Abstract

Deterministic timed automata are strictly less expressive than their non-deterministic counterparts, which are again less expressive than those with silent transitions. As a consequence, timed automata are in general non-determinizable. This is unfortunate since deterministic automata play a major role in model-based testing, observability and implementability. However, by bounding the length of the traces in the automaton, effective determinization becomes possible. We propose a novel procedure for bounded determinization of timed automata. The procedure unfolds the automata to bounded trees, removes all silent transitions and determinizes via disjunction of guards. The proposed algorithms are optimized to the bounded setting and thus are more efficient and can handle a larger class of timed automata than the general algorithms. We show how to apply the approach in a fault-based test-case generation method, called model-based mutation testing, that was previously restricted to deterministic timed automata. The approach is implemented in a prototype tool and evaluated on several scientific examples and one industrial case study. To our best knowledge, this is the first implementation of this type of procedure for timed automata.

Highlights

  • The design of modern embedded systems often involves the integration of interacting components I1 and I2 that realize some requested behavior

  • The additional content presented in this paper covers a short introduction into model-based mutation testing, which is our motivation behind the determinization, an industrial case study for evaluation, proofs of the theorems and an update of the algorithms, that allows to keep invariants in the final automata

  • First we model the correct specification as a non-deterministic timed automata with silent transitons, and mutate it to generate a set of non-deterministic mutants

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Summary

Introduction

The design of modern embedded systems often involves the integration of interacting components I1 and I2 that realize some requested behavior. The actions over which the two components interact are hidden and become unobservable to the user It follows that the overall specification I = I1 || I2 can be a non-deterministic partially observable model. Given an arbitrary strongly responsive eNTA A and a bound k, our algorithm computes a DTA D(A) in the form of a timed tree, such that every timed trace consisting of at most k observable actions is a trace in A if and only if it is a trace in D(A) It provides the basis for effectively implementing bounded refinement checking and test-case generation procedures. The additional content presented in this paper covers a short introduction into model-based mutation testing, which is our motivation behind the determinization, an industrial case study for evaluation, proofs of the theorems and an update of the algorithms, that allows to keep invariants in the final automata.

Timed automata with silent transitions
Practical motivation
Preprocessing
Renaming the clocks
Integrating invariants into guards
Removing the silent transitions
Determinization
Complexity
Implementation and experimental results
Scientific studies
Industrial case study
Related work
10 Conclusion
Full Text
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