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

TL;DR

This paper introduces a bisimulation-based technique to verify the validity of equations in GSOS languages, providing a sound method with some completeness results for specific classes of specifications.

Contribution

It proposes a novel bisimulation-based proof method for GSOS equations, extending de Simone's FH-bisimilarity and proving its soundness with applicability examples.

Findings

Method is sound for establishing equation validity in GSOS languages.

Examples demonstrate the method's applicability.

Some completeness results are provided for restricted GSOS classes.

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.