Non-closure under complementation for unambiguous linear grammars

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”, JACM, 1966) on the non-closure of the unambiguous languages under complementation.

Authors

• Olga Martynova
• Alexander Okhotin

Keywords

• Context-free grammars
• Unambiguous grammars
• Linear grammars
• Complementation
• Closure properties