On lattices of regular sets of natural integers closed under decrementation |
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| Authors: | Patrick Cé gielski,Serge Grigorieff,Irè ne Guessarian |
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| Affiliation: | 1. LACL, EA 4219, Université Paris-Est Créteil, IUT, route forestière Hurtault, 77300 Fontainebleau, France;2. LIAFA, CNRS UMR 7089 and Université Paris-Diderot Paris7, Case 7014, 75205 Paris Cedex 13, France |
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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. |
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| Keywords: | Lattices Lattices of subsets of N Formal languages Theory of computation Regular subsets of N Closure properties |
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