Forest Algebras

Mikolaj Bojanczyk (1) , Igor Walukiewicz (2)

1 Institute of Informatics [Warsaw]
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

There are at least as many interesting classes of regular tree lan- guages as there are of regular word languages. However, much less is known about the former ones. In particular, very few decidable char- acterizations of tree language classes are known. For words, most known characterizations are obtained using algebra. With this in mind, the present paper proposes an algebraic framework for classi- fying regular languages of finite unranked labeled trees. If in a transformation semigroup we assume that the set being acted upon has a semigroup structure, then the transformation semi- group can be used to recognize languages of unranked trees. This observation allows us to examine the relationship connecting tree lan- guages with standard algebraic concepts such as aperiodicity idem- potency, or commutativity. The new algebraic setting is used to give several examples of decidable algebraic characterizations.

Domaines: Logique en informatique [cs.LO]

Mikolaj Bojanczyk, Igor Walukiewicz. Forest Algebras. Logic and Automata, Amsterdam University Press, pp.107-132, 2007, Texts in Logic and Games. ⟨hal-00346087⟩