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Realizability of concurrent recursive programs

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Abstract

We study the realizability problem for concurrent recursive programs: given a distributed system architecture and a sequential specification over words, find a distributed automata implementation that is equivalent to the specification. This problem is well-studied as far as finite-state processes are concerned, and it has a solution in terms of Zielonka’s Theorem. We lift Zielonka’s Theorem to the case where processes are recursive and modeled as visibly pushdown (or, equivalently, nested-word) automata. However, contrarily to the finite-state case, it is undecidable whether a specification is realizable or not. Therefore, we also consider suitable underapproximation techniques from the literature developed for multi-pushdown systems, and we show that they lead to a realizability framework with effective algorithms.

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Notes

  1. In [5], pending calls or returns are possible. We can also include them without affecting any of the results, but do not do so to simplify the presentation.

  2. Here, we rather use \(\rho (e)_p\) than \(\rho (e)\), since, strictly speaking, the latter is a tuple consisting of one state, whereas \(\Delta _{\textsf {call}}\) and \(\Delta _{\textsf {ret}}\) refer to states.

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Acknowledgements

We are grateful to the reviewers for the careful reading and for the many pertinent suggestions, which helped to improve the presentation of the paper considerably.

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Authors and Affiliations

  1. CNRS, LSV, ENS Paris-Saclay, 61, avenue du Président Wilson, 94235, Cachan Cedex, France

    Benedikt Bollig & Manuela-Lidia Grindei

  2. Université Paris Diderot (Paris 7), IRIF, Bâtiment Sophie Germain, Bureau 4017, 8, place FM/13, 75013, Paris, France

    Peter Habermehl

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  1. Benedikt Bollig
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  2. Manuela-Lidia Grindei
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  3. Peter Habermehl
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Correspondence to Benedikt Bollig.

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Bollig, B., Grindei, ML. & Habermehl, P. Realizability of concurrent recursive programs. Form Methods Syst Des 53, 339–362 (2018). https://doi.org/10.1007/s10703-017-0282-y

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