Abstract
The degree of nondeterminism is a measure of syntactic complexity which was investigated for parallel and sequential rewriting systems. In this paper, we consider the degree of nondeterminsm for tree adjoining grammars and their languages and head grammars and their languages. We show that a degree of nondeterminism of 2 suffices for both formalisms in order to generate all languages in their respective language families. Furthermore, we show that deterministic tree adjoining grammars (those with degree of nondeterminism equal to 1), can generate non-context-free languages, in contrast to deterministic head grammars which can only generate languages containing a single word.
M. Hoeberechts—This research has been supported in part by an NSERC scholarship and by NSERC grant OGP 249 (Helmut Jürgensen).
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Notes
- 1.
This notation has been changed slightly from [10] to include an index on the sa and oa constraint.
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Acknowledgements
We thank Henning Bordihn for helping us to understand and define Degree of Nondeterminism for TAGs. Thank you to Helmut Jürgensen for his comments on drafts of this paper and for his support and encouragement for this project.
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Bensch, S., Hoeberechts, M. (2017). On the Degree of Nondeterminism of Tree Adjoining Languages and Head Grammar Languages. In: Pighizzini, G., Câmpeanu, C. (eds) Descriptional Complexity of Formal Systems. DCFS 2017. Lecture Notes in Computer Science(), vol 10316. Springer, Cham. https://doi.org/10.1007/978-3-319-60252-3_5
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DOI: https://doi.org/10.1007/978-3-319-60252-3_5
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