Relating Alternating Relations for Conformance and Refinement

TL;DR

This paper explores the relationship between various conformance and refinement relations in state-transition systems, revealing that uioco aligns with a variant of alternating-trace containment, and introduces a new, simpler refinement relation.

Contribution

It integrates ioco/uioco theory with alternating refinements for non-deterministic, non-input-enabled interface automata and clarifies their relationships, especially regarding quiescence.

Findings

uioco coincides with a variant of alternating-trace containment

ioco and original alternating-trace containment are too strong for practical scenarios

a new refinement relation is proposed that unifies and simplifies existing concepts

Abstract

Various relations have been defined to express refinement and conformance for state-transition systems with inputs and outputs, such as ioco and uioco in the area of model-based testing, and alternating simulation and alternating-trace containment originating from game theory and formal verification. Several papers have compared these independently developed relations, but these comparisons make assumptions (e.g., input-enabledness), pose restrictions (e.g., determinism - then they all coincide), use different models (e.g., interface automata and Kripke structures), or do not deal with the concept of quiescence. In this paper, we present the integration of the ioco/uioco theory of model-based testing and the theory of alternating refinements, within the domain of non-deterministic, non-input-enabled interface automata. A standing conjecture is that ioco and alternating-trace containment coincide. Our main result is that this conjecture does not hold, but that uioco coincides with a variant of alternating-trace containment, for image finite interface automata and with explicit treatment of quiescence. From the comparison between ioco theory and alternating refinements, we conclude that ioco and the original relation of alternating-trace containment are too strong for realistic black-box scenarios. We present a refinement relation which can express both uioco and refinement in game theory, while being simpler and having a clearer observational interpretation.