Conjunctive grammars with restricted disjunction

  • Authors:
  • Alexander Okhotin;Christian Reitwieβner

  • Affiliations:
  • Academy of Finland, Department of Mathematics, University of Turku, Turku FI20014, Finland;Julius-Maximilians-Universität Würzburg, Theoretische Informatik, Würzburg D97074, Germany

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2010

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Abstract

It is shown that every conjunctive language is generated by a conjunctive grammar from a special subclass, in which every nonterminal A has at most one rule of the general form A-@a"1&...&@a"n, while the rest of the rules for A must be of the type A-w, where w is a terminal string. For context-free grammars, a similar property does not hold (S.A. Greibach et al. (1992) [3]). If it is furthermore required that each rule A-w has a nonempty w, then a substantial subfamily of conjunctive languages can be generated, yet it remains unknown whether such grammars are as powerful as conjunctive grammars of the general form.