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Showing papers on "Indexed language published in 2012"


Journal ArticleDOI
TL;DR: FG, FL are the largest known subfamily of DCF having the same closure properties as VPL, and are structurally adequate to specify real programming languages.

43 citations


Proceedings ArticleDOI
25 Jun 2012
TL;DR: It is shown that the complexity of the verbal and pattern languages (in terms of level on the Chomsky hierarchy) does not depend on the Thurston automatic representation and that verbal languages cannot be context-free (unless they are either the empty word or the full group).
Abstract: This paper investigates the complexity of verbal languages and pattern languages of Thurston automatic groups in terms of the Chomsky hierarchy. Here the language generated by a pattern is taken as the set of representatives of all strings obtained when chosing values for the various variables. For noncommutative free groups, it is shown that the complexity of the verbal and pattern languages (in terms of level on the Chomsky hierarchy) does not depend on the Thurston automatic representation and that verbal languages cannot be context-free (unless they are either the empty word or the full group). They can however be indexed languages. Furthermore, it is shown that in the general case, it might depend on the exactly chosen Thurston automatic representation which level a verbal language takes in the Chomsky hierarchy. There are examples of groups where, in an appropriate representation, all pattern languages are regular or context-free, respectively.

15 citations


Journal ArticleDOI
TL;DR: Some results on the power of external contextual grammars with regular commutative, regular circular, definite, suffix-free, ordered, combinational, nilpotent, and union-free selection languages are given.

6 citations


Book ChapterDOI
14 Aug 2012
TL;DR: Dense completeness is introduced, which gives tighter connection between formal language classes and complexity classes than the usual notion of completeness, and it is proved that the regular languages are not densely complete in NC1.
Abstract: We introduce dense completeness, which gives tighter connection between formal language classes and complexity classes than the usual notion of completeness. A family of formal languages $\mathcal F$ is densely complete in a complexity class $\mathcal C$ iff ${\mathcal F}\subseteq{\mathcal C}$ and for each $C \in{\mathcal C}$ there is an $F \in{\mathcal F}$ such that F is many-one equivalent to C. For AC0-reductions we show the following results: the family CFL of context-free languages is densely complete in the complexity class SAC1. Moreover, we show that the indexed languages are densely complete in NP and the nondeterministic one-counter languages are densely complete in NL. On the other hand, we prove that the regular languages are not densely complete in NC1.

5 citations


Book ChapterDOI
23 Jul 2012
TL;DR: Four infinite hierarchies of the corresponding families of languages generated by internal contextual grammars with selection languages in the family of regular languages are obtained.
Abstract: In this paper, we study the power of internal contextual grammars with selection languages from subfamilies of the family of regular languages. If we consider families ${\cal F}_n$ which are obtained by restriction to n states or nonterminals or productions or symbols to accept or to generate regular languages, we obtain four infinite hierarchies of the corresponding families of languages generated by internal contextual grammars with selection languages in ${\cal F}_n$.

5 citations


Journal ArticleDOI
TL;DR: The present paper examines the source of this expressive power of graph grammars by analyzing complexity and decidability of the so-called k-connecting Lin-A-NLC (k-Lin-A -NLC) grammARS in which the right-hand side of each production contains at most k nodes that can be connected to outside nodes.

1 citations


01 Jan 2012
TL;DR: Examples of the transformation of context-free grammars in the objects of a new formalism, which is a special extension of the class of nondeterministic finite automata, can define all the possible context- free languages.
Abstract: Keywords: nondeterministic finite automata; context-free languages; algorithms of equivalent transformation.Annotation: This article provides examples of the transformation of context-free grammars in the objects of a new formalism, which is a special extension of the class of nondeterministic finite automata. The objects of this for-malism can define all the possible context-free languages.

1 citations


Book ChapterDOI
14 Aug 2012
TL;DR: It is shown that if the authors use arbitrary a-transducers, they can generate all recursively enumerable languages, and moreover, there exists a single fixed transducer, even over a two letter alphabet, which allows to generate all Recursively Enumerable languages.
Abstract: Synchronized context-free grammars are special context-free grammars together with a relation which must be satisfied between every pair of paths from root to leaf in a derivation tree, in order to contribute towards the generated language. In the past, only the equality relation and the prefix relation have been studied, with both methods generating exactly the ET0L languages. In this paper, we study arbitrary relations, and in particular, those defined by a transducer. We show that if we use arbitrary a-transducers, we can generate all recursively enumerable languages, and moreover, there exists a single fixed transducer, even over a two letter alphabet, which allows to generate all recursively enumerable languages. We also study the problem over unary transducers. Although it is left open whether or not we can generate all recursively enumerable languages with unary transducers, we are able to demonstrate that we can generate all ET0L languages as well as a language that is not an indexed language. Only by varying the transducer used to define the relation, this generalization is natural, and can give each of the following language families: context-free languages, a family between the E0L and ET0L languages, ET0L languages, and recursively enumerable languages.