The class of rational subsets of a group G is the smallest class that contains all finite subsets of G and that is closed with respect to union, product and taking the monoid generated by a set. The rational subset membership problem for a finitely generated group G is the decision problem, where for a given rational subset of G and a group element g it is asked whether g ∈ G. This paper presen...

We give in this paper an example of infinitary rational relation, accepted by a 2-tape Büchi automaton, which is Π 3 -complete in the Borel hierarchy. Moreover the example of infinitary rational relation given in this paper has a very simple structure and can be easily described by its sections.

Set constraints are inclusions between expressions denoting sets of ground terms They have been used extensively in program analysis and type inference In this paper we investigate the topological structure of the spaces of solutions to systems of set constraints We identify a family of topological spaces called rational spaces which formalize the notion of a topological space with a regular or...

In various distributed systems, it may happen that parties need to find a union of their data sets. This may happen in database synchronisation, shared file systems and during the use of gossip protocols. Generic approaches have been using interactive protocols where they also share common records. This approach leads to communication complexity being dependant of the size of sets and is clearl...

The classic knapsack and related problems have natural generalizations to arbitrary (non-commutative) groups, collectively called knapsacktype problems in groups. We study the effect of free and direct products on their time complexity. We show that free products in certain sense preserve time complexity of knapsack-type problems, while direct products may amplify it. Our methods allow to obtai...

(1.2) Let k be an algebraically closed field of arbitrary characteristic. For a ring A, an A-module means a left A-module, unless otherwise specified. However, an ideal of A means a two-sided ideal, not a left ideal. Amod denotes the category of finitely generated A-modules. For a group G, a G-module means a kG-module, where kG is the group algebra of G over k. If V is a finite dimensional vect...

— In this article, we define afamily of context free languages, the quasi deterministic languages, which is strictly inserted between the families of deterministic and non ambiguous context free languages. The family is closed under complement, intersection with a rational set, inverse homomorphism... On the contrary, it is not closed under mirror image but the languages the mirror image of whi...

This paper addresses methods for the development of quality standards for cross-national quantitative surveys. Five conceptual approaches to the development of standards are presented and the properties and consequences of each are discussed. The aim is to provide researchers with a rational set of arguments for choosing a particular approach in a given situation. The development of quality sta...