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Understanding Space in Proof Complexity: Separations and Trade-offs via Substitutions
TLDR
We prove that length-space trade-offs in resolution proofs can be optimized for length and space simultaneously, or whether there are trade-off between these two measures. Expand
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On the virtue of succinct proofs: amplifying communication complexity hardness to time-space trade-offs in proof complexity
TLDR
We propose a new two-player communication complexity lower bound for composed search problems in terms of block sensitivity, a contribution that we believe to be of independent interest. Expand
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Some trade-off results for polynomial calculus: extended abstract
TLDR
We present size-space trade-offs for the polynomial calculus (PC and PCR) proof systems, showing that size and space cannot be simultaneously optimized in these models. Expand
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Pebble Games, Proof Complexity, and Time-Space Trade-offs
TLDR
Pebble games were extensively studied in the 1970s and 1980s in a number of different contexts. Expand
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Towards an Understanding of Polynomial Calculus: New Separations and Lower Bounds - (Extended Abstract)
TLDR
We show that if a formula requires large resolution width, then making XOR substitution yields a formula requiring large PCR space, providing some circumstantial evidence that degree might be a lower bound for space. Expand
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Space Complexity in Polynomial Calculus
TLDR
Proof complexity is a measure of space and time-space trade-offs for proofs. Expand
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Short Proofs May Be Spacious: An Optimal Separation of Space and Length in Resolution
TLDR
We show that there are families of 6-CNF formulas of size n, for arbitrarily large n, that have resolution proofs of length O(n) but for which any proof requires space Omega(n/log n). Expand
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On the interplay between proof complexity and SAT solving
TLDR
This paper is intended as an informal and accessible survey of proof complexity for non-experts, focusing on some comparatively weak proof systems of particular interest in connection with SAT solving, and some complexity measures that have been studied for these proof systems. Expand
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Relating Proof Complexity Measures and Practical Hardness of SAT
TLDR
This paper sets out on a systematic study of the interconnections between theoretical complexity and practical SAT solver performance. Expand
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A Generalized Method for Proving Polynomial Calculus Degree Lower Bounds
TLDR
This is an updated and strengthened full-length version of the paper with the same title that appeared in the Proceedings of the 30th Annual Computational Complexity Conference (CCC '15). Expand
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