Revisiting Space in Proof Complexity: Treewidth and Pathwidth
So-called ordered variants of the classical notions of pathwidth and treewidth are introduced and proposed as proof theoretically meaningful complexity measures for the directed acyclic graphs underlying proofs. The ordered pathwidth of a proof is shown to be roughly the same as its formula space. Length-space lower bounds for R(k)-refutations are generalized to arbitrary infinity axioms and strengthened in that the space measure is relaxed to ordered treewidth.
KeywordsFunction Symbol Tree Decomposition Path Decomposition Teacher Position Graph Invariant
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