Results 1  10
of
14
Series Expansions of Lyapunov Exponents and Forgetful Monoids
, 2000
"... We consider Lyapunov exponents of random iterates of monotone homogeneous maps. We assume that the images of some iterates are lines, with positive probability. Using this memoryloss property which holds generically for random products of matrices over the maxplus semiring, and in particular, for ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
(Show Context)
We consider Lyapunov exponents of random iterates of monotone homogeneous maps. We assume that the images of some iterates are lines, with positive probability. Using this memoryloss property which holds generically for random products of matrices over the maxplus semiring, and in particular, for Tetrislike heaps of pieces models, we give a series expansion formula for the Lyapunov exponent, as a function of the probability law. In the case of rational probability laws, we show that the Lyapunov exponent is an analytic function of the parameters of the law, in a domain that contains the absolute convergence domain of a partition function associated to a special "forgetful" monoid, defined by generators and relations.
Small overlap monoids II: Automatic structures and normal forms
 J. Algebra
"... Abstract. We show that any finite monoid or semigroup presentation satisfying the small overlap condition C(4) has word problem which is a deterministic rational relation. It follows that the set of lexicographically minimal words forms a regular language of normal forms, and that these normal forms ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
(Show Context)
Abstract. We show that any finite monoid or semigroup presentation satisfying the small overlap condition C(4) has word problem which is a deterministic rational relation. It follows that the set of lexicographically minimal words forms a regular language of normal forms, and that these normal forms can be computed in linear time. We also deduce that C(4) monoids and semigroups are rational (in the sense of Sakarovitch), asynchronous automatic, and word hyperbolic (in the sense of Duncan and Gilman). From this it follows that C(4) monoids satisfy analogues of Kleene’s theorem, and admit decision algorithms for the rational subset and finitely generated submonoid membership problems. We also prove some automatatheoretic results which may be of independent interest. 1.
Recent results in the theory o rational sets
 Mathematical Foundations of Computer Science
, 1986
"... This paper presents a survey of recent results in the theory of rational sets in arbitrary monoids. Main topics considered here are: the socalled Kleene monoids (i.e. monoids where Kleene's theorem holds), rational functions and relations, rational sets in partially commutative monoids, and ra ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
This paper presents a survey of recent results in the theory of rational sets in arbitrary monoids. Main topics considered here are: the socalled Kleene monoids (i.e. monoids where Kleene's theorem holds), rational functions and relations, rational sets in partially commutative monoids, and rational sets in free groups.
Algorithms for computing finite semigroups
 FOUNDATIONS OF COMPUTATIONAL MATHEMATICS, RIO DE JANEIRO: BRAZIL
, 1997
"... The aim of this paper is to present algorithms to compute finite semigroups. The semigroup is given by a set of generators taken in a larger semigroup, called the “universe”. This universe can be for instance the semigroup of all functions, partial functions, or relations on the set {1,..., n}, or t ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
The aim of this paper is to present algorithms to compute finite semigroups. The semigroup is given by a set of generators taken in a larger semigroup, called the “universe”. This universe can be for instance the semigroup of all functions, partial functions, or relations on the set {1,..., n}, or the semigroup of n × n matrices with entries in a given finite semiring. The algorithm produces simultaneously a presentation of the semigroup by generators and relations, a confluent rewriting system for this presentation and the Cayley graph of the semigroup. The elements of the semigroup are identified with the reduced words of the rewriting system. We also give some efficient algorithms to compute the Green relations, the local subsemigroups and the syntactic quasiorder of a subset of the semigroup.
Series Expansions of Lyapunov Exponents and
, 2000
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
Abstract
 Add to MetaCart
(Show Context)
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
FINITE AUTOMATA AND RATIONAL LANGUAGES  An Introduction
 PART I MATHEMATICAL FOUNDATIONS OF THE THEORY OF AUTOMATA
"... ..."
Algebraic characterization of the finite power property
"... Abstract. We give a transparent characterization, by means of a certain syntactic semigroup, of regular languages possessing the finite power property. Then we use this characterization to obtain a short elementary proof for the uniform decidability of the finite power property for rational language ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We give a transparent characterization, by means of a certain syntactic semigroup, of regular languages possessing the finite power property. Then we use this characterization to obtain a short elementary proof for the uniform decidability of the finite power property for rational languages in all monoids defined by a confluent regular system of deletion rules. This result in particular covers the case of free groups solved earlier by d’Alessandro and Sakarovitch by means of an involved reduction to the boundedness problem for distance automata. 1