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On Lattices of Regular Sets of Natural Integers Closed under Decrementation

Patrick Cégielski 1 Serge Grigorieff 2 Guessarian Irene 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
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.
Keywords : Lattices lattices of subsets of N regular subsets of N closure properties
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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

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  • HAL Id : hal-01259673, version 1
  • ARXIV : 1310.1378

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CNRS | UNIV-PARIS7 | LACL | UPEC-UPEM | UPEC | UNIV-PARIS | UP-SCIENCES | ANR

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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⟩

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