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### Abstract

We present an Isabelle/HOL formalization of Gabow's algorithm for
finding the strongly connected components of a directed graph.
Using data refinement techniques, we extract efficient code that
performs comparable to a reference implementation in Java.
Our style of formalization allows for re-using large parts of the proofs
when defining variants of the algorithm. We demonstrate this by
verifying an algorithm for the emptiness check of generalized Büchi
automata, re-using most of the existing proofs.