Abstract
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.
This work was partially supported by EGIDE/DAAD-Procope TAMTV.
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Habermehl, P., Kuske, D. (2015). On Presburger Arithmetic Extended with Modulo Counting Quantifiers. In: Pitts, A. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 2015. Lecture Notes in Computer Science(), vol 9034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46678-0_24
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