The branching point approach to Conway's problem

Authors:
Juhani Karhumäki;Ion Petre
Affiliations:
Department of Mathematics, University of Turku and Turku Centre for Computer Science (TUCS), Turku, Finland;Department of Mathematics, University of Turku and Turku Centre for Computer Science (TUCS), Turku, Finland
Venue:
Formal and natural computing
Year:
2002

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Abstract

A word u is a branching point for a set of words X if there are two different letters a and b such that both ua and ub can be extended to words in X+. A branching point u is critical for X if u ∈ X+. Using these notions, we give an elementary solution for Conway's Problem in the case of finite biprefixes. We also discuss a possible extension of this approach rewards a complete solution for Conway's Problem.