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Pebble Games and Algebraic Proof Systems
Lisa-Marie Jaser, Jacobo Toran
https://arxiv.org/abs/2506.21149 https://arxiv.org/pdf/2506.2…

Pebble Games and Algebraic Proof Systems
Analyzing refutations of the well known 0pebbling formulas Peb$(G)$ we prove some new strong connections between pebble games and algebraic proof system, showing that there is a parallelism between the reversible, black and black-white pebbling games on one side, and the three algebraic proof systems Nullstellensatz, Monomial Calculus and Polynomial Calculus on the other side. In particular we prove that for any DAG $G$ with a single sink, if there is a Monomial Calculus refutation for Peb$(G)$…