From small space to small width in resolution
Research output: Contribution to journal › Journal article › Research › peer-review
In 2003, Atserias and Dalmau resolved a major open question about the resolution proof system by establishing that the space complexity of a Conjunctive Normal Form (CNF) formula is always an upper bound on the width needed to refute the formula. Their proof is beautiful but uses a nonconstructive argument based on Ehrenfeucht-Fraïssé games. We give an alternative, more explicit, proof that works by simple syntactic manipulations of resolution refutations. As a by-product, we develop a "black-box" technique for proving space lower bounds via a "static" complexitymeasure that works against any resolution refutation-previous techniques have been inherently adaptive. We conclude by showing that the related question for polynomial calculus (i.e., whether space is an upper bound on degree) seems unlikely to be resolvable by similarmethods.
Original language | English |
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Article number | 28 |
Journal | ACM Transactions on Computational Logic |
Volume | 16 |
Issue number | 4 |
ISSN | 1529-3785 |
DOIs | |
Publication status | Published - 1 Aug 2015 |
Externally published | Yes |
- degree, PCR, Polynomial calculus, Polynomial calculus resolution, Proof complexity, Resolution, Space, Width
Research areas
ID: 251869364