On Presburger Arithmetic Extended with Modulo Counting Quantifiers
نویسندگان
چکیده
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.
منابع مشابه
Deciding whether a relation defined in Presburger logic can be defined in weaker logics
We consider logics on Z and N which are weaker than Presburger arithmetic and we settle the following decision problem: given a k-ary relation on Z and N which are first order definable in Presburger arithmetic, are they definable in these weaker logics? These logics, intuitively, are obtained by adding modulo and threshold counting predicates. 1991 Mathematics Subject Classification. 03B10, 68...
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