On Lattices of Regular Sets of Natural Integers Closed under Decrementation

Patrick Cegielski (1) , Serge Grigorieff (2) , Irene Guessarian (2)

1 LACL - Laboratoire d'Algorithmique Complexité et Logique
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

We consider lattices of regular sets of non negative integers, i.e. of sets definable in Presbuger arithmetic. We prove that if such a lattice is closed under decrement then it is also closed under many other functions: quotients by an integer, roots, etc.

Mots clés: closure properties; Lattices; lattices of subsets of N; regular subsets of N; closure properties.

Domaines: Algorithme et structure de données [cs.DS]

Patrick Cegielski, Serge Grigorieff, Irene Guessarian. On Lattices of Regular Sets of Natural Integers Closed under Decrementation. 2013. ⟨hal-00870130⟩