Éric Laugerotte

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.

FROM REGULAR WEIGHTED EXPRESSIONS TO FINITE AUTOMATA

In this article we generalize concepts of the position automaton and ZPC-structure to the regular -expressions. We show that the extended ZPC-structure can be built in linear time w.r.t. the size of the -expression and that the associated position automaton can be deduced from it in quadratic time.

From Regular Tree Expression to Position Tree Automaton

The word position automaton was introduced by Glushkov and McNaughton in the early 1960. This automaton is homogeneous and has (||E|| + 1) states for an expression of alphabetic width ||E||. In this paper this type of automata is extended to regular tree expressions and it is shown that the conversion of a regular tree expression of size |E| and alphabetic width ||E|| into its reduced tree automaton can be done in O(|E|·||E||) time. The time complexity of the algorithm proposed by Dietrich Kuske and Ingmar Meinecke is also proved in order to reach an O(||E||·|E|) time complexity for the problem of the construction of the equation automaton from a regular tree expression.

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.

On the support of graph Lie algebras

We deal with the support of graph Lie algebras and we characterize the set of independence alphabets for which the noncommutative result can naturally be extended. We also provide an algorithm which decides if an independence alphabet fulfills the preceding condition.

From regular weighted expressions to finite automata

In this article we generalize the concepts of position automaton and ZPC structure to the regular K-expressions. We show that the ZPC structure can be built in linear time in the size of the expression and that the associated position automaton can be deduced from it in quadratic time.

Computing weights

This paper introduces an efficient weighted regognition algorithm. It is based on a suitable tree structure called ZPC without building the position automaton. The ZPC-structure results from the compact language and the polynomial structure of weighted expressions. We show that the time complexity of this algorithm is the best oneuntil now.