3 research outputs found
Optimizing a Certified Proof Checker for a Large-Scale Computer-Generated Proof
In recent work, we formalized the theory of optimal-size sorting networks
with the goal of extracting a verified checker for the large-scale
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.Comment: IMADA-preprint-c
Formalizing Size-Optimal Sorting Networks: Extracting a Certified Proof Checker
Since the proof of the four color theorem in 1976, computer-generated proofs
have become a reality in mathematics and computer science. During the last
decade, we have seen formal proofs using verified proof assistants being used
to verify the validity of such proofs.
In this paper, we describe a formalized theory of size-optimal sorting
networks. From this formalization we extract a certified checker that
successfully verifies computer-generated proofs of optimality on up to 8
inputs. The checker relies on an untrusted oracle to shortcut the search for
witnesses on more than 1.6 million NP-complete subproblems.Comment: IMADA-preprint-c
Efficient Certified Resolution Proof Checking
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