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From Hyperedge Replacement Grammars to Decidable Hyperedge Replacement Games

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Software Technologies: Applications and Foundations (STAF 2018)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11176))

Abstract

We consider correctness of hyperedge replacement grammars under adverse conditions. In contrast to existing approaches, the influence of an adverse environment is considered in addition to system behaviour. To this end, we construct a hyperedge replacement game where rules represent the moves available to players and a temporal condition specifies the desired properties of the system. In particular, the construction of parity pushdown games from hyperedge replacement grammars results in a decidable class of games.

This work is supported by the German Research Foundation through the Research Training Group (DFG GRK 1765) SCARE (www.scare.uni-oldenburg.de).

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Notes

  1. 1.

    \(\mathbb {N}\) is the set of all natural numbers, including 0.

  2. 2.

    \(V^*\) is the collection of all finite sequences over \(V\), including the empty sequence \(\epsilon \).

  3. 3.

    \(| att (e)|\) denotes the length of a sequence \( att (e)\).

  4. 4.

    For a function \(f:A\rightarrow B\), the free symbolwise extension \(f^*:A^* \rightarrow B^*\) is defined by \(f^*(a_1...a_n) = f(a_1)...f(a_n)\).

  5. 5.

    \(\uplus \) denotes the disjoint union, \(\setminus \) the difference of sets and \([ ext _R]\) denotes the set of elements of \( ext _R\).

  6. 6.

    The function \(f | S\) is the restriction of \(f\) to a set \(S\). The symbol \(;\) denotes forward composition of functions, i.e. \(f;g(x) = f(g(x))\).

  7. 7.

    \([1,n]\) denotes the set of natural numbers from \(1\) to \(n\).

  8. 8.

    A tree is a connected, cycle free graph with a designated root node.

  9. 9.

    \(\varGamma ^+\) denotes the set of nonempty sequences over \(\varGamma \).

  10. 10.

    The symbol \(\cdot \) denotes string concatenation.

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Acknowledgements

We would like to thank Annegret Habel, Reiko Heckel, Berthold Hoffmann and Mark Minas for helpful feedback on earlier versions of this paper.

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Authors and Affiliations

  1. Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany

    Christoph Peuser

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  1. Christoph Peuser
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Correspondence to Christoph Peuser .

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Editors and Affiliations

  1. Innopolis University, Innopolis, Russia

    Manuel Mazzara

  2. University of Toulouse, Toulouse Cedex 9, France

    Iulian Ober

  3. Grenoble Alpes University, Montbonnot, France

    Gwen Salaün

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Peuser, C. (2018). From Hyperedge Replacement Grammars to Decidable Hyperedge Replacement Games. In: Mazzara, M., Ober, I., Salaün, G. (eds) Software Technologies: Applications and Foundations. STAF 2018. Lecture Notes in Computer Science(), vol 11176. Springer, Cham. https://doi.org/10.1007/978-3-030-04771-9_33

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  • DOI: https://doi.org/10.1007/978-3-030-04771-9_33

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-04770-2

  • Online ISBN: 978-3-030-04771-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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