On the number of nonterminal symbols in unambiguous conjunctive grammars

Research output

Abstract

Unambiguous conjunctive grammars with 1 nonterminal symbol are shown to be strictly weaker than the grammars with 2 nonterminal symbols, which are in turn strictly weaker that the grammars with 3 or more nonterminal symbols. This hierarchy is established by considering grammars over a one-symbol alphabet, for which it is shown that 1-nonterminal grammars describe only regular languages, 2-nonterminal grammars describe some non-regular languages, but all of them are in a certain sense sparse, whereas 3-nonterminal grammars may describe some non-regular languages of non-zero density. It is also proved that one can test a 2-nonterminal grammar for equivalence with a regular language, whereas the equivalence between a pair of 2-nonterminal grammars is undecidable.

Original languageEnglish
Pages (from-to)43-72
Number of pages30
JournalFundamenta Informaticae
Volume162
Issue number1
DOIs
Publication statusPublished - 1 Jan 2018

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Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Information Systems
  • Computational Theory and Mathematics

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