway, J.R., de Vries, F.J.: Infinitary rewriting. In: Terese, J.W. (ed.) Term Rewriting Systems. Cambridge University Press, Cambridge (2002)Google Scholar
  15. 15.
    Klop, J.W.: Term rewriting systems. In: Abramsky, S., Gabbay, D., Maibaum, T. (eds.) Handbook of Logic in Computer Science, pp. 1–116. Oxford University Press, Oxford (1992)Google Scholar
  16. 16.
    Léonard, L., Leduc, G.: A formal definition of time in LOTOS. Formal Aspects of Computing 10, 248–266 (1998)zbMATHCrossRefGoogle Scholar
  17. 17.
    Milner, R.: A complete inference system for a class of regular behaviours. Journal of Computer System Sciences 28, 439–466 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Milner, R.: Communication and Concurrency. Prentice Hall, Englewood Cliffs (1989)zbMATHGoogle Scholar
  19. 19.
    Nicollin, X., Sifakis, J.: The algebra of timed processes, ATP: theory and application. Information and Computation 114, 131–178 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Plotkin, G.: A structural approach to operational semantics. Technical Report DAIMI FN-19, Aarhus University (1981)Google Scholar
  21. 21.
    Sakai, M., Toyama, Y.: Semantics and strong sequentiality of priority term rewriting systems. Theoretical Computer Science 208, 87–110 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Sims, S.: The Process Algebra Compiler, http://www.reactive-systems.com/pac/
  23. 23.
    Ulidowski, I.: Local Testing and Implementable Concurrent Processes. PhD thesis, Imperial College, University of London (1994)Google Scholar
  24. 24.
    Ulidowski, I.: Finite axiom systems for testing preorder and De Simone process languages. Theoretical Computer Science 239(1), 97–139 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  25. 25.
    Ulidowski, I.: Priority rewrite systems forOSOSprocess languages. Technical Report 2002/30, Department of Mathematics and Computer Science, Leicester University (2002), Updated version at http://www.mcs.le.ac.uk/~iulidowski/PRS.html
  26. 26.
    Ulidowski, I., Phillips, I.C.C.: Ordered SOS rules and process languages for branching and eager bisimulations. Information and Computation 178(1), 180–213 (2002)zbMATHMathSciNetGoogle Scholar
  27. 27.
    Ulidowski, I., Yuen, S.: General process languages with time. Technical Report 2000/41, Department of Mathematics and Computer Science, Leicester University (2000)Google Scholar
  28. 28.
    van de Pol, J.: Operational semantics of rewriting with priorities. Theoretical Computer Science 200, 289–312 (1998)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Irek Ulidowski
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of LeicesterLeicesterUK

Personalised recommendations