Real World Verification

Scalable handling of real arithmetic is a crucial part of the verification of hybrid systems, mathematical algorithms, and mixed analog/digital circuits. Despite substantial advances in verification technology, complexity issues with classical decision procedures are still a major obstacle for formal verification of real-world applications, e.g., in automotive and avionic industries. To identify strengths and weaknesses, we examine state of the art symbolic techniques and implementations for the universal fragment of real-closed fields: approaches based on quantifier elimination, Gr?obner Bases, and semidefinite programming for the Positivstellensatz. Within a uniform context of the verification tool KeYmaera, we compare these approaches qualitatively and quantitatively on verification benchmarks from hybrid systems, textbook algorithms, and on geometric problems. Finally, we introduce a new decision procedure combining Gr?obner Bases and semidefinite programming for the real Nullstell...

• Type: Conference
• Year: 2009
• Where: CADE
• Authors: André Platzer, Jan-David Quesel, Philipp Rümmer
• Keywords: Automated Reasoning, CADE 2009, Formal Verification, Verification Benchmarks, Verification Tool Keymaera