Inverse monoids of higher-dimensional strings

David Janin (1, 2)

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

Halfway between graph transformation theory and inverse semigroup theory, we define higher dimensional strings as bi-deterministic graphs with distinguished sets of input roots and output roots. We show that these generalized strings can be equipped with an associative product so that the resulting algebraic structure is an inverse semigroup. Its natural order is shown to capture existence of root preserving graph mor-phism. A simple set of generators is characterized. As a subsemigroup example, we show how all finite grids are finitely generated. Last, simple additional restrictions on products lead to the definition of subclasses with decidable Monadic Second Order (MSO) language theory.

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

David Janin. Inverse monoids of higher-dimensional strings. 12th International Colloquium on Theoretical Aspects of Computing (ICTAC 2015), 2015, Cali, Colombia. ⟨hal-01165724v2⟩