Tables, Memorized Semirings and Applications

Cyrille Bertelle (1) , Gérard Henry Edmond Duchamp (2) , Khalaf Khatatneh (3)

1 LIH - Laboratoire d'informatique du Havre
2 LIPN - Laboratoire d'Informatique de Paris-Nord
3 LIFAR - Laboratoire d'informatique fondamentale et appliquée de Rouen

We define and construct a new data structure, the tables, this structure generalizes the (finite) $k$-sets sets of Eilenberg \cite{Ei}, it is versatile (one can vary the letters, the words and the coefficients). We derive from this structure a new semiring (with several semiring structures) which can be applied to the needs of automatic processing multi-agents behaviour problems. The purpose of this account/paper is to present also the basic elements of this new structures from a combinatorial point of view. These structures present a bunch of properties. They will be endowed with several laws namely : Sum, Hadamard product, Cauchy product, Fuzzy operations (min, max, complemented product) Two groups of applications are presented. The first group is linked to the process of "forgetting" information in the tables. The second, linked to multi-agent systems, is announced by showing a methodology to manage emergent organization from individual behaviour models.

Mots clés: efficient algebraic structures; efficient data structures; tables; semirings

Domaines: Système multi-agents [cs.MA]; Mathématique discrète [cs.DM]

Cyrille Bertelle, Gérard Henry Edmond Duchamp, Khalaf Khatatneh. Tables, Memorized Semirings and Applications. 2005. ⟨hal-00004303⟩