On the Axiomatizability of Priority

This paper studies the equational theory of bisimulation equivalence over the process algebra BCCSP extended with the priority operator of Baeten, Bergstra and Klop. It is proven that, in the presence of an infinite set of actions, bisimulation equivalence has no finite, sound, ground-complete equational axiomatization 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 axiomatizations using conditional equations. In the presence of an infinite set of actions, it is shown that, in general, bisimulation equivalence has no finite, sound, ground-complete axiomatization consisting of conditional equations over BCCSP. Sufficient conditions on the priority structure over actions are identified that lead to a finite, ground-complete axiomatization of bisimulation equivalence using conditional equations

[1]  C. A. R. Hoare,et al.  Communicating sequential processes , 1978, CACM.

[2]  David Park,et al.  Concurrency and Automata on Infinite Sequences , 1981, Theoretical Computer Science.

[3]  Jan A. Bergstra,et al.  Process Algebra for Synchronous Communication , 1984, Inf. Control..

[4]  Robin Milner,et al.  Algebraic laws for nondeterminism and concurrency , 1985, JACM.

[5]  Jan A. Bergstra,et al.  Put and get, primitives for synchronous unreliable message passing , 1985 .

[6]  Jan A. Bergstra,et al.  Syntax and defining equations for an interrupt mechanism in process algebra , 1985 .

[7]  Ed Brinksma,et al.  A tutorial on LOTOS , 1985, PSTV.

[8]  Iso. Lotos,et al.  A Formal Description Technique Based on the Temporal Ordering of Observational Behaviour , 1985 .

[9]  Rance Cleaveland,et al.  Priorities in process algebras , 1988, [1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science.

[10]  Albert R. Meyer,et al.  Bisimulation can't be traced , 1988, POPL '88.

[11]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[12]  Faron Moller,et al.  The nonexistence of finite axiomatisations for CCS congruences , 1990, [1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science.

[13]  Sjouke Mauw,et al.  A process specification formalism , 1990 .

[14]  Robin Milner,et al.  Definition of standard ML , 1990 .

[15]  R. J. vanGlabbeek.  The linear time - branching time spectrum , 1990 .

[16]  Faron Moller.  The Importance of the Left Merge Operator in Process Algebras , 1990, ICALP.

[17]  Rob J. van Glabbeek,et al.  The Linear Time-Branching Time Spectrum (Extended Abstract) , 1990, CONCUR.

[18]  Jan Friso Groote.  A New Strategy for Proving omega-Completeness applied to Process Algebra , 1990, CONCUR.

[19]  Sjouke Mauw,et al.  PSF : a process specification formalism , 1991 .

[20]  Rob J. van Glabbeek,et al.  The Linear Time - Branching Time Spectrum II , 1993, CONCUR.

[21]  Mark V. Sapir,et al.  Algorithmic Problems in Varieties , 1995, Int. J. Algebra Comput..

[22]  Bard Bloom,et al.  On the Expressive Power of CCS , 1995, FSTTCS.

[23]  Lu Tian,et al.  On Deciding Readiness and Failure Equivalences for Processes , 1995, Inf. Comput..

[24]  Jan A. Bergstra,et al.  Equational specifications, complete term rewriting systems, and computable and semicomputable algebras , 1995, JACM.

[25]  Glynn Winskel,et al.  CCS with Priority Choice , 1995, Inf. Comput..

[26]  Rance Cleaveland,et al.  Priorities for Modeling and Verifying Distributed Systems , 1996, TACAS.

[27]  Peter Sewell,et al.  Nonaxiomatisability of Equivalences over Finite State Processes , 1997, Ann. Pure Appl. Log..

[28]  J. Bergstra,et al.  Mode transfer in process algebra , 2000 .

[29]  R. V. Glabbeek.  CHAPTER 1 – The Linear Time - Branching Time Spectrum I.* The Semantics of Concrete, Sequential Processes , 2001 .

[30]  Rance Cleaveland,et al.  Priority in Process Algebra , 2001, Handbook of Process Algebra.

[31]  Gordon D. Plotkin,et al.  A structural approach to operational semantics , 2004, J. Log. Algebraic Methods Program..

[32]  Karl Krukow,et al.  An Operational Semantics for Trust Policies , 2005 .

[33]  Luca Aceto,et al.  Bisimilarity is not finitely based over BPA with interrupt , 2005, Theor. Comput. Sci..

[34]  Bas Luttik,et al.  Finite Equational Bases in Process Algebra: Results and Open Questions , 2005, Processes, Terms and Cycles.

[35]  Bas Luttik,et al.  CCS with Hennessy's merge has no finite-equational axiomatization , 2005, Theor. Comput. Sci..

[36]  Kristian Støvring,et al.  Extending the Extensional Lambda Calculus with Surjective Pairing is Conservative , 2005, Log. Methods Comput. Sci..

[37]  Christian Kirkegaard,et al.  Type Checking with XML Schema in XACT , 2005, PLAN-X.

[38]  Olivier Danvy,et al.  On the static and dynamic extents of delimited continuations , 2005, Sci. Comput. Program..

[39]  Olivier Danvy,et al.  A syntactic correspondence between context-sensitive calculi and abstract machines , 2005, Theor. Comput. Sci..