On the number of nonterminal symbols in unambiguous conjunctive grammars

Research output


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
Issue number1
Publication statusPublished - 1 Jan 2018

Scopus subject areas

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

Fingerprint Dive into the research topics of 'On the number of nonterminal symbols in unambiguous conjunctive grammars'. Together they form a unique fingerprint.

Cite this