Abstract
We present a logical characterization of the Milner's notion of observation equivalence of processes (“at most one observable action at a time” variant) by using a restricted class of first order formulas. We use the game technique due to Ehrenfeucht as a means to achieve this characterization. First we extend the Ehrenfeucht game by introducing a pair of compatibility relations as a parameter to the game so that we can restrict the moves of the players on the basis of the previous moves. We then define the logic which corresponds to the extended game. Second we characterize the observation equivalence on a restricted class of labelled transition systems (with τ moves), called trace-unique labelled transition systems (t-τℓts's), as the equivalence induced by the games played on certain rcducts of the given t-τℓts's where the compatibility relations are defined in terms of bounded reachability in the t-τℓts's. Combining these two characterizations we get our main result.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
S.D. Brookes, W.C. Rounds: Behavioral equivalence relations induced by programming logics. Lecture Notes in Computer Science 154 (Proc. ICALP), Berlin: Springer-Verlag, 1983, pp. 97–108
A. Ehrenfeucht: An application of games to the completeness problem for formalized theories. Fundamenta Mathematicae XLIX, 1961, pp. 129–141
M. Hennessy, R. Milner: Algebraic laws for nondeterminism and concurrency. Journal of the ACM 32, no. 1, January 1985, pp. 137–161
R. Milner: A calculus of communicating systems. Lecture Notes in Computer Science 154, Berlin: Springer-Verlag, 1980
G.C. Nelson, H. O¯guztüzün: Characterization of finitely axiomatizable labelled transition trees. Submitted for publication
H. O¯guztüzün: A game characterization of the observational equivalence of processes (extended abstract). First Int. Conf. on Algebraic Methodology and Software Technology (AMAST), Iowa City, Iowa, May 22–24, 1989, pp. 195–196
H. O¯guztüzün: A logical characterization of the observation equivalence of processes. PhD Thesis, University of Iowa, Iowa City, Iowa, August 1991
J.G. Rosenstein: Linear Orderings. New York: Academic Press, 1982
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
O¯guztüzün, H. (1992). A fragment of first order logic adequate for observation equivalence. In: Börger, E., Jäger, G., Kleine Büning, H., Richter, M.M. (eds) Computer Science Logic. CSL 1991. Lecture Notes in Computer Science, vol 626. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023774
Download citation
DOI: https://doi.org/10.1007/BFb0023774
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55789-0
Online ISBN: 978-3-540-47285-8
eBook Packages: Springer Book Archive