Real World Verication

Scalable handling of real arithmetic is a crucial part of the verication of hybrid systems, mathematical algorithms, and mixed ana- log/digital circuits. Despite substantial advances in verication tech- nology, complexity issues with classical decision procedures are still a major obstacle for formal verication of real-world applications, e.g., in automotive and avionic industries. To identify strengths and weak- nesses, we examine state of the art symbolic techniques and implemen- tations for the universal fragment of real-closed elds: approaches based on quantier elimination, Grobner Bases, and semidenite programming for the Positivstellensatz. Within a uniform context of the verication tool KeYmaera, we compare these approaches qualitatively and quanti- tatively on verication benchmarks from hybrid systems, textbook algo- rithms, and on geometric problems. Finally, we introduce a new decision procedure combining Grobner Bases and semidenite programming for the real Nullstellensatz that outperforms the individual approaches on an interesting set of problems.

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