Compositional Liveness-Preserving Conformance Testing of Timed I/O Automata -- Technical Report

TL;DR

This paper introduces live timed ioco (ltioco), an improved conformance testing theory for Timed I/O Automata that addresses weaknesses of previous models, enabling finite, compositional, and more accurate real-time testing.

Contribution

It proposes ltioco, a novel extension of tioco, with refined quiescence handling, finite semantic models via zone graphs, and enhanced compositionality for practical real-time conformance testing.

Findings

ltioco effectively distinguishes safe and live outputs within specified time bounds.

Finite zone graph models enable practical implementation of ltioco testing.

Ltioco maintains compositional properties with parallel composition and silent transitions.

Abstract

I/O conformance testing theories (e.g., ioco) are concerned with formally defining when observable output behaviors of an implementation conform to those permitted by a specification. Thereupon, several real-time extensions of ioco, usually called tioco, have been proposed, further taking into account permitted delays between actions. In this paper, we propose an improved version of tioco, called live timed ioco (ltioco), tackling various weaknesses of existing definitions. Here, a reasonable adaptation of quiescence (i.e., observable absence of any outputs) to real-time behaviors has to be done with care: ltioco therefore distinguishes safe outputs being allowed to happen, from live outputs being enforced to happen within a certain time period thus inducing two different facets of quiescence. Furthermore, tioco is frequently defined on Timed I/O Labeled Transition Systems (TIOLTS), a semantic model of Timed I/O Automata (TIOA) which is infinitely branching and thus infeasible for practical testing tools. Instead, we extend the theory of zone graphs to enable ltioco testing on a finite semantic model of TIOA. Finally, we investigate compositionality of ltioco with respect to parallel composition including a proper treatment of silent transitions.