Parallel computation for well-endowed rings and space-bounded probabilistic machines
Information and Control
The probabilistic communication complexity of set intersection
SIAM Journal on Discrete Mathematics
On the distributional complexity of disjointness
Theoretical Computer Science
Theoretical Computer Science - Special issue on complexity theory and the theory of algorithms as developed in the CIS
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Communication complexity
Quantum circuits with mixed states
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Quantum vs. classical communication and computation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Space-bounded Quantum complexity
Journal of Computer and System Sciences
Quantum lower bounds by polynomials
Journal of the ACM (JACM)
Quantum computation and quantum information
Quantum computation and quantum information
Quantum communication and complexity
Theoretical Computer Science - Natural computing
Improved Quantum Communication Complexity Bounds for Disjointness and Equality
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Nondeterministic Quantum Query and Communication Complexities
SIAM Journal on Computing
Exponential separation of quantum and classical one-way communication complexity
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
On the complexity of simulating space-bounded quantum computations
Computational Complexity
Quantum weakly nondeterministic communication complexity
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Improved Constructions of Quantum Automata
Theory of Quantum Computation, Communication, and Cryptography
Improved constructions of quantum automata
Theoretical Computer Science
State succinctness of two-way finite automata with quantum and classical states
Theoretical Computer Science
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The main objective of quantum computation is to exploit the natural parallelism of quantum mechanics to solve problems using less computational resources than classical computers. Although quantum algorithms realizing an exponential time speed-up over the best known classical algorithms exist, no quantum algorithm is known performing computation using less space resources than classical algorithms. In this paper, we study, for the first time explicitly, spacebounded quantum algorithms for computational problems where the input is given not as a whole, but bit by bit. We show that there exist such problems that a quantum computer can solve using exponentiallyless work space than a classical computer. More precisely, we introduce a very natural and simple model of a space-bounded quantum online machine and prove an exponential separation of classical and quantum online space complexity, in the bounded-error setting and for a total language. The language we consider is inspired bya communication problem that Buhrman, Cleve and Wigderson used to show an almost quadratic separation of quantum and classical bounded-error communication complexity. We prove that, in the framework of online space complexity, the separation becomes exponential.