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We present a formalization of the Ford-Fulkerson method for computing the maximum flow in a network. Our formal proof closely follows a standard textbook proof, and is accessible even without being an expert in Isabelle/HOL-the interactive theorem prover used for the formalization. We then use stepwise refinement to obtain the Edmonds-Karp algorithm, and formally prove a bound on its complexity. Further refinement yields a verified implementation, whose execution time compares well to an unverified reference implementation in Java.

Computer-aided cryptography increases the rigour of cryptographic proofs by mechanizing their verification. Existing tools focus mainly on game-based proofs, and efforts to formalize composable frameworks such as Universal Composability have met with limited success. In this paper, we formalize an instance of Constructive Cryptography, a generic theory allowing for clean, composable cryptographic security statements. Namely, we extend CryptHOL, a framework for game-based proofs, with an abstract model of Random Systems and provide proof rules for their equality and composition. We formalize security as a special kind of system construction in which a complex system is built from simpler ones. As a simple case study, we formalize the construction of an information-theoretically secure channel from a key, a random function, and an insecure channel.

We present a formalization of classical algorithms for computing the maximum flow in a network: The Edmonds-Karp algorithm and the push-relabel algorithm. We prove correctness and time complexity of these algorithms. Our formal proof closely follows a standard textbook proof, and is accessible even without being an expert in Isabelle/HOL -the interactive theorem prover used for the formalization.Using stepwise refinement techniques, we instantiate the generic Ford-Fulkerson algorithm to Edmonds-Karp algorithm, and the generic push-relabel algorithm of Goldberg and Tarjan to both the relabel-to-front and the FIFO push-relabel algorithm. Further refinement then yields verified efficient implementations of the algorithms, which compare well to unverified reference implementations.

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