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» Mining Circuit Lower Bound Proofs for Meta-Algorithms
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CSL
2007
Springer
15 years 6 months ago
Propositional Logic for Circuit Classes
Abstract. By introducing a parallel extension rule that is aware of independence of the introduced extension variables, a calculus for quantified propositional logic is obtained w...
Klaus Aehlig, Arnold Beckmann
IPL
2007
111views more  IPL 2007»
14 years 11 months ago
Powering requires threshold depth 3
We study the circuit complexity of the powering function, defined as POWm(Z) = Zm for an n-bit integer input Z and an integer exponent m poly(n). Let LTd denote the class of func...
Alexander A. Sherstov
STOC
2010
ACM
168views Algorithms» more  STOC 2010»
15 years 9 months ago
Non-commutative circuits and the sum-of-squares problem
We initiate a direction for proving lower bounds on the size of non-commutative arithmetic circuits. This direction is based on a connection between lower bounds on the size of no...
Pavel Hrubes, Avi Wigderson and Amir Yehudayoff
ECCC
2010
117views more  ECCC 2010»
14 years 10 months ago
Nearly Tight Bounds for Testing Function Isomorphism
We study the problem of testing isomorphism (equivalence up to relabelling of the variables) of two Boolean functions f, g : {0, 1}n → {0, 1}. Our main focus is on the most stud...
Sourav Chakraborty, David García-Soriano, A...
ECCC
2008
168views more  ECCC 2008»
14 years 12 months ago
Algebrization: A New Barrier in Complexity Theory
Any proof of P = NP will have to overcome two barriers: relativization and natural proofs. Yet over the last decade, we have seen circuit lower bounds (for example, that PP does n...
Scott Aaronson, Avi Wigderson