Off-line test selection with test purposes for non-deterministic timed automata

TL;DR

This paper introduces off-line test generation methods for non-deterministic timed automata using approximate determinization and expressive test purposes, ensuring sound and precise test cases within the tioco conformance framework.

Contribution

It presents a novel approximate determinization algorithm for non-deterministic timed automata and a test case selection method based on expressive test purposes, enhancing test generation accuracy.

Findings

The approximate determinization preserves conformance relations.

Test case generation is guided by expressive test purposes.

When determinization is exact, test verdicts are guaranteed to be adequate.

Abstract

This article proposes novel off-line test generation techniques from non-deterministic timed automata with inputs and outputs (TAIOs) in the formal framework of the tioco conformance theory. In this context, a first problem is the determinization of TAIOs, which is necessary to foresee next enabled actions after an observable trace, but is in general impossible because not all timed automata are determinizable. This problem is solved thanks to an approximate determinization using a game approach. The algorithm performs an io-abstraction which preserves the tioco conformance relation and thus guarantees the soundness of generated test cases. A second problem is the selection of test cases from a TAIO specification. The selection here relies on a precise description of timed behaviors to be tested which is carried out by expressive test purposes modeled by a generalization of TAIOs. Finally, an algorithm is described which generates test cases in the form of TAIOs equipped with verdicts, using a symbolic co-reachability analysis guided by the test purpose. Properties of test cases are then analyzed with respect to the precision of the approximate determinization: when determinization is exact, which is the case on known determinizable classes, in addition to soundness, properties characterizing the adequacy of test cases verdicts are also guaranteed.