Advertisement

Algebraic formulations of trace theory

  • N. J. Drost
Selected Presentations
Part of the Lecture Notes in Computer Science book series (LNCS, volume 527)

Abstract

In this paper mathematical models are given for Trace Theory as described in [Rem85] and [Kal86]. They model a process by a trace structure: a pair consisting of an alphabet and a trace set over this alphabet. We show that in fact two incompatible process models are used, and we devise a new model that has all essential characteristics of the two former models. A complete axiomatization of this model is given. It is shown that a distinction between successful and unsuccessful termination is needed to effectuate associativity of parallel composition with communication in the presence of sequential composition. Two operators generating infinite processes are added, which makes a verification of the alternating bit protocol possible.

Key words and phrases

concurrency process algebra trace models complete axiomatization infinite processes verification alternating bit protocol 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AH88]
    Aceto, L., and M. Hennessy: Termination, Deadlock and Divergence. Report 6/88, Computer Science, Univ. of Sussex, Brighton BN1 9QH. 1988.Google Scholar
  2. [BW90]
    Baeten, J.M.C. and W.P. Weijland: Process Algebra. Cambridge University Press, Cambridge, 1990.Google Scholar
  3. [BG89]
    Baeten, J.M.G. and R.J. van Glabbeek: Abstraction and Empty Process in Process Algebra. Fund. Inf. XII, pp. 221–241. 1989.Google Scholar
  4. [BM88]
    Bakker, J.W. de, and J.-J.Ch. Meyer: Metric Semantics for Concurrency. BIT 28, pp. 504–529. 1988.Google Scholar
  5. [BK84a]
    Bergstra, J.A., and J.W. Klop: The algebra of Recursively Defined Processes and the the Algebra of Regular Processes. Proceedings 11th ICALP, LNCS 172, pp. 82–95. 1984.Google Scholar
  6. [BK84b]
    Bergstra, J.A., and J.W. Klop: Verification of an Alternating Bit Protocol by means of Process Algebra. CWI report CS-R8404, Amsterdam. 1984.Google Scholar
  7. [BK85]
    Bergstra, J.A., and J.W. Klop: Algebra of Communicating Processes with Abstraction. TCS 37(1): pp. 77–121. 1985.Google Scholar
  8. [BKO88]
    Bergstra, J.A., J.W. Klop, and E.-R. Olderog: Readies and Failures in the Algebra of Communicating Processes. Siam J. Comput. 17(6): pp. 1134–1177. 1988.Google Scholar
  9. [Dro90]
    Drost, N.: Algebraic Formulations of Trace Theory. Report P9004, Programming Research Group, Dept. of Math. and Comp. Sci., Univ. of Amsterdam. 1990.Google Scholar
  10. [Gla90]
    Glabbeek, R.J. van: Comparative Concurrency Semantics, with Refinement of Actions. Ph.D.Thesis, Free University, Amsterdam. 1990.Google Scholar
  11. [Hoa85]
    Hoare, C.A.R.: Communicating Sequential Processes. Prentice Hall, London. 1985.Google Scholar
  12. [Kal86]
    Kaldewaij, A.: A Formalism for Concurrent Processes. Ph.D.Thesis, Technical University, Eindhoven. 1986.Google Scholar
  13. [Mil89]
    Milner, R.: Communication and Concurrency. Prentice Hall, London. 1989.Google Scholar
  14. [OH86]
    Olderog, E.-R. and C.A.R. Hoare: Specification-Oriented Semantics for Communicating Processes. Acta Inf. 23, pp. 9–66. 1986.Google Scholar
  15. [Rem85]
    Rem, M.: Concurrent Computations and VLSI Circuits. in: M. Broy (ed.): Control Flow and Data Flow: Concepts of Distributed Programming, pp. 399–437. Springer, Berlin. 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • N. J. Drost
    • 1
  1. 1.Programming Research GroupUniversity of AmsterdamAmsterdamThe Netherlands

Personalised recommendations