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Average-case complexity

About: Average-case complexity is a research topic. Over the lifetime, 1749 publications have been published within this topic receiving 44972 citations.


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Journal ArticleDOI
TL;DR: The intrinsic complexity of learning compares the difficulty of learning classes of objects by using some reducibility notion and the structure of the intrinsic complexity is shown to be much richer than theructure of the mind change complexity, though in general, intrinsic complexity andMind change complexity can behave "orthogonally".
Abstract: The intrinsic complexity of learning compares the difficulty of learning classes of objects by using some reducibility notion. For several types of learning recursive functions, both natural complete classes are exhibited and necessary and sufficient conditions for completeness are derived. Informally, a class is complete iff both its topological structure is highly complex while its algorithmic structure is easy. Some self-describing classes turn out to be complete. Furthermore, the structure of the intrinsic complexity is shown to be much richer than the structure of the mind change complexity, though in general, intrinsic complexity and mind change complexity can behave "orthogonally".

8 citations

Proceedings ArticleDOI
22 Jun 1992
TL;DR: A reconstruction of the foundations of complexity theory relative to random oracles is begun and a technique called average dependence is introduced and used to investigate what is the best lower bound on the size of nondeterministic circuits that accept coNP/sup R/ sets.
Abstract: A reconstruction of the foundations of complexity theory relative to random oracles is begun. The goals are to identify the simple, core mathematical principles behind randomness; to use these principles to push hard on the current boundaries of randomness; and to eventually apply these principles in unrelativized complexity. The focus in this work is on quantifying the degree of separation between NP/sup R/ and coNP/sup R/ relative to a random oracle R. A technique called average dependence is introduced and used to investigate what is the best lower bound on the size of nondeterministic circuits that accept coNP/sup R/ sets and how close a coNP/sup R/ set can come to 'approximating' an arbitrary NP/sup R/ set. The results show that the average dependence technique is a powerful method for addressing certain random oracle questions but that there is still much room for improvement. Some open questions are briefly discussed. >

8 citations

Journal Article
TL;DR: In this paper, the authors provide a unified guide to all the key proofs of Sherstov's degree/discrepancy theorem, which translates lower bounds on the threshold degree of a Boolean function into upper bounds on discrepancy of a related function.
Abstract: Representations of Boolean functions by real polynomials play an important role in complexity theory. Typically, one is interested in the least degree of a polynomial p(x_1,...,x_n) that approximates or sign-represents a given Boolean function f(x_1,...,x_n). This article surveys a new and growing body of work in communication complexity that centers around the dual objects, i.e., polynomials that certify the difficulty of approximating or sign-representing a given function. We provide a unified guide to the following results, complete with all the key proofs: (1) Sherstov's Degree/Discrepancy Theorem, which translates lower bounds on the threshold degree of a Boolean function into upper bounds on the discrepancy of a related function; (2) Two different methods for proving lower bounds on bounded-error communication based on the approximate degree: Sherstov's pattern matrix method and Shi and Zhu's block composition method; (3) Extension of the pattern matrix method to the multiparty model, obtained by Lee and Shraibman and by Chattopadhyay and Ada, and the resulting improved lower bounds for DISJOINTNESS; (4) David and Pitassi's separation of NP and BPP in multiparty communication complexity for k=(1-eps)log n players.

8 citations

Journal ArticleDOI
TL;DR: A novel polynomial-time divide-and-conquer algorithm is proposed (called the multi-phase algorithm) and it is proved that it has a computational complexity of O ( n log)?

8 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20222
20216
202010
20199
201810
201732