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arXiv · 2210.02329

Non-closure under complementation for unambiguous linear grammars

Olga Martynova·Alexander Okhotin
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Abstract

The paper demonstrates the non-closure of the family of unambiguous linear languages (that is, those defined by unambiguous linear context-free grammars) under complementation. To be precise, a particular unambiguous linear grammar is presented, and it is proved that the complement of this language is not defined by any context-free grammar. This also constitutes an alternative proof for the result of Hibbard and Ullian ("The independence of inherent ambiguity from complementedness among context-free languages", J.ACM, 1966) on the non-closure of the unambiguous languages under complementation.

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Olga Martynova, Alexander Okhotin. 2022-10-05. Non-closure under complementation for unambiguous linear grammars. https://arxiv.org/abs/2210.02329

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