Regular realizability problems and context-free languages

We investigate regular realizability (RR) problems, which are the problems of verifying whether intersection of a regular language -- the input of the problem -- and fixed language called filter is non-empty. In this paper we focus on the case of context-free filters. Algorithmic complexity of the RR problem is a very coarse measure of context-free languages complexity. This characteristic is compatible with rational dominance. We present examples of P-complete RR problems as well as examples of RR problems in the class NL. Also we discuss RR problems with context-free filters that might have intermediate complexity. Possible candidates are the languages with polynomially bounded rational indices.Comment: conference DCFS 201

The Lambek calculus with iteration: two variants

Formulae of the Lambek calculus are constructed using three binary connectives, multiplication and two divisions. We extend it using a unary connective, positive Kleene iteration. For this new operation, following its natural interpretation, we present two lines of calculi. The first one is a fragment of infinitary action logic and includes an omega-rule for introducing iteration to the antecedent. We also consider a version with infinite (but finitely branching) derivations and prove equivalence of these two versions. In Kleene algebras, this line of calculi corresponds to the *-continuous case. For the second line, we restrict our infinite derivations to cyclic (regular) ones. We show that this system is equivalent to a variant of action logic that corresponds to general residuated Kleene algebras, not necessarily *-continuous. Finally, we show that, in contrast with the case without division operations (considered by Kozen), the first system is strictly stronger than the second one. To prove this, we use a complexity argument. Namely, we show, using methods of Buszkowski and Palka, that the first system is $\Pi_1^0$-hard, and therefore is not recursively enumerable and cannot be described by a calculus with finite derivations

Groups whose word problem is a Petri net language

There has been considerable interest in exploring the connections between the word problem of a finitely generated group as a formal language and the algebraic structure of the group. However, there are few complete characterizations that tell us precisely which groups have their word problem in a specified class of languages. We investigate which finitely generated groups have their word problem equal to a language accepted by a Petri net and give a complete classification, showing that a group has such a word problem if and only if it is virtually abelian

An Infinite Sequence of Full AFL-Structures, Each of Which Possesses an Infinite Hierarchy

We investigate different sets of operations on languages which results in corresponding algebraic structures, viz.\ in different types of full AFL's (full Abstract Family of Languages). By iterating control on ETOL-systems we show that there exists an infinite sequence ${\cal C}_m$ ($m\geq1$) of classes of such algebraic structures (full AFL-structures): each class is a proper superset of the next class (${\cal C}_m\supset{\cal C}_{m+1}$). In turn each class ${\cal C}_m$ contains a countably infinite hierarchy, i.e., a countably infinite chain of language families $K_{m,n}$ ($n\geq1$) such that (i) each $K_{m,n}$ is closed under the operations that determine ${\cal C}_m$, and (ii) each $K_{m,n}$ is properly included in the next one: $K_{m,n}\subset K_{m,n+1}$

Incidents dans la manipulation des sources radioactives. Vingt annees d'experience au C.E.N.-Saclay

SIGLEAvailable from CEN Saclay, Service de Documentation, 91191 Gif-sur-Yvette Cedex (France) / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc