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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Superposition Modulo Non-linear Arithmetic
verfasst von : Andreas Eggers, Evgeny Kruglov, Stefan Kupferschmid, Karsten Scheibler, Tino Teige, Christoph Weidenbach
Erschienen in: Frontiers of Combining Systems
Verlag: Springer Berlin Heidelberg
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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.