Non-closure under complementation for unambiguous linear grammars
Formal Languages and Automata Theory
2022-10-06 v1
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.
Cite
@article{arxiv.2210.02329,
title = {Non-closure under complementation for unambiguous linear grammars},
author = {Olga Martynova and Alexander Okhotin},
journal= {arXiv preprint arXiv:2210.02329},
year = {2022}
}