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arXiv · 2605.09732

TreeWidzard: An Engine for Width-Based Dynamic Programming and Automated Theorem Proving

Mateus de Oliveira Oliveria·Sam Urmian
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Abstract

In this work, we introduce TreeWidzard, an engine for developing dynamic programming algorithms that decide graph-theoretic properties parameterized by treewidth and pathwidth. Besides providing a unified framework for algorithms deciding atomic graph-theoretic properties, our engine allows one to combine such algorithms for two purposes: to obtain dynamic programming algorithms for more complex graph properties, and to support treewidth-based automated theorem proving. Within this context, given the specification of a Boolean combination \(P\) of graph properties \(P_1, P_2, \ldots, P_r\), and a positive integer \(k\), our engine can be used to determine whether all graphs of treewidth at most \(k\) satisfy \(P\). The main goal of the present work is to provide a system description of TreeWidzard. In particular, we provide a step-by-step account of how to implement dynamic programming algorithms in our framework and how to combine these algorithms for model checking and automated theorem proving.

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Mateus de Oliveira Oliveria, Sam Urmian. 2026-05-10. TreeWidzard: An Engine for Width-Based Dynamic Programming and Automated Theorem Proving. https://arxiv.org/abs/2605.09732

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