The probably approximately correct learning model Occam's razor the Vapnik-Chervonenkis dimension weak and strong learning learning in the presence of noise inherent unpredictability reducibility in… Expand

This paper gives the first formal evidence that quantum Turing machines violate the modern (complexity theoretic) formulation of the Church--Turing thesis, and proves that bits of precision suffice to support a step computation.Expand

This work applies the general approach to data structures, bin packing, graph coloring, and graph coloring to bipartite matching and shows that a simple randomized on-line algorithm achieves the best possible performance.Expand

This dissertation proves that relative to an oracle chosen uniformly at random, the class NP cannot be solved on a quantum Turing machine in time $o(2\sp{n/2}).$ and gives evidence suggesting that quantum Turing Machines cannot efficiently solve all of NP.Expand

It is proved that relative to an oracle chosen uniformly at random with probability 1 the class $\NP$ cannot be solved on a quantum Turing machine (QTM) in time $o(2^{n/2})$.Expand

A new algorithm for finding a maximum matching in a general graph with special feature is that its only computationally non-trivial step is the inversion of a single integer matrix, the isolating lemma.Expand

An interesting and natural "certificate" for a graph's expansion is described, by embedding an n-node expander in it with appropriate dilation and congestion, and is called an expander flow.Expand

A lower bound on the possible speed up by quantum walks for general graphs is given, showing that quantum walks can be at most polynomially faster than their classical counterparts.Expand

The notion of a tradeoff revealing LP is introduced and used to derive two optimal algorithms achieving competitive ratios of 1-1/e for this problem of online bipartite matching.Expand

An interesting and natural “approximate certificate” for a graph's expansion, which involves embedding an n-node expander in it with appropriate dilation and congestion, is described.Expand