On DR tree automata, unary algebras and syntactic path monoids

  • Magnus Steinby

Abstract

We consider deterministic root-to-frontier (DR) tree recognizers and the tree languages recognized by them from an algebraic point of view. We make use of a correspondence between DR algebras and unary algebras shown by Z. Esik (1986). We also study a question raised by F. Gécseg (2007) that concerns the definability of families of DR-recognizable tree languages by syntactic path monoids. We show how the families of DR-recognizable tree languages path-definable by a variety of finite monoids (or semigroups) can be derived from varieties of string languages. In particular, the three pathdefinable families of Gécseg and B. Imreh (2002, 2004) are obtained this way.
Published
2017-01-01
How to Cite
Steinby, M. (2017). On DR tree automata, unary algebras and syntactic path monoids. Acta Cybernetica, 23(1), 159-174. https://doi.org/10.14232/actacyb.23.1.2017.10
Section
Regular articles