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» Rewrite Systems for Integer Arithmetic
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ARITH
2005
IEEE
14 years 1 months ago
Arithmetic Operations in the Polynomial Modular Number System
We propose a new number representation and arithmetic for the elements of the ring of integers modulo p. The socalled Polynomial Modular Number System (PMNS) allows for fast polyn...
Jean-Claude Bajard, Laurent Imbert, Thomas Plantar...
RTA
2010
Springer
13 years 5 months ago
Polynomial Interpretations over the Reals do not Subsume Polynomial Interpretations over the Integers
Polynomial interpretations are a useful technique for proving termination of term rewrite systems. They come in various flavors: polynomial interpretations with real, rational and...
Friedrich Neurauter, Aart Middeldorp
CAV
2008
Springer
158views Hardware» more  CAV 2008»
13 years 9 months ago
Linear Arithmetic with Stars
We consider an extension of integer linear arithmetic with a "star" operator takes closure under vector addition of the solution set of a linear arithmetic subformula. We...
Ruzica Piskac, Viktor Kuncak
JSC
2006
147views more  JSC 2006»
13 years 7 months ago
An algorithm to solve integer linear systems exactly using numerical methods
In this paper, we present a new algorithm for the exact solutions of linear systems with integer coefficients using numerical methods. It terminates with the correct answer in wel...
Zhendong Wan
LPAR
2010
Springer
13 years 5 months ago
Satisfiability of Non-linear (Ir)rational Arithmetic
Abstract. We present a novel way for reasoning about (possibly ir)rational quantifier-free non-linear arithmetic by a reduction to SAT/SMT. The approach is incomplete and dedicated...
Harald Zankl, Aart Middeldorp