Notion Of Recognizability Research Articles

Treewidth, pathwidth and cospan decompositions with applications to graph-accepting tree automata

We will revisit the categorical notion of cospan decompositions of graphs and compare it to the well-known notions of path decomposition and tree decomposition from graph theory. More specifically, we will define several types of cospan decompositions with appropriate width measures and show that these width measures coincide with pathwidth and treewidth. Such graph decompositions of small width are used to efficiently decide graph properties, for instance via graph automata. Hence we will give an application by defining graph-accepting tree automata, thus integrating previous work by Courcelle into the setting of cospan decompositions. Furthermore we will show that regardless of whether we consider path or tree decompositions, we arrive at the same notion of recognizability.

Regular sets of infinite message sequence charts

This paper resumes the study of regular sets of message sequence charts (MSC) initiated by Henriksen et al. [Technical Report, BRICS RS-99-52, 1999]. Differently from their results, we consider infinite MSCs. It is shown that for bounded sets of infinite MSCs, the notions of recognizability, axiomatizability in monadic second order logic, and acceptance by a deterministic message passing automaton with Muller acceptance condition coincide. We furthermore characterize the expressive power of first order logic and of its extension by modulo-counting quantifiers over bounded infinite MSCs. In order to prove our results, we exhibit a new connection to the theory of Mazurkiewicz traces using relabeling techniques.

On syntactic congruences for ω-languages

In this paper we investigate several questions related to syntactic congruences and to minimal automata associated with ω-languages. In particular we investigate relationships between the so-called simple (because it is a simple translation from the usual definition in the case of finitary languages) syntactic congruence and its infinitary refinement (the iteration congruence) investigated by Arnold (Theoret. Comput. Sci. 39 (1985) 333–335). We show that in both cases not every ω-language having a finite syntactic monoid is regular and we give a characterization of those ω-languages having finite syntactic monoids. Among the main results we derive a condition which guarantees that the simple syntactic congruence and Arnold's syntactic congruence coincide and show that all (including infinitestate) ω-languages in the Borel class Fσ∩ G δ satisfy this condition. We also show that all ω-languages in this class are accepted by their minimal-state automaton — provided they are accepted by any Muller automaton. Finally we develop an alternative theory of recognizability of ω-languages by families of right-congruence relations, and define a canonical object (much smaller then Arnold's monoid) associated with every ω-language. Using this notion of recognizability we give a necessary and sufficient condition for a regular ω-language to be accepted by its minimal-state automaton.

Logique, effectivité et faisabilité

AbstractThis paper can be read as an attempt at providing philosophical foundations to linear logic. The only plausible form of philosophical antirealism deals with practical feasibility rather than with effectivity in principle. The very notion of recognizability is ambiguous, audit has to be considered from a stricter perspective than currently done. The intuitionistic assertability conditions are to be reinforced. This change requires a move towards a frame in which the circumstances of the application of a logical rule can be specified. Gentzen's sequential calculi provide such a frame, when some structural rules have been removed or limited.