Forest Algebras

Mikolaj Bojanczyk (1) , Igor Walukiewicz (2)

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

If in a transformation semigroup we assume that the set being acted upon has a semigroup structure, then the transformation semigroup can be used to recognize languages of unranked trees. This observation allows us to examine the relationship connecting languages of unranked trees with standard algebraic concepts such as aperiodicity, idempotency, commutativity and wreath product. In particular, we give algebraic characterizations of first-order logic, chain logic, CTL* and PDL. These do not, however, yield decidability results.

Mots clés: tree languages; algebraic characterization; first-order logic; recognition

Domaines: Logique en informatique [cs.LO]

Mikolaj Bojanczyk, Igor Walukiewicz. Forest Algebras. 2006. ⟨hal-00105796⟩