Embedding finite and infinite words into overlapping tiles

Anne Dicky (1) , David Janin (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

Omega-semigroups are to languages of infinite strings what semigroups are to languages of finite strings: they allow for obtaining an algebraic characterization of regular languages of infinite words. Defined as two-sorted algebras, ω-semigroups distinguish (images of) finite words from (images of) infinite ones. Recently, it has been shown that there are some benefits in embedding finite words (strings) and infinite words (streams) into finite or infinite birooted words (tiled streams). In this paper, we show that such an embedding is robust enough to be extended to the algebraic level by embedding the two-sorted ω-semigroups into (some notion of) one-sorted Ehresmann ordered ω-monoids. As a byproduct, we obtain an algebraic characterization of regular languages of finite and infinite birooted words that generalizes and unifies the alge- braic characterizations of regular languages of finite and infinite words.

Domaines: Théorie et langage formel [cs.FL]

Anne Dicky, David Janin. Embedding finite and infinite words into overlapping tiles. 2013. ⟨hal-00910002v1⟩