A Complete Equational Axiomatization for Prefix Iteration with Silent Steps

Forfattere

  • Luca Aceto
  • Anna Ingólfsdóttir

DOI:

https://doi.org/10.7146/brics.v2i5.19507

Resumé

Fokkink ((1994) Inf. Process. Lett. 52: 333{337) has recently proposed a complete
equational axiomatization of strong bisimulation equivalence for MPA_delta^*(A_tau),
i.e., the language obtained by extending Milner's basic CCS with prefix iteration.
Prefix iteration is a variation on the original binary version of the Kleene star operation
p*q obtained by restricting the first argument to be an atomic action. In this
paper, we extend Fokkink's results to a setting with the unobservable action by
giving a complete equational axiomatization of Milner's observation congruence over
MPA_delta^*(A_tau ).
The axiomatization is obtained by extending Fokkink's axiom system
with two of Milner's standard tau-laws and the following three equations that describe
the interplay between the silent nature of tau and prefix iteration:
tau . x = tau*x
a*(x+tau.y) = a*(x+tau.y + a.y)
tau.(a*x) = a*(tau.a*x) .
Using a technique due to Groote, we also show that the resulting axiomatization is
omega-complete, i.e., complete for equality of open terms.
AMS Subject Classification (1991): 68Q40, 68Q42.
CR Subject Classification (1991): D.3.1, F.3.2, F.4.2.
Keywords and Phrases: Minimal Process Algebra, prefix iteration, equational
logic, omega-completeness, observation congruence.

Downloads

Publiceret

1995-01-05

Citation/Eksport

Aceto, L., & Ingólfsdóttir, A. (1995). A Complete Equational Axiomatization for Prefix Iteration with Silent Steps. BRICS Report Series, 2(5). https://doi.org/10.7146/brics.v2i5.19507

Nummer

Nr. 5 (1995): RS-05 A Complete Equational Axiomatization for Prefix Iteration with Silent Steps

Sektion

Artikler

Licens

Authors who publish with this journal agree to the following terms:

    1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

    1. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.

  1. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).