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On constructibility and unconstructibility of LTS operators from other LTS operators

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Abstract

An LTS operator can be constructed from a set of LTS operators up to an equivalence if and only if there is an LTS expression that only contains operators from the set and whose result is equivalent to the result of the operator. In this publication this idea is made precise in the context where each LTS has an alphabet of its own and the operators may depend on the alphabets. Then the extent to which LTS operators are constructible is studied. Most, if not all, established LTS operators have the property that each trace of the result arises from the execution of no more than one trace of each of its argument LTSs, and similarly for infinite traces. All LTS operators that have this property and satisfy some other rather weak regularity properties can be constructed from parallel composition and hiding up to the equivalence that compares the alphabets, traces, and infinite traces of the LTSs. Furthermore, a collection of other miscellaneous constructibility and unconstructibility results is presented.

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Notes

  1. For any binary relation symbol \(\propto \), by “\(\propto \)” we refer to the set of pairs that specifies the relation, while \(\propto \) is used in the claims that the relation holds. That is, “\(\propto \)” \(=\) \(\{ (x,y) \mid x \propto y \}\). The benefit of this convention is illustrated by comparing \(< \cup = \ =\ \le \) to “\(<\)” \(\cup \) “\(=\)” \(=\) “\(\le \)”. More generally, we use “ and ” whenever we believe that it helps to avoid confusion.

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Acknowledgments

I thank Walter Vogler for the helpful discussions on “\(\approx _{{\mathsf {shd}}}\)” and other topics that we have had every now and then. I also thank the anonymous reviewers for their valuable comments, written in a very helpful way, on related work and other issues.

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  1. Department of Mathematics, Tampere University of Technology, Tampere, Finland

    Antti Valmari

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  1. Antti Valmari
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Valmari, A. On constructibility and unconstructibility of LTS operators from other LTS operators. Acta Informatica 52, 207–234 (2015). https://doi.org/10.1007/s00236-015-0217-2

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