One-Nonterminal Conjunctive Grammars over a Unary Alphabet

Research output

9 Citations (Scopus)


Conjunctive grammars over an alphabet Σ={a} are studied, with the focus on the special case with a unique nonterminal symbol. Such a grammar is equivalent to an equation X=φ{symbol}(X) over sets of natural numbers, using union, intersection and addition. It is shown that every grammar with multiple nonterminals can be encoded into a grammar with a single nonterminal, with a slight modification of the language. Based on this construction, the compressed membership problem for one-nonterminal conjunctive grammars over {a} is proved to be EXPTIME-complete; the same problem for the context-free grammars is decidable in NLOGSPACE, but becomes NP-complete if the grammar is compressed as well. The equivalence problem for these grammars is shown to be co-r. e.-complete, both finiteness and co-finiteness are r. e.-complete, while equivalence to a fixed unary language with a regular positional notation is decidable.

Original languageEnglish
Pages (from-to)319-342
Number of pages24
JournalTheory of Computing Systems
Issue number2
Publication statusPublished - 1 Aug 2011

Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics

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