Results 271 to 280 of about 236,217 (313)

Complexity of Propositional Proofs

Computer Science Symposium in Russia, 2010
A. Razborov
semanticscholar   +2 more sources

On the Bit Complexity of Sum-of-Squares Proofs

International Colloquium on Automata, Languages and Programming, 2017
It has often been claimed in recent papers that one can find a degree d Sum-of-Squares proof if one exists via the Ellipsoid algorithm. In a recent paper, Ryan O'Donnell notes this widely quoted claim is not necessarily true.
P. Raghavendra, Benjamin Weitz
semanticscholar   +1 more source

Highly complex proofs and implications of such proofs

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2005
Conventional wisdom says the ideal proof should be short, simple, and elegant. However there are now examples of very long, complicated proofs, and as mathematics continues to mature, more examples are likely to appear. Such proofs raise various issues.
openaire   +3 more sources

Multi-prover interactive proofs: how to remove intractability assumptions

Symposium on the Theory of Computing, 2019
Quite complex cryptographic machinery has been developed based on the assumption that one-way functions exist, yet we know of only a few possible such candidates.
M. Ben-Or, S. Goldwasser, J. Kilian, A. Wigderson   +3 more
semanticscholar   +1 more source

Logical Foundations of Proof Complexity

2010
This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. Associated with each of many complexity classes are both a two-sorted predicate calculus theory, with ...
Stephen Cook, Phuong Nguyen
openaire   +1 more source

On Proof Complexity of Circumscription

1998
Circumscription is a non-monotonic formalism based on the idea that objects satisfying a certain predicate expression are considered as the only objects satisfying it. Theoretical complexity results imply that circumscription is (in the worst case) computationally harder than classical logic.
Uwe Egly, Hans Tompits
openaire   +1 more source

Proof Complexity of Pigeonhole Principles

2002
The pigeonhole principle asserts that there is no injective mapping from m pigeons to n holes as long as m > n. It is amazingly simple, expresses one of the most basic primitives in mathematics and Theoretical Computer Science (counting) and, for these reasons, is probably the most extensively studied combinatorial principle.
openaire   +1 more source

On the Complexity of Scrypt and Proofs of Space in the Parallel Random Oracle Model

International Conference on the Theory and Application of Cryptographic Techniques, 2016
J. Alwen, Binyi Chen, Chethan Kamath, Vladimir Kolmogorov, Krzysztof Pietrzak, Stefano Tessaro   +5 more
semanticscholar   +1 more source

Complexity of Proofs and Their Transformations in Axiomatic Theories

, 1993
V. Orevkov
semanticscholar   +1 more source

The Proof Complexity of Polynomial Identities

2009 24th Annual IEEE Conference on Computational Complexity, 2009
Devising an efficient deterministic -- or even a non-deterministic sub-exponential time -- algorithm for testing polynomial identities is a fundamental problem in algebraic complexity and complexity at large. Motivated by this problem, as well as by results from proof complexity, we investigate the complexity of _proving_ polynomial identities. To this
openaire   +1 more source