Mathematical Structures in Computer Science

Table of Contents - April 2012 - Volume 22, Special Issue 02 (Express '09, Ice '09 and Sos '09)  

Paper

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

LUCA ACETOa1†‡, MATTEO CIMINIa1† and ANNA INGOLFSDOTTIRa1†

a1 School of Computer Science, Reykjavik University, Menntavegur 1, Nauthólsvík, IS-101 Reykjavík, Iceland Email: luca@ru.is, matteo@ru.is, annai@ru.is

Abstract

This paper presents a bisimulation-based method for establishing the soundness of equations between terms constructed using operations whose semantics are 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 proved and examples showing its applicability are provided. The proposed bisimulation-based proof method is incomplete, but we do offer some completeness results for restricted classes of GSOS specifications. An extension of the proof method to the setting of GSOS languages with predicates is also offered.

(Received February 26 2010)

(Revised October 18 2010)

Footnotes

† The work of the authors has been partially supported by the projects ‘The Equational Logic of Parallel Processes’ (nr. 060013021), ‘New Developments in Operational Semantics’ (nr. 080039021) and ‘Meta-theory of Algebraic Process Theories’ (nr. 100014021) of the Icelandic Research Fund.

‡ The paper was revised while Luca Aceto held an Abel Extraordinary Chair at Universidad Complutense de Madrid, Spain, supported by the NILS Mobility Project.