Algebraic tools for the overlapping tile product

Etienne Dubourg (1, 2, 3) , David Janin (3, 2)

1 methodes formelles
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique
3 PoSET - Models for a Structured Programming of Space and Time

Overlapping tile automata and the associated notion of recognizability by means of (adequate) premorphisms in finite ordered monoids have recently been defined for coping with the collapse of classical recognizability in inverse monoids. In this paper, we investigate more in depth the associated algebraic tools that allows for a better understanding of the underlying mathematical theory. In particular, addressing the surprisingly difficult problem of language product and star, we eventually found some deep links with classical notions of inverse semigroup theory such as the notion of restricted product.

Mots clés: inverse semigroup; partially ordered monoid; restricted product; premorphism

Domaines: Théorie et langage formel [cs.FL]; Langage de programmation [cs.PL]; Logique [math.LO]

Etienne Dubourg, David Janin. Algebraic tools for the overlapping tile product. 8th International Conference on Language and Automata Theory and Applications (LATA), Mar 2014, Madrid, Spain. pp.335-346. ⟨hal-00879465⟩