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arXiv AI By Johannes K. Fichte, Stefan Szeider

count-catcher: Lean Theorems from Model Counting Certificates

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count-catcher is a tool that transforms a CPOG certificate produced by the exact model counter d4 into a Lean theorem asserting that a CNF formula defined in Lean has exactly N models over V variables. It verifies the equivalence between the formula and a Boolean circuit via forward and reverse checks, using Lean’s LRAT checker and formally verified computations. The resulting theorems are combined with Mathlib results, such as Burnside’s lemma, to count combinatorial objects—for example, proving the number of Latin squares of order 8 as a weighted sum of certified counts from terabytes of certificates.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

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