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Computer Science, Logic in Computer Science, cs.LO,Computer Science, Data Structures and Algorithms, cs.DS,Computer Science, Formal Languages and Automata Theory, cs.FL
Abstract:
Formal verification of complex algorithms is challenging. Verifying their
implementations goes beyond the state of the art of current automatic
verification tools and usually involves intricate mathematical theorems.
Certifying algorithms compute in addition to each output a witness certifying
that the output is correct. A checker for such a witness is usually much
simpler than the original algorithm - yet it is all the user has to trust. The
verification of checkers is feasible with current tools and leads to
computations that can be completely trusted. We describe a framework to
seamlessly verify certifying computations. We use the automatic verifier VCC
for establishing the correctness of the checker and the interactive theorem
prover Isabelle/HOL for high-level mathematical properties of algorithms. We
demonstrate the effectiveness of our approach by presenting the verification of
typical examples of the industrial-level and widespread algorithmic library
LEDA.
