Deduction Modulo Real Algebra and Computer Algebra

Chapter

Synopsis

We show how deductive, real algebraic, and computer algebraic methods can be combined for verifying hybrid systems in an automated theorem proving approach. In particular, we highlight the interaction of deductive and algebraic reasoning that is used for handling the joint discrete and continuous behaviour of hybrid systems. Systematically, we derive a canonical tableau procedure modulo from the calculus of differential dynamic logic. We delineate the nondeterminisms in the tableau procedure carefully and analyse their practical impact in the presence of computationally expensive handling of real algebraic constraints. Based on experience with larger case studies, we analyse proof strategies for dealing with the practical challenges for integrated algebraic and deductive verification of hybrid systems. To overcome the complexity pitfalls of integrating real arithmetic, we propose the iterative background closure and iterative inflation order strategies, with which we achieve substantial computational improvements.

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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.School of Computer ScienceCarnegie Mellon UniversityPittsburghUSA

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