Arto Lepistö

Computer Science – Theory and Applications

Classical error-correcting codes deal with the problem of data transmission over a noisy channel. There are efficient error-correcting codes that work even when the noise is adversarial. In the interactive setting, the goal is to protect an entire conversation between two (or more) parties from adversarial errors. The area of interactive error correcting codes has experienced a substantial amount of activity in the last few years. In this talk we will introduce the problem of interactive errorcorrection and discuss some of the recent results. Finding All Solutions of Equations in Free Groups and Monoids with Involution Volker Diekert, Artur Jeż , and Wojciech Plandowski 1 Institut für Formale Methoden der Informatik, University of Stuttgart, Germany 2 Institute of Computer Science, University of Wroclaw, Poland 3 Max Planck Institute für Informatik, Saarbrcken, Germany 4 Institute of Informatics, University of Warsaw, Poland Abstract. The aim of this paper is to present a PSPACE algorithm The aim of this paper is to present a PSPACE algorithm which yields a finite graph of exponential size and which describes the set of all solutions of equations in free groups and monoids with involution in the presence of rational constraints. This became possible due to the recently invented recompression technique of the second author. He successfully applied the recompression technique for pure word equations without involution or rational constraints. In particular, his method could not be used as a black box for free groups (even without rational constraints). Actually, the presence of an involution (inverse elements) and rational constraints complicates the situation and some additional analysis is necessary. Still, the recompression technique is powerful enough to simplify proofs for many existing results in the literature. In particular, it simplifies proofs that solving word equations is in PSPACE (Plandowski 1999) and the corresponding result for equations in free groups with rational constraints (Diekert, Hagenah and Gutiérrez 2001). As a byproduct we obtain a direct proof that it is decidable in PSPACE whether or not the solution set is finite. * Supported by Humboldt Research Fellowship for Postdoctoral Researchers. 1 A full version of the present paper with detailed proofs can be found on arXiv. Algorithmic Meta Theorems for Sparse Graph Classes

Locally Periodic Infinite Words and a Chaotic Behaviour

We call a one-way infinite word w over a finite alphabet

Comparing Descriptional and Computational Complexity of Infinite Words

(\rho,p)

Transposition invariant words

-repetitive if all long enough prefixes of w contain as a suffix a

Combinatorics on Infinite Words

\rho

Developments in Language Theory

th power (or more generally a repetition of order

Relations between Local and Global Periodicity of Words (Extended Abstract)

\rho

On the Power of Periodic Iteration of Morphisms

) of a word of length at most p. We show that each (2,4)-repetitive word is ultimately periodic, as well as that there exist nondenumerably many, and hence also nonultimately periodic, (2,5)-repetitive words. Further we characterize nonultimately periodic (2,5)-repetitive words both structurally and algebraically.

Automata, Languages and Programming

This paper searches for connections between descriptional and computational complexities of infinite words. In the former one the complexity is measured by the complexity of the mechanism used to generate infinite words, typical examples being iterated morphisms, iterated dgsms and double D0L TAG systems. In the latter on the complexity is measured by resourses used by Turing machines to generate infinite words.

Proceedings of the 9th International Conference on Combinatorics on Words - Volume 8079

We define an operation called transposition on words of fixed length. This operation arises naturally when the letters of a word are considered as entries of a matrix. Words that are invariant with respect to transposition are of special interest. It turns out that transposition invariant words have a simple interpretation by means of elementary group theory. This leads us to investigate some properties of the ring of integers modulo n and primitive roots. In particular, we show that there are infinitely many prime numbers p with a primitive root dividing p+1 and infinitely many prime numbers p without a primitive root dividing p+1. We also consider the orbit of a word under transposition.