On shuffle ideals of general algebras

We extend a word language concept called shuffle ideal to general algebras. For this purpose, we introduce the relation SH and show that there exists a natural connection between this relation and the homeomorphic embedding order on trees. We establish connections between shuffle ideals, monotonically ordered algebras and automata, and piecewise testable tree languages

Regular tree languages and quasi orders

Regular languages were characterized as sets closed with respect to monotone well-quasi orders. A similar result is proved here for tree languages. Moreover, families of quasi orders that correspond to positive varieties of tree languages and varieties of finite ordered algebras are characterized

On nilpotent languages and their characterization by regular expressions

Tree languages recognized by deterministic root-to-frontier recognizers are also called DR-languages. The concept of generalized R-chain languages was introduced by the author in his paper On monotone languages and their characterization by regular expressions (Acta Cybernetica, 18 (2007), 117-134.) and it has turned out that the monotone DR-languages are exactly those languages that can be given by generalized R-chain languages. In this paper we give a similar characterization for nilpotent DR-languages by means of plain R-chain languages. Also a regular expression based characterization is given for nilpotent string languages

On monotone languages and their characterization by regular expressions

In one of their papers, F. Gécseg and B. Imreh gave a characterization for monotone string languages by regular expressions. It has turned out that the monotone string languages are exactly those languages that can be represented by finite unions of seminormal chain languages. In this paper a similar characterization is given for monotone DR-languages

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. 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