Hostname: page-component-848d4c4894-sjtt6 Total loading time: 0 Render date: 2024-07-04T06:23:58.500Z Has data issue: false hasContentIssue false
  • English
  • Français

On the axiomatisability of priority

Published online by Cambridge University Press:  01 February 2008

LUCA ACETO ,
TAOLUE CHEN ,
WAN FOKKINK  and
ANNA INGOLFSDOTTIR
LUCA ACETO
Affiliation:
Reykjavík University, Department of Computer Science, Kringlan 1, 103 Reykjavík, Iceland Email: luca@ru.is, annai@ru.is
TAOLUE CHEN
Affiliation:
CWI, Embedded Systems Group, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands
WAN FOKKINK
Affiliation:
CWI, Embedded Systems Group, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands Vrije Universiteit, Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
ANNA INGOLFSDOTTIR
Affiliation:
Reykjavík University, Department of Computer Science, Kringlan 1, 103 Reykjavík, Iceland Email: luca@ru.is, annai@ru.is
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper studies the equational theory of bisimulation equivalence over the process algebra BCCSP extended with the priority operator of Baeten, Bergstra and Klop. We prove that, in the presence of an infinite set of actions, bisimulation equivalence has no finite, sound, ground-complete equational axiomatisation over that language. This negative result applies even if the syntax is extended with an arbitrary collection of auxiliary operators, and motivates the study of axiomatisations using equations with action predicates as conditions. In the presence of an infinite set of actions, it is shown that, in general, bisimulation equivalence has no finite, sound, ground-complete axiomatisation consisting of equations with action predicates as conditions over the language studied in this paper. Finally, sufficient conditions on the priority structure over actions are identified that lead to a finite, ground-complete axiomatisation of bisimulation equivalence using equations with action predicates as conditions.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 18 , Special Issue 1: in memory of Sauro Tulipani , February 2008 , pp. 5 - 28
Copyright
Copyright © Cambridge University Press2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aceto, L., Fokkink, W., Ingolfsdottir, A. and Luttik, B. (2005) CCS with Hennessy's merge has no finite equational axiomatization. Theoretical Computer Science 330 (3)377–405.CrossRefGoogle Scholar
Aceto, L., Fokkink, W., Ingolfsdottir, A. and Nain, S. (2006) Bisimilarity is not finitely based over BPA with interrupt. Theoretical Computer Science 366 (1–2)60–81. (An extended abstract of this paper appeared in Fiadeiro, J. Harman, N. Roggenbach, M. and Rutten, J. (eds.) Proc. 1st Conference on Algebra and Coalgebra in Computer Science (CALCO'05). Springer-Verlag Lecture Notes in Computer Science (2005) 3629 52–66.)CrossRefGoogle Scholar
Baeten, J., Bergstra, J. and Klop, J. W. (1986) Syntax and defining equations for an interrupt mechanism in process algebra. Fundamenta Informaticae IX (2)127–168.CrossRefGoogle Scholar
Baeten, J. and Bergstra, J. (2000) Mode Transfer in Process Algebra. Report CSR00–01, Eindhoven University of Technology.Google Scholar
Bergstra, J. (1985) Put and get primitives for synchronous unreliable message passing. Logic Group Preprint Series 3, Utrecht University, Department of Philosophy.Google Scholar
Bergstra, J. and Klop, J. W. (1984) Process algebra for synchronous communication. Information and Control 60 (1/3)109–137.CrossRefGoogle Scholar
Bloom, B., Istrail, S. and Meyer, A. R. (1995) Bisimulation can't be traced. Journal of the ACM 42 (1)232–268.CrossRefGoogle Scholar
Brinksma, E. (1985) A tutorial on LOTOS. In: Diaz, M. (ed.) Proc. 5th IFIP Workshop on Protocol Specification, Testing and Verification (PSTV'85), North-Holland 171–194.Google Scholar
Camilleri, J. and Winskel, G. (1985) CCS with priority choice. Information and Computation 116 (1)26–37.CrossRefGoogle Scholar
Cleaveland, R. and Hennessy, M. (1990) Priorities in process algebras. Information and Computation 87 (1-2)58–77.CrossRefGoogle Scholar
Cleaveland, R., Lüttgen, G. and Natarajan, V. (2001) Priorities in process algebra. In: Bergstra, J., Ponse, A. and Smolka, S. (eds.) Handbook of Process Algebra, Elsevier 711–765.CrossRefGoogle Scholar
Cleaveland, R., Lüttgen, G., Natarajan, V. and Sims, S. (1996) Priorities for modeling and verifying distributed systems. In: Margaria, T. and Steffen, B. (eds.) Proc. 2nd Workshop on Tools and Algorithms for Construction and Analysis of Systems (TACAS'96). Springer-Verlag Lecture Notes in Computer Science 1055 278–297.CrossRefGoogle Scholar
Dsouza, A. and Bloom, B. (1995) On the expressive power of CCS. In: Thiagarajan, P. S. (ed.) Proc. 15th Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS'95). Springer-Verlag Lecture Notes in Computer Science 1026 309–323.CrossRefGoogle Scholar
van Glabbeek, R. (1990) The linear time-branching time spectrum. In: Baeten, J. and Klop, J. W. (eds.) Proc. 1st Conference on Concurrency Theory: Unification and Extension (CONCUR'90). Springer-Verlag Lecture Notes in Computer Science 458 278–297.CrossRefGoogle Scholar
van Glabbeek, R. (2001) The linear time-branching time spectrum I. The semantics of concrete, sequential processes. In: Bergstra, J., Ponse, A. and Smolka, S. (eds.) Handbook of Process Algebra, Elsevier 3–99.CrossRefGoogle Scholar
Groote, J. F. (1990) A new strategy for proving ω-completeness with applications in process algebra. In: Baeten, J. and Klop, J. W. (eds.) 1st Conference on Concurrency Theory (CONCUR'90). Springer-Verlag Lecture Notes in Computer Science 458 314–331.CrossRefGoogle Scholar
Hennessy, M. and Milner, R. (1985) Algebraic laws for nondeterminism and concurrency. Journal of the ACM 32 (1)137–161.CrossRefGoogle Scholar
ISO (1987) Information processing systems – open systems interconnection – LOTOS – a formal description technique based on the temporal ordering of observational behaviour. ISO/TC97/SC21/N DIS8807.Google Scholar
Mauw, S. (1991) PSF – A Process Specification Formalism, Ph.D. thesis, University of Amsterdam.Google Scholar
Milner, R. (1989) Communication and Concurrency, Prentice-Hall.Google Scholar
Milner, R., Tofte, M., Harper, R. and MacQueen, D. (1987) The Definition of Standard ML (Revised), MIT Press.Google Scholar
Moller, F. (1990a) The importance of the left merge operator in process algebras. In: Paterson, M. (ed.) Proc. 17th Colloquium on Automata and Languages (ICALP'90). Springer-Verlag Lecture Notes in Computer Science 443 752–764.CrossRefGoogle Scholar
Moller, F. (1990b) The nonexistence of finite axiomatisations for CCS congruences. In: Proc. 5th Symposium on Logic in Computer Science (LICS'90), IEEE Computer Society Press 142–153.Google Scholar
Sewell, P. (1997) Nonaxiomatisability of equivalences over finite state processes. Annals of Pure and Applied Logic 90 (1–3)163–191.CrossRefGoogle Scholar