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Separating the Words of a Language by Counting Factors

Saarela Aleksi

Fundamenta Informaticae

2021

Vol. 180, nr 4

375--393

For a given language L, we study the languages X such that for all distinct words u, v ∈ L, there exists a word x ∈ X that appears a different number of times as a factor in u and in v. In particular, we are interested in the following question: For which languages L does there exist a finite language X satisfying the above condition? We answer this question for all regular languages and for all sets of factors of infinite words.

Equality of Measure and Topological Entropies for Cellular Automata

Foryś W., Matyja J.

Schedae Informaticae

2006

Vol. 15

151-164

In the paper we consider cellular automata defined on metric spaces (AN, d) or (AZ, d) endowed with the uniform Bernoulli measure ž and present general constructions of such automata which are sur- jective, not positively expansive and ž is the measure of the maximal and positive entropy.