Idempotent tree languages

Finite idempotent groupoids and regular languages

On Varieties of Literally Idempotent Languages

A language L ⊆ A∗ is literally idempotent in case that uav ∈ L if and only if uav ∈ L for each u, v ∈ A∗, a ∈ A. Such classes result naturally by taking all literally idempotent languages in a classical (positive) variety or by considering a certain closure operator. We initiate their systematic study. Various classes of such languages can be characterized using syntactic methods. A starting ex...

Literally idempotent languages and their varieties - two letter case

A language L ⊆ A∗ is literally idempotent in case that uav ∈ L if and only if uav ∈ L, for each u, v ∈ A∗, a ∈ A. We already studied classes of such languages closely related to the (positive) varieties of the famous StraubingThérien hierarchy. In the present paper we start a systematic study of literal varieties of literally idempotent languages, namely we deal with the case of two letter alph...

Systolic Tree !-Languages

The class of !-languages recognized by systolic tree automa-ta is introduced. That class extends the class of B uchi !-languages and is closed under boolean operations. The emptiness problem for systolic tree automata on innnite sequences is decidable. A characterization of sys-tolic tree !-languages in terms of a (suitable) concatenation of ((nitary) systolic tree languages is also provided.

Local Weighted Tree Languages

Local weighted tree languages over semirings are introduced. For an arbitrary semiring, a weighted tree language is shown to be recognizable iff it appears as the image of a local weighted tree language under a deterministic relabeling.