Related papers: Non-closure under complementation for unambiguous …

We give in this paper a logical characterization for unambiguous Context Free Languages, in the vein of descriptive complexity. A fragment of the logic characterizing context free languages given by Lautemann, Schwentick and Th\'erien [18]…

We show that the set of binary words containing overlaps is not unambiguously context-free and that the set of ternary words containing overlaps is not context-free. We also show that the set of binary words that are not subwords of the…

We prove that the class of linear context-free tree languages is not closed under inverse linear tree homomorphisms. The proof is by contradiction: we encode Dyck words into a context-free tree language and prove that its preimage under a…

We propose a scalable framework for deciding, proving, and explaining (in-)equivalence of context-free grammars. We present an implementation of the framework and evaluate it on large data sets collected within educational support systems.…

A new family of categorial grammars is proposed, defined by enriching basic categorial grammars with a conjunction operation. It is proved that the formalism obtained in this way has the same expressive power as conjunctive grammars, that…

Answering a recent question of Crochemore, we prove that the language of words that are not abelian squares is not context-free.

We study a standard operator on classes of languages: unambiguous polynomial closure. We prove that for every class C of regular languages satisfying mild properties, the membership problem for its unambiguous polynomial closure UPol(C)…

This paper presents a restricted form of linear indexed grammars, called even linear indexed grammars, which yield the even linear indexed languages. These languages properly contain the context-free languages and are contained in the set…

Context-free language theory is a well-established area of mathematics, relevant to computer science foundations and technology. This paper presents the preliminary results of an ongoing formalization project using context-free grammars and…

We consider the class of groups whose word problem is poly-context-free; that is, an intersection of finitely many context-free languages. We show that any group which is virtually a finitely generated subgroup of a direct product of free…

Techniques are developed for creating new and general language families of only semilinear languages, and for showing families only contain semilinear languages. It is shown that for language families L that are semilinear full trios, the…

Nonterminal complexity of a context-free language is the smallest possible number of nonterminals in its generating grammar. While in general case nonterminal complexity computation problem is unsolvable, it can be computed for different…

This work is a survey of the main results reported for the degree of extension of two models defining non-regular languages, namely the context-free grammar and the extended automaton over groups. More precisely, we recall the main results…

In this paper, homological methods together with the theory of formal languages of theoretical computer science are proved to be effective tools to determine the growth and the Hilbert series of an associative algebra. Namely, we construct…

It is well-known that: (i) every context-free language over a singleton terminal alphabet is regular, and (ii) the class of languages that satisfy the Pumping Lemma is a proper super-class of the context-free languages. We show that any…

Recently researchers working in the LFG framework have proposed algorithms for taking advantage of the implicit context-free components of a unification grammar [Maxwell 96]. This paper clarifies the mathematical foundations of these…

The hairpin completion is an operation on formal languages that has been inspired by the hairpin formation in DNA biochemistry and by DNA computing. In this paper we investigate the hairpin completion of regular languages. It is well known…

Pumping lemmas are created to prove that given languages are not belong to certain language classes. There are several known pumping lemmas for the whole class and some special classes of the context-free languages. In this paper we prove…

In this paper we introduce a class of noncommutative (finitely generated) monomial algebras whose Hilbert series are algebraic functions. We use the concept of graded homology and the theory of unambiguous context-free grammars for this…

In this paper we consider the problem of context-free grammars comparison from the analysis point of view. We show that the problem can be reduced to numerical solution of systems of nonlinear matrix equations. The approach presented here…