Monoid automata for displacement context-free languages

In 2007 Kambites presented an algebraic interpretation of Chomsky-Schutzenberger theorem for context-free languages. We give an interpretation of the corresponding theorem for the class of displacement context-free languages which are equivalent to well-nested multiple context-free languages. We also obtain a characterization of k-displacement context-free languages in terms of monoid automata and show how such automata can be simulated on two stacks. We introduce the simultaneous two-stack automata and compare different variants of its definition. All the definitions considered are shown to be equivalent basing on the geometric interpretation of memory operations of these automata.Comment: Revised version for ESSLLI Student Session 2013 selected paper

A Chomsky-Schützenberger-Stanley type characterization of the class of slender context-free languages

Slender context-free languages have a complete algebraic characterization by L. Ilie in [13]. In this paper we give another characterization of this class of languages. In particular, using linear Dyck languages instead of unrestricted ones, we obtain a Chomsky-Schützenberger-Stanley type characterization of slender context-free languages

Linear indexed languages

AbstractIn this paper one characterization of linear indexed languages based on controlling linear context-free grammars with context-free languages and one based on homomorphic images of context-free languages are given. By constructing a generator for the family of linear indexed languages, it is shown that this family is a full principal semi-AFL. Furthermore a Parikh theorem for linear indexed languages is stated which implies that there are indexed languages which are not linear

Strict deterministic grammars

A grammatical definition of a family of deterministic context free languages is presented. It is very easy to decide if a context free grammar is strict deterministic. A characterization theorem involving pushdown automata is proved, and it follows that the strict deterministic languages are coextensive with the family of prefix free deterministic languages. It is possible to obtain an infinite hierarchy of strict deterministic languages as defined by their degree

Abstract Interpretation of Indexed Grammars.

Indexed grammars are a generalization of context-free grammars and recognize a proper subset of context-sensitive languages. The class of languages recognized by indexed grammars are called indexed languages and they correspond to the languages recognized by nested stack automata. For example indexed grammars can recognize the language {a^n b^n c^n | n > = 1} which is not context-free, but they cannot recognize {(ab^n)^n) | n >= 1} which is context-sensitive. Indexed grammars identify a set of languages that are more expressive than context-free languages, while having decidability results that lie in between the ones of context-free and context-sensitive languages. In this work we study indexed grammars in order to formalize the relation between indexed languages and the other classes of languages in the Chomsky hierarchy. To this end, we provide a fixpoint characterization of the languages recognized by an indexed grammar and we study possible ways to abstract, in the abstract interpretation sense, these languages and their grammars into context-free and regular languages

Circular Languages Generated by Complete Splicing Systems and Pure Unitary Languages

Circular splicing systems are a formal model of a generative mechanism of circular words, inspired by a recombinant behaviour of circular DNA. Some unanswered questions are related to the computational power of such systems, and finding a characterization of the class of circular languages generated by circular splicing systems is still an open problem. In this paper we solve this problem for complete systems, which are special finite circular splicing systems. We show that a circular language L is generated by a complete system if and only if the set Lin(L) of all words corresponding to L is a pure unitary language generated by a set closed under the conjugacy relation. The class of pure unitary languages was introduced by A. Ehrenfeucht, D. Haussler, G. Rozenberg in 1983, as a subclass of the class of context-free languages, together with a characterization of regular pure unitary languages by means of a decidable property. As a direct consequence, we characterize (regular) circular languages generated by complete systems. We can also decide whether the language generated by a complete system is regular. Finally, we point out that complete systems have the same computational power as finite simple systems, an easy type of circular splicing system defined in the literature from the very beginning, when only one rule is allowed. From our results on complete systems, it follows that finite simple systems generate a class of context-free languages containing non-regular languages, showing the incorrectness of a longstanding result on simple systems