Formal Probabilistic Methods for Combinatorial Structures using the Lovász Local Lemma

Explore a 32-minute conference talk from CPP 2024 that delves into formalizing probabilistic methods for combinatorial structures using the Lovász Local Lemma. Learn how Chelsea Edmonds and Lawrence Paulson present a modular framework in Isabelle/HOL to translate intuitive probabilistic arguments into formal proofs. Discover the challenges and insights in formalizing the basic existence method and the first formalization of the Lovász local lemma. Gain understanding of general, reusable formal probabilistic lemmas for combinatorial structures and their application to classic lemmas on hypergraph colorings. Examine the gaps between intuitive probabilistic reasoning and formal proofs, and see how this work contributes to expanding formalized libraries of combinatorial mathematics using probability.