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On Lattices of Regular Sets of Natural Integers Closed under Decrementation

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.
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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


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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