While this submission is a draft, it cannot be used by other submissions.

Proof of `Saturating and Perfect Matchings, Decided in the Same Time` (4th statement)

groundedproofs/Lax117284Proofs/Bipartite/MachineTotal.lean · lax-117284

What this proof establishes

Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.

Read the Lean proof on GitHub

Description

The total program reads the word into an array, validates the syntactic conditions of WellFormedWellFormed in linear time, checks that every listed edge crosses the split while counting the degrees of the symmetrized word, builds that word by a counting sort (each left row the union of its own row and the transposed right rows), runs Kuhn's algorithm on it and compares the size of the matching with the number of left vertices; on any failed check it answers 00. The program is compiled for the length-prefixed word, runs at every word length from bitSizex+11bitSize x + 11 on, and within 20000⋅(bitSizex+1)220000 · (bitSize x + 1)² instructions.