Fixed points of endomorphisms over special confluent rewriting systems.
Monoids defined by special confluent rewriting systems have been studied through an approach that preserves some of the properties of the case of free groups and contains the particular case of free products of cyclic groups. Cayley graphs of these monoids are known to be hyperbolic and to have a compact completion for the prefix metric. In this very interesting and well written paper, the author pursues this approach to investigate the dynamics of finite and infinite fixed point submonoids for two important classes of monoid endomorphisms: boundary-injective endomorphisms and bounded length decrease endomorphisms. He does this by using automata-theoretic, combinatorial, and topological techniques. In particular, he introduces and explores the automata-theoretic, not known to be decidable, property of finite-splitting for endomorphisms.
scientific article; zbMATH DE number 5815567
scientific article