Superposition modulo non-linear arithmetic

Authors:
Andreas Eggers;Evgeny Kruglov;Stefan Kupferschmid;Karsten Scheibler;Tino Teige;Christoph Weidenbach
Affiliations:
Dept. of Computing Science, Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany;Universität des Saarlandes, Max-Planck-Institut für Informatik, Saarbrücken, Germany;Institute of Computer Science, Albert-Ludwigs-University, Freiburg im Breisgau, Germany;Institute of Computer Science, Albert-Ludwigs-University, Freiburg im Breisgau, Germany;Dept. of Computing Science, Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany;Universität des Saarlandes, Max-Planck-Institut für Informatik, Saarbrücken, Germany
Venue:
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
Year:
2011

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Abstract

The first-order theory over non-linear arithmetic including transcendental functions (NLA) is undecidable. Nevertheless, in this paper we show that a particular combination with superposition leads to a sound and complete calculus that is useful in practice. We follow basically the ideas of the SUP(LA) combination, but have to take care of undecidability, resulting in "unknown" answers by the NLA reasoning procedure. A pipeline of NLA constraint simplification techniques related to the SUP(NLA) framework significantly decreases the number of "unknown" answers. The resulting approach is implemented as SUP(NLA) by a system combination of Spass and iSAT. Applied to various scenarios of traffic collision avoidance protocols, we show by experiments that Spass(iSAT) can fully automatically proof and disproof safety properties of such protocols using the very same formalization.