Periodicity and roots of transfinite strings

Periodicity and roots of transfinite strings

This contribution extends the notions of roots and periodicity to strings of transfinite lengths. It shows that given a transfinite string, either it possesses a unique root or the set of its roots are equivalent in a strong way. Mathematics Subject Classification. 68R15.

Transfinite Equations in Transfinite Strings

Approximate Periodicity in Strings

In many application areas (for instance, DNA sequence analysis), it becomes important to compute various kinds of \approximate period" of a given string y. Here we discuss three such approximate periods and the algorithms which compute them: an Abelian generator, a cover, and a seed. Let u be a substring of y. Then u is an Abelian generator of y ii y is a concatenation of substrings which are p...

The Theory of Rational Relations on Transfinite Strings

In order to explain the purpose of this paper, we recall briefly how the theory of “rationality” developed in the last fourty years. The theory of sets of finite strings recognized by finite automata, also known as regular or rational sets was developed in the fifties. It rapidly extended in two directions. Indeed, by solving the decidability problem of the second order monadic theory of one su...

Periodicity and Almost-periodicity