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

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

doi:10.1007/s00224-014-9534-z

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 journal › Article › peer-review

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...w_2mⁱu_2m {pipe} i ∈ ℕ}, where w₁⋯w_2n≠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⋯w_2mu_2m with w₁⋯w_2m≠ε and {u₀w₁ⁱu₁...w_2mⁱu_2m {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 language	English
Pages (from-to)	250-278
Number of pages	29
Journal	Theory of Computing Systems
Volume	55
Issue number	1
DOIs	https://doi.org/10.1007/s00224-014-9534-z
Publication status	Published - 2014 Jul
Externally published	Yes

Keywords

Multiple context-free grammar
Pumping lemma

ASJC Scopus subject areas

Theoretical Computer Science
Computational Theory and Mathematics

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title = "The Failure of the Strong Pumping Lemma for Multiple Context-Free Languages",

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.",

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AU - Yoshinaka, Ryo

PY - 2014/7

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N2 - 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.

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

Abstract

Keywords

ASJC Scopus subject areas

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