Bounded nondeterminism and the approximation induction principle in process algebra

  • R. J. van Glabbeek
Contributed Papers Semantics Of Parallelism
Part of the Lecture Notes in Computer Science book series (LNCS, volume 247)

Abstract

This paper presents a new semantics of ACPτ, the Algebra of Communicating Processes with abstraction. This leads to a term model of ACPτ which is isomorphic to the model of process graphs modulo rooted τδ-bisimulation of Baeten, Bergstra & Klop

In this model, the Recursive Definition Principle (RDP), the Commutativity of Abstraction (CA) and Koomen's Fair Abstraction Rule (KFAR) are satisfied, but the Approximation Induction Principle (AIP) is not. The combination of these four principles is proven to be inconsistent, while any combination of three of them is not.

In [2] a restricted version of AIP is proved valid in the graph model. This paper proposes a simpler and less restrictive version of AIP, not containing guarded recursive specifications as a parameter, which is still valid. This infinitary rule is formulated with the help of a family Bn of unary predicates, expressing bounded nondeterminism.

1980 Mathematics Subject Classification (version 1985)

68Q10 68Q45 68Q55 68N15 

1982 CR Categories

F.1.2 F.3.2 F.4.3 D.3.1 

Key Words & Phrases

Concurrency Process algebra ACP Approximation Induction Principle Recursion Abstraction Fairness Liveness Consistency Bisimulation Bounded Nondeterminism 

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References

  1. [1]
    J.C.M. Baeten, J.A. Bergstra & J.W. Klop, Conditional axioms and α/β calculus in process algebra, report CS-R8502, Centrum voor Wiskunde en Informatica, Amsterdam 1985, to appear in: Proc. IFIP Conference on Formal Description of Programming Concepts, Gl. Avernaes 1986, (M. Wirsing, ed.), North-Holland.Google Scholar
  2. [2]
    J.C.M. Baeten, J.A. Bergstra & J.W. Klop, On the consistency of Koomen's Fair Abstraction Rule, report CS-R8511, Centrum voor Wiskunde en Informatica, Amsterdam 1985, to appear in Theoretical Computer Science.Google Scholar
  3. [3]
    J.W. de Bakker & J.I. Zucker, Processes and the denotational semantics of concurrency, Information & Control 54 (1/2), pp. 70–120, 1982.Google Scholar
  4. [4]
    J.A. Bergstra & J.W. Klop, Algebra of communicating processes, Proc. of the CWI Symp. Math. & Comp. Sci., eds. J.W. de Bakker, M. Hazewinkel & J.K. Lenstra, Amsterdam 1986.Google Scholar
  5. [5]
    J.A. Bergstra & J.W. Klop, Algebra of communicating processes with abstraction, Theoretical Computer Science 37(1), pp. 77–121, 1985.Google Scholar
  6. [6]
    J.A. Bergstra, J.W. Klop & E.-R. Olderog, Failures without chaos: a new process semantics with fair abstraction, report CS-R8625, Centrum voor Wiskunde en Informatica, Amsterdam 1986, to appear in: Proc. IFIP Conference on Formal Description of Programming Concepts, Gl. Avernaes 1986, (M. Wirsing, ed.), North-Holland.Google Scholar
  7. [7]
    S.D. Brookes, C.A.R. Hoare & W. Roscoe, A theory of communicating sequential processes, Journal ACM 31(3), pp. 560–599, 1984.Google Scholar
  8. [8]
    R.J. van Glabbeek, Bounded nondeterminism and the approximation induction principle in process algebra, report CS-R8634, Centrum voor Wiskunde en Informatica, Amsterdam 1986.Google Scholar
  9. [9]
    G.J. Milne, CIRCAL and the representation of communication, concurrency, and time, Transactions on Programming Languages and Systems (ACM) 7(2), pp. 270–298, 1985.Google Scholar
  10. [10]
    R. Milner, A calculus for communicating systems, Springer LNCS 92, 1980.Google Scholar
  11. [11]
    R. Milner, Lectures on a calculus for communicating systems, Seminar on Concurrency, Springer LNCS 197, pp. 197–220, 1985.Google Scholar
  12. [12]
    D.M.R. Park, Concurrency and automata on infinite sequences, Proc. 5th GI Conference, Springer LNCS 104, 1981.Google Scholar
  13. [13]
    W. Reisig, Petri Nets, An Introduction, EATCS Monographs on Theoretical Computer Science, Springer-Verlag 1985.Google Scholar
  14. [14]
    M. Rem, Partially ordered computations, with applications to VLSI design, Proc. 4th Advanced Course on Foundations of Computer Science, part 2, (eds.) J.W. de Bakker & J. van Leeuwen, Tract 159, Mathematisch Centrum, Amsterdam 1983.Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • R. J. van Glabbeek
    • 1
  1. 1.Centre for Mathematics and Computer ScienceAmsterdamThe Netherlands

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