In this article we define the semigroup associated to a primitive substitution. We use it construct minimal automaton which generates substitution sequence u in reverse reading. show, case where has coincidence, that completely describes semicocycle discontinuities of u.

In this paper we describe a “light” algorithm for the on-line construction of a small automaton recognising a finite set of words. The algorithm runs in linear time. We carried out good experimental results on real dictionaries, on biological sequences and on the sets of suffixes (resp. factors) of a set of words that shows how our automaton is near to the minimal one. For the suffixes of a tex...

There exist various well-known characterizations of sets of numbers recognizable by a nite automaton, when they are represented in some integer base p 2. We show how to modify these characterizations, when integer bases p are replaced by linear numeration systems whose characteristic polynomial is the minimal polynomial of a Pisot number. We also prove some related interesting properties.

We study a connection between synchronizing automata and its set M of minimal reset words, i.e., such that no proper factor is a reset word. We first show that any synchronizing automaton having the set of minimal reset words whose set of factors does not contain a word of length at most 1 4 min{|u| : u ∈ I} + 1 16 has a reset word of length at most (n − 1 2 ) 2. In the last part of the paper w...

A homomorphism of an automaton A without outputs onto a subau-tomaton B of A is called a retract homomorphism if it leaves the elements of B fixed. An automaton A is called a retractable automaton if, for every subautomaton B of A, there is a retract homomorphism of A onto B. In [1] and [3], special retractable automata are examined. The purpose of this paper is to give a construction for state...

A deterministic automaton accepting a regular language L is a state-partition automaton with respect to a projection P if the state set of the deterministic automaton accepting the projected language P (L), obtained by the standard subset construction, forms a partition of the state set of the automaton. In this paper, we study fundamental properties of state-partition automata. We provide a co...

We investigate weak recognizability of deterministic languages of infinite trees. We prove that for deterministic languages the Borel hierarchy and the weak index hierarchy coincide. Furthermore, we propose a procedure computing for a deterministic automaton an equivalent minimal index weak automaton with a quadratic number of states. The algorithm works within the time of solving the emptiness...

We propose a practical technique to compile pattern-matching for prioritised overlapping patterns in equational languages into a minimal, deterministic, left-toright, matching automaton. First, we present a method for constructing a tree matching automaton for such patterns. This allows pattern-matching to be performed without any backtracking. Space requirements are reduced by using a directed...

We propose the characterization of binary cellular automata using a set of behavioral metrics that are applied to the minimal Boolean form of a cellular automaton’s transition function. These behavioral metrics are formulated to satisfy heuristic criteria derived from elementary cellular automata. Behaviors characterized through these metrics are growth, decrease, chaoticity, and stability. Fro...

It is decidable if a set of numbers, whose representation in a base b is a regular language, is ultimately periodic. This was established by Honkala in 1986. We give here a structural description of minimal automata that accept an ultimately periodic set of numbers. We then show that it can be verified in linear time if a given minimal automaton meets this description. This yields a O(n log(n))...