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Idempotent tree languages

Denecke K., Sarasit N., Wismath S.

Demonstratio Mathematica

2013

Vol. 46, nr 1

1--14

A tree language of a fixed type τ is any set of terms of type τ. We consider here a binary operation +n on the set Wτ(Xn) of all n-ary terms of type τ, which results in semigroup (Wτ(Xn),+n). We characterize languages which are idempotent with respect to this binary operation, and look at varieties of tree languages containing idempotent languages. We also compare properties of semigroup homomorphisms from (P(Wτ(Xn));+n) to (P(Wτ(Xm));+m) with properties of homomorphisms between the corresponding absolutely free algebras Fτ(Xn) and Fτ(Xm).