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

Seki et al. (Theor. Comput. Sci. 88(2):191–229, 1991 ) showed that every m -multiple context-free language L is weakly 2 m -iterative in the sense that either L is finite or L contains a subset of the form , where w 1 ⋯ w 2 n ≠ ε . Whether every m -multiple context-free language L is 2 m -iterative,...

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Published in:Theory of computing systems Vol. 55; no. 1; pp. 250 - 278
Main Authors: Kanazawa, Makoto, Kobele, Gregory M., Michaelis, Jens, Salvati, Sylvain, Yoshinaka, Ryo
Format: Journal Article
Language:English
Published: Boston Springer US 01.07.2014
Springer Nature B.V
Springer Verlag
Subjects:
Analysis
Computation
Computation and Language
Computer Science
Failure
Formal Languages and Automata Theory
Grammar
Informatics
Language
Mathematical analysis
Pumping
Studies
Texts
Theory of Computation
Trees
Multiple context-free grammar
Pumping lemma
ISSN:1432-4350, 1433-0490
Online Access:Get full text
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Summary:Seki et al. (Theor. Comput. Sci. 88(2):191–229, 1991 ) showed that every m -multiple context-free language L is weakly 2 m -iterative in the sense that either L is finite or L contains a subset of the form , where w 1 ⋯ w 2 n ≠ ε . Whether every m -multiple context-free language L is 2 m -iterative, that is to say, whether all but finitely many elements z of L can be written as z = u 0 w 1 u 1 ⋯ w 2 m u 2 m with w 1 ⋯ w 2 m ≠ ε and , 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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ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-014-9534-z