On lattices of regular sets of natural integers closed under decrementation

  • Authors:

  • Patrick Cégielski;Serge Grigorieff;Irène Guessarian

  • Affiliations:

  • LACL, EA 4219, Université Paris-Est Créteil, IUT, route forestière Hurtault, 77300 Fontainebleau, France;LIAFA, CNRS UMR 7089 and Université Paris-Diderot Paris7, Case 7014, 75205 Paris Cedex 13, France;LIAFA, CNRS UMR 7089 and Université Paris-Diderot Paris7, Case 7014, 75205 Paris Cedex 13, France

  • Venue:
  • Information Processing Letters
  • Year:
  • 2014

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Abstract

We consider lattices of regular sets of non negative integers, i.e. of sets definable in Presburger 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. We characterize the family of such functions.