Computational limitations of small-depth circuits
Computational limitations of small-depth circuits
Algebraic methods in the theory of lower bounds for Boolean circuit complexity
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
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Size--Depth Tradeoffs for Threshold Circuits
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Nondeterministic NC1 computation
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Fast Probabilistic Algorithms for Verification of Polynomial Identities
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Probabilistic Algorithms for Deciding Equivalence of Straight-Line Programs
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On TC0, AC0, and arithmetic circuits
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Geometric Complexity Theory I: An Approach to the P vs. NP and Related Problems
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Circuit Complexity before the Dawn of the New Millennium
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Journal of the ACM (JACM)
The correlation between parity and quadratic polynomials mod 3
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Undirected ST-connectivity in log-space
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Derandomizing polynomial identity tests means proving circuit lower bounds
Computational Complexity
On the Complexity of Numerical Analysis
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Separating AC0 from depth-2 majority circuits
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Algebrization: a new barrier in complexity theory
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Amplifying Lower Bounds by Means of Self-Reducibility
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Separating the polynomial-time hierarchy by oracles
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Lower bounds for depth-2 and depth-3 Boolean circuits with arbitrary gates
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
Lower bounds for circuits with few modular and symmetric gates
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Proving lower bounds via pseudo-random generators
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Amplifying lower bounds by means of self-reducibility
Journal of the ACM (JACM)
Journal of Computer and System Sciences
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Razborov and Rudich identified an imposing barrier that stands in the way of progress toward the goal of proving superpolynomial lower bounds on circuit size. Their work on "natural proofs" applies to a large class of arguments that have been used in complexity theory, and shows that no such argument can prove that a problem requires circuits of superpolynomial size, even for some very restricted classes of circuits (under reasonable cryptographic assumptions). This barrier is so daunting, that some researchers have decided to focus their attentions elsewhere. Yet the goal of proving circuit lower bounds is of such importance, that some in the community have proposed concrete strategies for surmounting the obstacle. This lecture will discuss some of these strategies, and will dwell at length on a recent approach proposed by Michal Koucky and the author.