A note on Thue games
Discrete Mathematics
2016-01-12 v1 Formal Languages and Automata Theory
Abstract
In this work we improve on a result from~\cite{GryKosZma15}. In particular, we investigate the situation where a word is constructed jointly by two players who alternately append letters to the end of an existing word. One of the players (Ann) tries to avoid (non-trivial) repetitions, while the other one (Ben) tries to enforce them. We show a construction that is closer to the lower bound showed in~\cite{GryKozMic13} using entropy compression, and building on the probabilistic arguments based on a version of the Lov\'asz Local Lemma from~\cite{Peg11}. We provide an explicit strategy for Ann to avoid (non-trivial) repetitions over a -letter alphabet.
Cite
@article{arxiv.1601.02453,
title = {A note on Thue games},
author = {Robert Mercaş and Dirk Nowotka},
journal= {arXiv preprint arXiv:1601.02453},
year = {2016}
}