Formalizing Randomized Matching Algorithms

Using Je\v{r}\'abek 's framework for probabilistic reasoning, we formalizethe correctness of two fundamental RNC^2 algorithms for bipartite perfectmatching within the theory VPV for polytime reasoning. The first algorithm isfor testing if a bipartite graph has a perfect matching, and is based on theSchwartz-Zippel Lemma for polynomial identity testing applied to the Edmondspolynomial of the graph. The second algorithm, due to Mulmuley, Vazirani andVazirani, is for finding a perfect matching, where the key ingredient of thisalgorithm is the Isolating Lemma