this paper, based on notes by R. Beals and M. Spivak, methods of nite semigroups were introduced to obtain some of the results of G. Hedlund.

Abstract not found

This paper presents a survey on length distributions of regular languages. The accent is problems in coding theory and the relation with symbolic dynamics.

| We give a new text compression scheme based on Forbidden Words ("antidictionary"). We prove that our algorithms attain the entropy for balanced binary sources. They run in linear time. Moreover, one of the main advantages of this approach is that it produces very fast decompressors. A second advantage is a synchronization property that is helpful to search compressed data and allows parallel compression. The techniques used in this paper are from Information Theory and Finite Automata. Keywords| Data Compression, Lossless compression, Information Theory, Finite Automaton, Forbidden Word, Pattern Matching. I.

We study whether the entropy (or growth rate) of minimal forbidden patterns of symbolic dynamical shifts of dimension 2 or more, is a conjugacy invariant. We prove that the entropy of minimal forbidden patterns is a conjugacy invariant for uniformly semi-strongly irreducible shifts. We prove a weaker invariant in the general case.

Abstract. The paper contains all the definitions and notations needed to understand the results concerning the field dealing with occurrences of patterns in permutations and words. Also, this paper includes a historical overview on the results obtained in this subject. The authors tried to collect all the currently existing references to the papers directly related to the subject. Moreover, a number of basic approaches to study the pattern problems are discussed.

A factor u of a word w is (right) univalent if there exists a unique letter a such that ua is still a factor of w. A univalent factor is minimal if none of its proper suffixes is univalent. The starting block of w is the shortest prefix hw of w such that all proper prefixes of w of length ≥|hw| are univalent. We study univalent factors of a word and their relationship with the well known notions of boxes, superboxes, and minimal forbidden factors. Moreover, we prove some new uniqueness conditions for words based on univalent factors. In particular, we show that a word is uniquely determined by its starting block, the set of the extensions of its minimal univalent factors, and its length or its terminal box. Finally, we show how the results and techniques presented can be used to solve the problem of sequence assembly for DNA molecules, under reasonable assumptions on the repetitive structure of the considered molecule and on the set of known fragments.

We give a quadratic-time algorithm to compute the set of minimal forbidden words of a factorial regular language. We give a linear-time algorithm to compute the minimal forbidden words of a finite set of words. This extends a previous result given for the case of a single word only. We also

We give an automatic method to generate transition matrices associated with two-dimensional contraints of finite type by using squared substitutions of constant dimension.