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.
Keywords
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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- 1.
\(\mathbb {N}\) is the set of all natural numbers, including 0.
- 2.
\(V^*\) is the collection of all finite sequences over \(V\), including the empty sequence \(\epsilon \).
- 3.
\(| att (e)|\) denotes the length of a sequence \( att (e)\).
- 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.
\(\uplus \) denotes the disjoint union, \(\setminus \) the difference of sets and \([ ext _R]\) denotes the set of elements of \( ext _R\).
- 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.
\([1,n]\) denotes the set of natural numbers from \(1\) to \(n\).
- 8.
A tree is a connected, cycle free graph with a designated root node.
- 9.
\(\varGamma ^+\) denotes the set of nonempty sequences over \(\varGamma \).
- 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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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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