On the degree of Boolean functions as real polynomials
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
On the degree of polynomials that approximate symmetric Boolean functions (preliminary version)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
On randomized one-round communication complexity
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
On the Power of Quantum Computation
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Communication complexity
Quantum vs. classical communication and computation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Exponential separation of quantum and classical communication complexity
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Complexity measures and decision tree complexity: a survey
Theoretical Computer Science - Complexity and logic
Quantum Entanglement and the Communication Complexity of the Inner Product Function
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
Improved Quantum Communication Complexity Bounds for Disjointness and Equality
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
The Quantum Communication Complexity of Sampling
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Quantum Lower Bounds by Polynomials
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Communication Complexity Lower Bounds by Polynomials
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Lower Bounds for Quantum Communication Complexity
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Quantum Search of Spatial Regions
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
A Lower Bound for the Bounded Round Quantum Communication Complexity of Set Disjointness
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Exponential separation of quantum and classical one-way communication complexity
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The query complexity of order-finding
Information and Computation
Bounded-error quantum state identification and exponential separations in communication complexity
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The communication complexity of the Hamming distance problem
Information Processing Letters
Separating AC0 from depth-2 majority circuits
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Lower bounds in communication complexity based on factorization norms
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
Learning Complexity vs. Communication Complexity
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
Disjointness Is Hard in the Multi-party Number-on-the-Forehead Model
CCC '08 Proceedings of the 2008 IEEE 23rd Annual Conference on Computational Complexity
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Distillation and bound entanglement
Quantum Information & Computation
Composition theorems in communication complexity
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Strong direct product theorems for quantum communication and query complexity
Proceedings of the forty-third annual ACM symposium on Theory of computing
On quantum-classical equivalence for composed communication problems
Quantum Information & Computation
The multiparty communication complexity of set disjointness
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
The NOF multiparty communication complexity of composed functions
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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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A major open problem in communication complexity is whether or not quantum protocolscan be exponentially more efficient than classical ones for computing a total Booleanfunction in the two-party interactive model. Razborov's result (Izvestiya: Mathematics,67(1):145-159, 2002) implies the conjectured negative answer for functions F of thefollowing form: F(x, y) = fn(x1 ċ y1, x2 ċ y2, ..., xn ċ yn), where fn is a symmetric Booleanfunction on n Boolean inputs, and xi, yi are the i'th bit of x and y, respectively. Hisproof critically depends on the symmetry of fn. We develop a lower-bound method that does not require symmetry and prove theconjecture for a broader class of functions. Each of those functions F is the "block-composition" of a "building block" gk : {0, 1}k × {0, 1}k → {0, 1}, and an fn : {0, 1}n →{0, 1}, such that F(x, y) = fn(gk(x1, y1), gk(x2, y2), ..., gk(xn, yn)), where xi and xi arethe i'th k-bit block of x, y ∈ {0, 1}nk, respectively. We show that as long as gk itselfis "hard" enough, its block-composition with an arbitrary fn has polynomially relatedquantum and classical communication complexities. For example, when gk is the InnerProduct function with k = Ω(log n), the deterministic communication complexity of itsblock-composition with any fn is asymptotically at most the quantum complexity to thepower of 7.