Refinements for Open Automata

Abstract

Establishing equivalence and refinement relations between programs is an important mean for verifying their correctness. By establishing that the behaviours of a modified program simulate those of the source one, simulation relations formalise the desired relationship between a specification and an implementation, two equivalent implementations, or a program and its optimised implementation. This article discusses a notion of simulation between open automata, which are symbolic behavioural models for communicating systems. Open automata may have holes modelling elements of their context, and can be composed by instantiation of the holes. This allows for a compositional approach for verification of their behaviour. We define a simulation between open automata that may or may not have the same holes, and show under which conditions these refinements are preserved by composition of open automata.