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

8 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

Access to Document

10.1007/s00224-014-9534-z

Cite this

@article{6e123d148f3a48f7ba6f5cd5fa3f1131,

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.",

keywords = "Multiple context-free grammar, Pumping lemma",

author = "Makoto Kanazawa and Kobele, {Gregory M.} and Jens Michaelis and Sylvain Salvati and Ryo Yoshinaka",

year = "2014",

month = jul,

doi = "10.1007/s00224-014-9534-z",

language = "English",

volume = "55",

pages = "250--278",

journal = "Theory of Computing Systems",

issn = "1432-4350",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - The Failure of the Strong Pumping Lemma for Multiple Context-Free Languages

AU - Kanazawa, Makoto

AU - Kobele, Gregory M.

AU - Michaelis, Jens

AU - Salvati, Sylvain

AU - Yoshinaka, Ryo

PY - 2014/7

Y1 - 2014/7

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.

AB - 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.

KW - Multiple context-free grammar

KW - Pumping lemma

UR - http://www.scopus.com/inward/record.url?scp=84901831016&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84901831016&partnerID=8YFLogxK

U2 - 10.1007/s00224-014-9534-z

DO - 10.1007/s00224-014-9534-z

M3 - Article

AN - SCOPUS:84901831016

VL - 55

SP - 250

EP - 278

JO - Theory of Computing Systems

JF - Theory of Computing Systems

SN - 1432-4350

IS - 1

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this