Marianne Flouret

Direct and dual laws for automata with multiplicities

We present here theoretical results coming from the implementation of the package called AMULT (automata with multiplicities). We show that classical formulas are optimal for the bounds. Especially they are almost everywhere optimal for the fields R and C. We characterize the dual laws preserving rationality and examine compatibility between the geometry of the K-automata andthese laws. Copyright 2001 Elsevier Science B.V.

Glushkov Construction for Multiplicities

We present an extension to multiplicities of a classical algorithm for computing a boolean automaton from a regular expression. The Glushkov construction computes an automaton with n + 1 states from a regular expression with n occurences of letters. We show that the Glushkov algorithm still suits to the multiplicity case. Next, we give three equivalent extended step by step algorithms.

Glushkov Construction For Series: The Non Commutative Case

We present an extension to multiplicities of a classical algorithm for computing a boolean automaton from a regular expression. The Glushkov construction computes an automaton with n +1 states from a regular expression with n occurences of letters. We give an extension of the Glushkov algorithm for the multiplicity case in a non commutative semiring. Next, we give four equivalent extended step by step algorithms.

From Glushkov WFAs to \mathbb{K}-Expressions

We take an active interest in the problem of conversion of a Weighted Finite Automaton (WFA) into a \mathbb{K}-expression. The known algorithms give an exponential size expression in the number of states of the given automaton. We study the McNaughton-Yamada algorithm in the case of multiplicities and then we show that the resulting \mathbb{K}-expression is in the Star Normal Form (SNF) defined by Bruggemann-Klein [3]. The Glushkov algorithm computes an (n + 1)-state automaton from an expression having n occurrences of letters even in the multiplicity case [5]. We reverse this procedure and get a linear size \mathbb{K}-expression from a Glushkov WFA. A characterization of Glushkov WFAs which are not in SNF is given. This characterization allows us to emphasize a normal form for \mathbb{K}-expressions. As for SNF in the boolean case, we show that every \mathbb{K}-expression has an equivalent one in normal form having the same Glushkov WFA. We end with an algorithm giving a small normal form \mathbb{K}-expression from a Glushkov WFA.

Implementing validated agents behaviours with automata based on goal decomposition trees

In order to provide an effective tool allowing to implement validated agents behaviours, this paper first presents a Goal Decomposition Tree (GDT), a model to specify behaviours both in procedural and declarative ways. A GDT allows the designer to verify the specified behaviour. This model is then used to generate a behaviour automaton using automata composition patterns associated to operators used in the tree. This process allows to obtain a finite expression representing all valid behaviours of agents of a MAS.

A Methodology to Solve Optimisation Problems with MAS Application to the Graph Colouring Problem

Developing multi-agent systems may be a rather difficult task. Having confidence in the result is still more difficult. In this article, we describe a methodology that helps in this task. This methodology is dedicated to global optimization problems that can be solved combining local constraints. We developed CASE tools to support this methodology which are also presented. Finally, we show how this methodology has been successfully used to develop a multi-agent system for the graph colouring problem.

k,l-Unambiguity and Quasi-Deterministic Structures: An Alternative for the Determinization

We focus on the family of k,l-unambiguous automata that encompasses the one of deterministic k-lookahead automata introduced by Han and Wood. We show that this family presents nice theoretical properties that allow us to compute quasi-deterministic structures. These structures are smaller than DFAs and can be used to solve the membership problem faster than NFAs.

SPACE: A method to increase tracability in MAS development

This paper deals with a method and a model called SPACE allowing to design multiagent systems. Their main interest is to introduce tools to design and to validate the produced system at the same time. First, the main steps of the proposed method are described. Then, the different components of the SPACE model are defined. Finally, two case studies (on a BDI model and on a graph colouring problem) show how the method and the model can be applied.

SEA: A Symbolic Environment for Automata Theory

We here present the system SEA which integrates manipulations over boolean and multiplicity automata. The system provides also self development facilities.

Star normal form, rational expressions, and glushkov WFAs properties

In this paper, we extend the characterisation of Glushkov automata to multiplicities. We consider automata obtained from rational expressions in star normal form. We show that for this class of automata, the graphical Boolean properties are preserved. We prove that this new characterization only depends on conditions on coefficients and we explicit these conditions.