On Lattices of Regular Sets of Natural Integers Closed under Decrementation

Patrick Cégielski (1) , Serge Grigorieff (2) , Irene Guessarian (3)

1 LACL - Laboratoire d'Algorithmique Complexité et Logique
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications
3 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale

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: Lattices; lattices of subsets of N; regular subsets of N; closure properties

Domaines: Informatique [cs]; Logique [math.LO]

Patrick Cégielski, Serge Grigorieff, Irene Guessarian. On Lattices of Regular Sets of Natural Integers Closed under Decrementation. Information Processing Letters, 2014, 114 (4), pp.197-202. ⟨10.1016/j.ipl.2013.11.013⟩. ⟨hal-01259673⟩