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- Christiane Frougny, Jacques Sakarovitch
- Theor. Comput. Sci.
- 1993

- Jacques Sakarovitch
- Inf. Comput.
- 1987

We study here the properties of a family of monoids, which we call the rational monoids, and which are monoids with a multiplication of low complexity. A monoid is rational if its multiplication may be described by a rational function from a free monoid into itself. The main results are that rational monoids, like finite ones, have the properties that… (More)

- Sylvain Lombardy, Jacques Sakarovitch
- Logic and Automata
- 2008

This paper is a survey on the universal automaton, which is an automaton canonically associated with every language. In the last forty years, many objects have been defined or studied, that are indeed closely related to the universal automaton. We first show that every automaton that accepts a given language has a morphic image which is a subautomaton of… (More)

- Jacques Sakarovitch
- LATIN
- 1992

It is established here that it is decidable whether a rational set of a free partially commutative monoid (i.e. trace monoid) is recognizable or not if and only if the commutation relation is transitive (i.e. if the trace monoid is isomorphic to a free product of free commutative monoids). The bulk of the paper consists in a characterization of recognizable… (More)

We prove that two automata with multiplicity in Z are equivalent, i.e. define the same rational series, if and only if there is a sequence of Z-coverings, co-Z-coverings, and circulations of −1, which transforms one automaton into the other. Moreover, the construction of these transformations is effective. This is obtained by combining two results: the… (More)

- Jacques Sakarovitch
- IMYCS
- 1986

- Sylvain Lombardy, Jacques Sakarovitch
- Theor. Comput. Sci.
- 2002

This paper addresses the problem of turning a rational (ie regular) expression into a finite automaton. We formalize and generalize the idea of “partial derivatives” introduced in 1995 by V. Antimirov, in order to obtain a construction of an automaton with multiplicity from a rational expression describing a formal power series with coefficients in a… (More)

- Christiane Frougny, Jacques Sakarovitch
- STACS
- 1991

The purpose of this paper is the s tudy of the rational relations tha t is relations on words that are computable by finite 2-tape au tomata with the Proper ty that the difference of the length of two words in relation is bounded. The first motivat ion for this work has been the problem of representations of integers by means of non classical numerat ion… (More)

We show that two equivalent K-automata are conjugate to a third one, when K is equal to B, N, Z, or any (skew) field and that the same holds true for functional tranducers as well.