Parameterized Proof Complexity and W[1]
Barnaby Martin
TL;DR
This paper explores parameterized proof complexity to differentiate FPT from W[1], establishing bounds for W[1]-parameterized Resolution to advance understanding of computational class separations.
Contribution
It introduces a new program for W[1]-parameterized proof complexity and provides upper and lower bounds for W[1]-parameterized Resolution, expanding the theoretical framework.
Findings
Established upper bounds for W[1]-parameterized Resolution.
Proved lower bounds for W[1]-parameterized Resolution.
Compared W[1] program with existing classes W[2] and W[SAT].
Abstract
We initiate a program of parameterized proof complexity that aims to provide evidence that FPT is different from W[1]. A similar program already exists for the classes W[2] and W[SAT]. We contrast these programs and prove upper and lower bounds for W[1]-parameterized Resolution.
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Taxonomy
TopicsLogic, programming, and type systems · semigroups and automata theory · Formal Methods in Verification