Expressive power of LL(k) Boolean grammars

  • Authors:
  • Alexander Okhotin

  • Affiliations:
  • Academy of Finland and Department of Mathematics, University of Turku, Turku, Finland

  • Venue:
  • FCT'07 Proceedings of the 16th international conference on Fundamentals of Computation Theory
  • Year:
  • 2007

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Abstract

The family of languages generated by Boolean grammars and usable with recursive descent parsing is studied. It is demonstrated that Boolean LL languages over a unary alphabet are regular, while Boolean LL subsets of Σ*a* obey a certain periodicity property, which, in particular, makes the language {anb2n | n ≥ 0} nonrepresentable. It is also shown that {anbncs | n ≥ 0, s ∈ {a, b}} is not generated by any linear conjunctive LL grammar, while linear Boolean LL grammars cannot generate {anbnc* | n ≥ 0}.