Separating AC0 from depth-2 majority circuits
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
The pattern matrix method for lower bounds on quantum communication
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Evolvability from learning algorithms
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Algebrization: a new barrier in complexity theory
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Computational Complexity
Algebrization: A New Barrier in Complexity Theory
ACM Transactions on Computation Theory (TOCT)
On Toda's Theorem in Structural Communication Complexity
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Problems of Information Transmission
A lower bound for agnostically learning disjunctions
COLT'07 Proceedings of the 20th annual conference on Learning theory
Unbounded-error classical and quantum communication complexity
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Optimal bounds for sign-representing the intersection of two halfspaces by polynomials
Proceedings of the forty-second ACM symposium on Theory of computing
SIAM Journal on Computing
Unbounded-error quantum query complexity
Theoretical Computer Science
Quantum interpolation of polynomilas
Quantum Information & Computation
On the uselessness of quantum queries
Theoretical Computer Science
Making polynomials robust to noise
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Lower bound on weights of large degree threshold functions
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
The approximate rank of a matrix and its algorithmic applications: approximate rank
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Communication lower bounds using directional derivatives
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Dual lower bounds for approximate degree and markov-bernstein inequalities
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We present two results for computational models that allow error probabilities close to 1/2. First, most computational complexity classes have an analogous class in communication complexity. The class PP in fact has two, a version with weakly restricted bias called PP^cc, and a version with unrestricted bias called UPP^cc. Ever since their introduction by Babai, Frankl, and Simon in 1986, it has been open whether these classes are the same. We show that PP^cc \varsubsetneq UPP^cc. Our proof combines a query complexity separation due to Beigel with a technique of Razborov that translates the acceptance probability of quantum protocols to polynomials. Second, we study how small the bias of minimal-degree polynomials that sign-represent Boolean functions needs to be. We show that the worst-case bias is at worst double-exponentially small in the sign-degree (which was very recently shown to be optimal by Podolski), while the averagecase bias can be made single-exponentially small in the sign-degree (which we show to be close to optimal).