A Bisimulation-based Method for Proving the Validity of Equations in GSOS Languages

Abstract

This paper presents a bisimulation-based method for establishing the soundness of equations between terms constructed using operations whose semantics is specified by rules in the GSOS format of Bloom, Istrail and Meyer. The method is inspired by de Simone's FH-bisimilarity and uses transition rules as schematic transitions in a bisimulation-like relation between open terms. The soundness of the method is proven and examples showing its applicability are provided. The proposed bisimulation-based proof method is incomplete, but the article offers some completeness results for restricted classes of GSOS specifications

Proving the validity of equations in GSOS languages using rule-matching bisimilarity

“…This paper extends the workshop article Aceto et al (2010a) by providing a more technically detailed description of the background material for this work, proofs of the main technical results and further examples. In addition, Theorem 5.8 and the material in Section 8 are new.…”

Incremental Pattern-Based Coinduction for Process Algebra and Its Isabelle Formalization

“…Other related work includes frameworks for bisimilarity of open terms in [29,8,4] (also building on the seminal work from [11]), where open terms are considered universally quantified, as we do in this paper for universal bisimilarity. Our soundness result for w.r.t.…”

“…the notion of bisimulation under formal hypotheses from [11,29]; on the other, w.r.t. to the relation from [4] (which is essentially universal bisimilarity in any conservative extension of the SOS system). All works cited in this paragraph discuss non-incremental proof systems, where the desired bisimulation relation needs to be fed by the user.…”

“…A in [28] gives the general definition. (In [6,4], where what we call "matched derived rules" are called "ruloids", mdr is not even defined, but rather the existence of such an operator satisfying suitable properties (essentially the same with what we call below soundness and completeness of the matched derived rules) is proved. )…”

Rule Formats for Distributivity

“…It is possible to find syntactic conditions on the set of rules for some operator f guaranteeing that f is always moving. For instance, the decidable logic of initial transition formulae offered in [3], which is able to reason about firability of GSOS rules, can be used in order to check whether operators are always moving. The development of rule formats for always-moving operators is, however, orthogonal to the gist of this paper and therefore we do not address it here.…”