On Presburger Arithmetic Extended with Modulo Counting Quantifiers

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9034)


We consider Presburger arithmetic (PA) extended with modulo counting quantifiers. We show that its complexity is essentially the same as that of PA, i.e., we give a doubly exponential space bound. This is done by giving and analysing a quantifier elimination procedure similar to Reddy and Loveland’s procedure for PA. We also show that the complexity of the automata-based decision procedure for PA with modulo counting quantifiers has the same triple-exponential time complexity as the one for PA when using least significant bit first encoding.


Decision Procedure Free Variable Atomic Formula Elimination Procedure Extended Logic 
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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.LIAFAUniversity Paris DiderotParisFrance
  2. 2.TU IlmenauIlmenauGermany

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