Biologically Unavoidable Sequences
Samuel Alexander
TL;DR
This paper explores the concept of biologically unavoidable sequences in infinite genealogical networks, proving certain sequences are unavoidable and others avoidable, with applications to cellular automata.
Contribution
It introduces the notion of biologically unavoidable sequences, generalizes Koenig's Lemma, and demonstrates their relevance to cellular automata.
Findings
Every eventually periodic sequence is biologically unavoidable.
Some sequences are shown to be biologically avoidable.
Application to cellular automata demonstrates practical relevance.
Abstract
A biologically unavoidable sequence is an infinite gender sequence which occurs in every gendered, infinite genealogical network satisfying certain tame conditions. We show that every eventually periodic sequence is biologically unavoidable (this generalizes Koenig's Lemma), and we exhibit some biologically avoidable sequences. Finally we give an application of unavoidable sequences to cellular automata.
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