Reproduce “Formalizing Graph Trail Properties in Isabelle/HOL” on OpenResearch
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About this paper
Laura Kovacs, Hanna Lachnitt, Stefan Szeider
The paper formalizes strictly increasing and decreasing trails in edge-weighted graphs within Isabelle/HOL. It presents a verified algorithm for computing the longest strictly decreasing trails and proves a known lower bound on their existence, with the formalization enabling the extraction of verified executable code.
Key insights
- A duality exists between strictly increasing and strictly decreasing trails, where reversing the edge order can transform one into the other under specific conditions.
- Formal verification provides a robust method to establish the correctness of graph algorithms, producing strong guarantees for properties like termination, soundness, and completeness.
- Building specialized algorithms and formally verifying them in proof assistants like Isabelle/HOL can overcome the scalability challenges faced by general automated reasoning engines on complex graph problems.
Summary by alphaXiv.
Tip: change arxiv.org to autoarxiv.org in any arXiv abstract link to open the paper here.