Abstract : 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.
https://hal.archives-ouvertes.fr/hal-01259673 Contributor : Irene GuessarianConnect in order to contact the contributor Submitted on : Thursday, January 21, 2016 - 10:10:44 AM Last modification on : Friday, November 19, 2021 - 6:06:03 PM Long-term archiving on: : Friday, November 11, 2016 - 1:43:52 PM
Patrick Cégielski, Serge Grigorieff, Guessarian Irene. On Lattices of Regular Sets of Natural Integers Closed under Decrementation. Information Processing Letters, Elsevier, 2014, 114, pp.197-202. ⟨hal-01259673⟩