Robustness of Equations Under Operational Extensions

Peter D. Mosses
(Department of Computer Science, Swansea University)
MohammadReza Mousavi
(Department of Computer Science, Eindhoven University of Technology)
Michel A. Reniers
(Department of Computer Science, Eindhoven University of Technology)

Sound behavioral equations on open terms may become unsound after conservative extensions of the underlying operational semantics. Providing criteria under which such equations are preserved is extremely useful; in particular, it can avoid the need to repeat proofs when extending the specified language.

This paper investigates preservation of sound equations for several notions of bisimilarity on open terms: closed-instance (ci-)bisimilarity and formal-hypothesis (fh-)bisimilarity, both due to Robert de Simone, and hypothesis-preserving (hp-)bisimilarity, due to Arend Rensink. For both fh-bisimilarity and hp-bisimilarity, we prove that arbitrary sound equations on open terms are preserved by all disjoint extensions which do not add labels. We also define slight variations of fh- and hp-bisimilarity such that all sound equations are preserved by arbitrary disjoint extensions. Finally, we give two sets of syntactic criteria (on equations, resp. operational extensions) and prove each of them to be sufficient for preserving ci-bisimilarity.

In Sibylle Fröschle and Frank D. Valencia: Proceedings 17th International Workshop on Expressiveness in Concurrency (EXPRESS'10), Paris, France, August 30th, 2010, Electronic Proceedings in Theoretical Computer Science 41, pp. 106–120.
Published: 28th November 2010.

ArXived at: http://dx.doi.org/10.4204/EPTCS.41.8 bibtex PDF

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