In recent works, a general framework for constraint satisfaction over nite domains has been proposed, based on the concept of semiring-valued constraints. Classical CSPs, fuzzy CSPs, hierachical CSPs can be easily cast in this general framework. In this paper, we claim that translating any constraint problem into a semiring-based constraint problem makes it possible to express global in-formati...

The automata arising from the well known conversion of regular expression to non deterministic automata have rather particular transition graphs. We refer to them as the Glushkov graphs, to honour his nice expression-to-automaton algorithmic short cut [10]. The Glushkov graphs have been characterized [6] in terms of simple graph theoretical properties and certain reduction rules. We show how to...

Wepresent a suite of algorithms for inference tasks over (finite and infinite) context-free sets. For generality and clarity, we have chosen the framework of semiring parsingwith support to the most common semirings (e.g. F, V, k- and I). We see parsing from themore general viewpoint of weighted deduction allowing for arbitrary weighted finite-state input and provide impleme...

Exotic semirings such as the “(max;+) semiring” (R[f 1g;max;+), or the “tropical semiring” (N[f+1g;min;+), have been invented and reinvented many times since the late fifties, in relation with various fields: performance evaluation of manufacturing systems and discrete event system theory; graph theory (path algebra) and Markov decision processes, Hamilton-Jacobi theory; asymptotic analysis (lo...

We consider the following matrix reachability problem: given r square matrices with entries in a semiring, is there a product of these matrices which attains a prescribed matrix? We define similarly the vector (resp. scalar) reachability problem, by requiring that the matrix product, acting by right multiplication on a prescribed row vector, gives another prescribed row vector (resp. when multi...