Formalizing Size-Optimal Sorting Networks: Extracting a Certified Proof Checker

Cruz-Filipe, Luís; Schneider–Kamp, Peter

doi:10.1007/978-3-319-22102-1_10

Cited by 3 publications

(10 citation statements)

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“…This is the first time that the symbiosis between the prune algorithm and the implementation of the untrusted oracle becomes a key ingredient for optimization. As we use an offline oracle [6], we can actually reorder the oracle information to suit the needs of the checker with an efficient (untrusted) preprocessor. An inspection of the definition of Generate shows that comparators are added in lexicographic order, and we can pre-process the oracle information such that the subsumptions are provided in the same order.…”

Section: Optimizing the Removal Stepmentioning

confidence: 99%

“…Subsequently [6], we formalized the relevant theory of sorting networks in Coq, therefrom extracting a certified checker able to confirm the validity of our informal computer-generated proof. The checker bypasses the original search steps by means of an untrusted oracle, implemented by reading the log file produced by the original program, and could verify the proof for the smaller case of 8 inputs, thereby constituting the first computer-validated proof of the results in [7].…”

Section: Introductionmentioning

confidence: 99%

“…Section 2 shortly introduces the basic of sorting networks, the generate-andprune algorithm from [3], and our formalization from [6] to the degree necessary to understand the improvements. In Section 3 we change the checker algorithm in the formalization in order to bring runtime down by at least an order of magnitude, while we reduce memory footprint by a factor of 3 in Section 4.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, we formalized the soundness of generate-and-prune in the theorem prover Coq with the goal of extracting a provenly correct checker of the same result [6] to Haskell. 1 In order to eliminate the search step in Prune, this formalization is parameterized on an oracle, which produces triples C a , C b , π such that C a ≤ π C b .…”

Section: Introductionmentioning

confidence: 99%

“…We then specify what it means for a comparator network to be a sorting network on n channels, and show that this is a decidable predicate. The details of the formalization of the theory of sorting networks can be found in [6].…”

Section: Introductionmentioning

confidence: 99%

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Optimizing a Certified Proof Checker for a Large-Scale Computer-Generated Proof

Cruz-Filipe

Schneider–Kamp

2015

Lecture Notes in Computer Science

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Abstract. In recent work, we formalized the theory of optimal-size sorting networks with the goal of extracting a verified checker for the largescale computer-generated proof that 25 comparisons are optimal when sorting 9 inputs, which required more than a decade of CPU time and produced 27 GB of proof witnesses. The checker uses an untrusted oracle based on these witnesses and is able to verify the smaller case of 8 inputs within a couple of days, but it did not scale to the full proof for 9 inputs. In this paper, we describe several non-trivial optimizations of the algorithm in the checker, obtained by appropriately changing the formalization and capitalizing on the symbiosis with an adequate implementation of the oracle. We provide experimental evidence of orders of magnitude improvements to both runtime and memory footprint for 8 inputs, and actually manage to check the full proof for 9 inputs.

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Section: Optimizing the Removal Stepmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Optimizing a Certified Proof Checker for a Large-Scale Computer-Generated Proof

Cruz-Filipe

Schneider–Kamp

2015

Lecture Notes in Computer Science

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Efficient Certified Resolution Proof Checking

Cruz-Filipe

Marques-Silva

Schneider–Kamp

2017

Lecture Notes in Computer Science

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Abstract. We present a novel propositional proof tracing format that eliminates complex processing, thus enabling efficient (formal) proof checking. The benefits of this format are demonstrated by implementing a proof checker in C, which outperforms a state-of-the-art checker by two orders of magnitude. We then formalize the theory underlying propositional proof checking in Coq, and extract a correct-by-construction proof checker for our format from the formalization. An empirical evaluation using 280 unsatisfiable instances from the 2015 and 2016 SAT competitions shows that this certified checker usually performs comparably to a state-of-the-art non-certified proof checker. Using this format, we formally verify the recent 200 TB proof of the Boolean Pythagorean Triples conjecture.

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