10 research outputs found
On DR tree automata, unary algebras and syntactic path monoids
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. GĂ©cseg (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 GĂ©cseg and B. Imreh (2002, 2004) are obtained this way