The Failure of the Strong Pumping Lemma for Multiple Context-Free Languages

Makoto Kanazawa, Gregory M. Kobele, Jens Michaelis, Sylvain Salvati, Ryo Yoshinaka

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

Seki et al. (Theor. Comput. Sci. 88(2):191-229, 1991) showed that every m-multiple context-free language L is weakly 2m-iterative in the sense that either L is finite or L contains a subset of the form {u0w1iu1...w2miu2m {pipe} i ∈ ℕ}, where w1⋯w2n≠ε. Whether every m-multiple context-free language L is 2m-iterative, that is to say, whether all but finitely many elements z of L can be written as z=u0w1u1⋯w2mu2m with w1⋯w2m≠ε and {u0w1iu1...w2miu2m {pipe} i ∈ ℕ} ⊂ L, has been open. We show that there is a 3-multiple context-free language that is not k-iterative for any k.

Original languageEnglish
Pages (from-to)250-278
Number of pages29
JournalTheory of Computing Systems
Volume55
Issue number1
DOIs
Publication statusPublished - 2014 Jul
Externally publishedYes

Keywords

  • Multiple context-free grammar
  • Pumping lemma

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics

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