Alexander Meduna, Roman Lukás
Note on Iteratively Extendable Strings
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 59, 71-73(2005)

MSC:

68Q45 Formal languages, See also {03D05, 20M35, 94A45}

68Q70 Algebraic theory of automata, See also {18B20, 20M35}

Abstract: This scientific note introduces the notion of an iteratively
extendable string within a language. It demonstrates that every
language that has such an iteratively extendable string $z$
contains infinitely many strings whose length is divisible by the
length of $z$. Some consequences and applications of this result
are given.
Keywords: Formal languages, Pumping lemmas, Primes
Notes: Acknowledgement.
This work was supported by GACR grant GA201/04/0441
and GACR grant GA102/05/H050.