Membership problem for head languages and multiple context-free languages

1989 ◽  
Vol 20 (6) ◽  
pp. 43-51
Author(s):  
Tadao Kasami ◽  
Hiroyuki Seki ◽  
Mamoru Fujii
Keyword(s):  
Membership Problem ◽  
Multiple Context ◽  
Context Free

WHEN CHURCH-ROSSER BECOMES CONTEXT FREE

2007 ◽  
Vol 18 (06) ◽  
pp. 1293-1302 ◽  
Author(s):  
MARTIN KUTRIB ◽  
ANDREAS MALCHER
Keyword(s):  
Linear Time ◽  
Membership Problem ◽  
Closure Properties ◽  
Context Free Language ◽  
Arithmetic Hierarchy ◽  
Context Free ◽  
Free Language

We investigate the intersection of Church-Rosser languages and (strongly) context-free languages. The intersection is still a proper superset of the deterministic context-free languages as well as of their reversals, while its membership problem is solvable in linear time. For the problem whether a given Church-Rosser or context-free language belongs to the intersection we show completeness for the second level of the arithmetic hierarchy. The equivalence of Church-Rosser and context-free languages is Π1-complete. It is proved that all considered intersections are pairwise incomparable. Finally, closure properties under several operations are investigated.

PUZZLE GRAMMARS AND CONTEXT-FREE ARRAY GRAMMARS

1991 ◽  
Vol 05 (05) ◽  
pp. 663-676 ◽  
Author(s):  
M. NIVAT ◽  
A. SAOUDI ◽  
K. G. SUBRAMANIAN ◽  
R. SIROMONEY ◽  
V. R. DARE
Keyword(s):  
Membership Problem ◽  
Generative Power ◽  
New Model ◽  
Regular Control ◽  
Emptiness Problem ◽  
Np Complete ◽  
Context Free ◽  
Rewriting Rules

We introduce a new model for generating finite, digitized, connected pictures called puzzle grammars and study its generative power by comparison with array grammars. We note how this model generalizes the classical Chomskian grammars and study the effect of direction-independent rewriting rules. We prove that regular control does not increase the power of basic puzzle grammars. We show that for basic and context-free puzzle grammars, the membership problem is NP-complete and the emptiness problem is undecidable.

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

2014 ◽  
Vol 55 (1) ◽  
pp. 250-278 ◽  
Author(s):  
Makoto Kanazawa ◽  
Gregory M. Kobele ◽  
Jens Michaelis ◽  
Sylvain Salvati ◽  
Ryo Yoshinaka
Keyword(s):  
Multiple Context ◽  
Pumping Lemma ◽  
Context Free

scholarly journals Second-position clitics and the syntax-phonology interface: The case of ancient Greek

2016 ◽  
Author(s):  
David M. Goldstein ◽  
Dag T. T. Haug
Keyword(s):  
Ancient Greek ◽  
Context Free Grammar ◽  
Multiple Context ◽  
Yield Functions ◽  
Break Up ◽  
Context Free

In this paper we discuss second position clitics in Ancient Greek, which show a remarkable ability to break up syntactic constituents. We argue against attempts to capture such data in terms of a mismatch between c-structure yield and surface string and instead propose to enrich c-structure by using a multiple context free grammar with explicit yield functions rather than an ordinary CFG.

scholarly journals Groups whose word problems are not semilinear

2018 ◽  
Vol 0 (0) ◽  
Author(s):  
Robert H. Gilman ◽  
Robert P. Kropholler ◽  
Saul Schleimer
Keyword(s):  
Fundamental Group ◽  
Nilpotent Group ◽  
Finite Volume ◽  
Formal Language ◽  
Artin Group ◽  
Infinite Class ◽  
Context Free Language ◽  
Multiple Context ◽  
Context Free ◽  
Free Language

Abstract Suppose that G is a finitely generated group and {\operatorname{WP}(G)} is the formal language of words defining the identity in G. We prove that if G is a virtually nilpotent group that is not virtually abelian, the fundamental group of a finite volume hyperbolic three-manifold, or a right-angled Artin group whose graph lies in a certain infinite class, then {\operatorname{WP}(G)} is not a multiple context-free language.

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