A Framework for the Verification of Certifying Computations View Full Text


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Article Info

DATE

2013-06-29

AUTHORS

Eyad Alkassar, Sascha Böhme, Kurt Mehlhorn, Christine Rizkallah

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. More... »

PAGES

241-273

References to SciGraph publications

  • 1979. Edinburgh LCF, A Mechanised Logic of Computation in NONE
  • 2011. Verification of Certifying Computations in COMPUTER AIDED VERIFICATION
  • 2002-04-10. Isabelle/HOL, A Proof Assistant for Higher-Order Logic in NONE
  • 2009-07-08. HOL-Boogie—An Interactive Prover-Backend for the Verifying C Compiler in JOURNAL OF AUTOMATED REASONING
  • 2009. VCC: A Practical System for Verifying Concurrent C in THEOREM PROVING IN HIGHER ORDER LOGICS
  • 2008. Z3: An Efficient SMT Solver in TOOLS AND ALGORITHMS FOR THE CONSTRUCTION AND ANALYSIS OF SYSTEMS
  • 2008. Imperative Functional Programming with Isabelle/HOL in THEOREM PROVING IN HIGHER ORDER LOGICS
  • 2008. HOL-Boogie — An Interactive Prover for the Boogie Program-Verifier in THEOREM PROVING IN HIGHER ORDER LOGICS
  • 2010. Extending Coq with Imperative Features and Its Application to SAT Verification in INTERACTIVE THEOREM PROVING
  • 2004. Interactive Theorem Proving and Program Development, Coq’Art: The Calculus of Inductive Constructions in NONE
  • 2007-01-01. The Why/Krakatoa/Caduceus Platform for Deductive Program Verification in COMPUTER AIDED VERIFICATION
  • 2010. Industrial-Strength Certified SAT Solving through Verified SAT Proof Checking in THEORETICAL ASPECTS OF COMPUTING – ICTAC 2010
  • 1990. A theorem prover for a computational logic in 10TH INTERNATIONAL CONFERENCE ON AUTOMATED DEDUCTION
  • 2012. Bridging the Gap: Automatic Verified Abstraction of C in INTERACTIVE THEOREM PROVING
  • 2009. Certification of Termination Proofs Using CeTA in THEOREM PROVING IN HIGHER ORDER LOGICS
  • 2006. Boogie: A Modular Reusable Verifier for Object-Oriented Programs in FORMAL METHODS FOR COMPONENTS AND OBJECTS
  • 2009. Formal Verification of a Microkernel Used in Dependable Software Systems in COMPUTER SAFETY, RELIABILITY, AND SECURITY
  • 2005. A Verification Environment for Sequential Imperative Programs in Isabelle/HOL in LOGIC FOR PROGRAMMING, ARTIFICIAL INTELLIGENCE, AND REASONING
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10817-013-9289-2

    DOI

    http://dx.doi.org/10.1007/s10817-013-9289-2

    DIMENSIONS

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