Work

Non-Terminal Complexity of Simple Semi-Conditional Grammars

Year: 2026

Type: preprint

Abstract: We study the complexity of simple semi-conditional grammars (SSCGs) in terms of the number of their terminals and non-terminals. We show that SSCGs with three non-terminals can generate all RE languages; two non-terminals suffice for linear languages; and one suffices for unary regular languages. We also determine both upper bounds and fundamental limitations of SSCGs: while certain one-non-terminal SSCGs can generate non-context-free languages, every language generated by a one-non-terminal SSCG is in non-deterministic linear space. We also prove that there exists a regular language of alphabet size at least 3 which cannot be generated by any one-non-terminal SSCG. Finally, we prove that membership testing for SSCGs of two non-terminals is already NP-hard.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.14181

Authors: Fernau, Henning, Jain, Sanjay, Richter, Linus, Stephan, Frank, Turetsky, Dan

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Royal Society Te Apārangi, Ministry of Education, India

OpenAlex ID: W7213363428

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