Certifying algorithms

McConnell, Ross M.; Mehlhorn, Kurt; Näher, Stefan; Schweitzer, Pascal

doi:10.1016/j.cosrev.2010.09.009

Cited by 141 publications

(128 citation statements)

References 93 publications

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“…Our approach applies to any problem for which a certifying algorithm is known; see [13] for a survey. Most algorithms in LEDA [14] are certifying and, in future work, we plan to verify all of them.…”

Section: Discussionmentioning

confidence: 99%

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Verification of Certifying Computations

Alkassar

Böhme

Mehlhorn

et al. 2011

Computer Aided Verification

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Abstract. Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current verification tools and proving their correctness usually involves non-trivial 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. Verification of checkers is feasible with current tools and leads to computations that can be completely trusted. In this paper we develop a framework to seamlessly verify certifying computations. The automatic verifier VCC is used for checking code correctness, and the interactive theorem prover Isabelle/HOL targets high-level mathematical properties of algorithms. We demonstrate the effectiveness of our approach by applying it to the verification of the algorithmic library LEDA.

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Section: Discussionmentioning

confidence: 99%

“…A certifying algorithm [3,18,13] produces with each output a certificate or witness that the particular output is correct. By inspecting the witness, the user can convince himself that the output is correct, or reject the output as buggy.…”

Section: Introductionmentioning

confidence: 99%

Verification of Certifying Computations

Alkassar

Böhme

Mehlhorn

et al. 2011

Computer Aided Verification

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“…A state of art of certifying algorithms was published in 2011 [59] by McConell, Mehlhorn, Näher and Schweitzer.…”

Section: Theorem 12mentioning

confidence: 99%

Recognition of split-graphic sequences

Chat

Pirzada

Iványi

2014

Acta Universitatis Sapientiae, Informatica

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“…McConnell, Mehlhorn, Näher, and Schweitzer [80] review certifiable algorithms that produce an easy-toverify certificate that the output of the algorithm is correct. Yet such designs in general are not tolerant against tail events.…”

Section: Verifiable or Error-tolerant Algorithmsmentioning

confidence: 99%

Engineering a Delegatable and Error-Tolerant Algorithm for Counting Small Subgraphs

Kaski

2018

2018 Proceedings of the Twentieth Workshop on Algorithm Engineering and Experiments (ALENEX)

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We study the problem of counting the number of occurrences of a given six-vertex pattern graph S in an n-vertex host graph H. We engineer an open-source GPU implementation of a distributed algorithm design of Björklund and Kaski [PODC 2016] where (i) the execution of the algorithm can be delegated [Goldwasser, Kalai, and Rothblum, J. ACM 2015] to produce a noninteractive probabilistically checkable proof of correctness, and (ii) the execution of the algorithm when preparing the proof tolerates a controllable number of adversarial errors. Experiments with NVIDIA Tesla K80 and Tesla P100 Accelerators demonstrate that the framework is practical for inputs of up to 512 vertices, with proof checking being several orders of magnitude more efficient than preparing the proof; however, proof preparation still carries at least one order of magnitude overhead compared with just solving the problem.

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Certifying algorithms

Cited by 141 publications

References 93 publications

Verification of Certifying Computations

Verification of Certifying Computations

Recognition of split-graphic sequences

Engineering a Delegatable and Error-Tolerant Algorithm for Counting Small Subgraphs

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