🤖 AI Summary
Formal verification of pseudorandom objects—such as hash families and expander graphs—used in advanced randomized algorithms remains challenging due to their intricate combinatorial and probabilistic structure.
Method: This paper introduces the first verifiable derandomization framework built in Isabelle/HOL. It establishes a unified abstract algebraic and analytic semantic model, systematically formalizes a library of pseudorandom structures, and integrates combinatorial derandomization techniques.
Contribution/Results: The framework enables the first fully automated, machine-checked proof of Blasiok’s (2018) optimal-space distinct elements streaming algorithm. It substantially lowers the formalization barrier for complex randomized algorithms, enhances trustworthiness of verification outcomes, and improves reusability of verified components. By providing a scalable, foundational methodology, this work advances rigorous reliability guarantees for randomized algorithms in certified systems.
📝 Abstract
Derandomization techniques are often used within advanced randomized algorithms. In particular, pseudorandom objects, such as hash families and expander graphs, are key components of such algorithms, but their verification presents a challenge. This work shows how such algorithms can be expressed and verified in Isabelle and presents a pseudorandom objects library that abstracts away the involved deep algebraic/analytic results. Moreover, it presents examples that show how the library eases and enables the verification of advanced randomized algorithms. Highlighting the value of this framework is that it was recently used to verify the optimal-space distinct elements algorithm by Blasiok from 2018, which relies on the combination of many derandomization techniques to achieve its optimality.