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Distributional Learning of Some Nonlinear Tree Grammars

Clark A., Kobele G. M., Kanazawa M., Yoshinaka R.

Fundamenta Informaticae

2016

Vol. 146, nr 4

339--377

A key component of Clark and Yoshinaka’s distributional learning algorithms is the extraction of substructures and contexts contained in the input data. This problem often becomes intractable with nonlinear grammar formalisms due to the fact that more than polynomially many substructures and/or contexts may be contained in each object. Previous works on distributional learning of nonlinear grammars avoided this difficulty by restricting the substructures or contexts that are made available to the learner. In this paper, we identify two classes of nonlinear tree grammars for which the extraction of substructures and contexts can be performed in polynomial time, and which, consequently, admit successful distributional learning in its unmodified, original form.

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).

Regular elements and Green's relations in power Menger algebras of terms

Denecke K., Glubudom P.

Demonstratio Mathematica

2008

Vol. 41, nr 1

11-22

Sets of terms of type r are called tree languages (see [5]). On sets of tree languages superposition operations can be defined in such a way that the collection of all tree languages of type r forms an abstract clone. Considering only sets of n-ary terms one obtains a Menger algebra (see e.g. [3]). From the superposition operations binary operations on tree languages can be derived. For the corresponding sernigroups of tree languages we study idempotent and regular elements as well as Green's relations L and R.