Guest column: a casual tour around a circuit complexity bound

Authors:
Ryan Williams
Affiliations:
Stanford University, Stanford, CA
Venue:
ACM SIGACT News
Year:
2011

Citing 35
Cited 1

Separating the polynomial-time hierarchy by oracles

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An O(T log T) reduction from RAM computations to satisfiability

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Separating Nondeterministic Time Complexity Classes

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CSL '92 Selected Papers from the Workshop on Computer Science Logic
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Some connections between nonuniform and uniform complexity classes

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Sparse sets in NP-P: Exptime versus nexptime

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An algorithm for the satisfiability problem of formulas in conjunctive normal form

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Derandomizing polynomial identity tests means proving circuit lower bounds

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An improved exponential-time algorithm for k-SAT

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Time-space lower bounds for satisfiability

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A Duality between Clause Width and Clause Density for SAT

CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
A (de)constructive approach to program checking

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Parity, circuits, and the polynomial-time hierarchy

SFCS '81 Proceedings of the 22nd Annual Symposium on Foundations of Computer Science
ON ACC and threshold circuits

SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
A New Characterization of ACC^0 and Probabilistic CC^0

CCC '09 Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity
The Complexity of Satisfiability of Small Depth Circuits

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Solving satisfiability in less than 2n steps

Discrete Applied Mathematics
On the Power of Small-Depth Computation

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Improving exhaustive search implies superpolynomial lower bounds

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A full derandomization of schöning's k-SAT algorithm

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Non-uniform ACC Circuit Lower Bounds

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3-SAT Faster and Simpler - Unique-SAT Bounds for PPSZ Hold in General

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Nonuniform ACC Circuit Lower Bounds

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Abstract

I will discuss the recent proof that the complexity class NEXP (nondeterministic exponential time) lacks nonuniform ACC circuits of polynomial size. The proof will be described from the perspective of someone trying to discover it.