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 language | English |
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Pages (from-to) | 250-278 |
Number of pages | 29 |
Journal | Theory of Computing Systems |
Volume | 55 |
Issue number | 1 |
DOIs | |
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