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Showing 1 to 12 of 12 for “"Computational complexity theory"”.
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Some hardness escalation results in computational complexity theory
… we prove new hardness escalation results in computational complexity theory; a phenomenon where hardness results against seemingly weak models of computation for any problem can be lifted, in a black box manner, to much stronger models of computation by considering a simple gadget composed …
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Abstract Complexity Theory and the Degrees of Unsolvability
We focus on the A° sets and show that abstract complexity theory can be applied to the degrees of unsolvability simply by relativizing the notion of a complexity measure to 0'. Since the Gap Theorem holds in our context, we need to develop the concept of a A° honest function just as one needs to …
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A complexity theoretic approach to learning
… problems in machine learning. We use tools from computational complexity theory to make progress on problems from computational learning theory. Our methods yield the fastest and most expressive algorithms to date for learning several fundamental concept classes: * We show that any s-term DNF …
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An Interactive Tutorial for NP-Completeness
A Theory of Algorithms course is essential to any Computer Science curriculum at both the undergraduate and graduate levels. It is also considered to be difficult material to teach or to learn. In particular the topics of Computational Complexity Theory, reductions, and the NP-Complete class of …
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Complexity and Partitions
Computational complexity theory usually investigates the complexity of sets, i.e., the complexity of partitions into two parts. But often it is more appropriate to represent natural problems by partitions into more than two parts. A particularly interesting class of such problems consists of …
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Spectral methods and computational trade-offs in high-dimensional statistical inference
… time algorithms by exhibiting statistical and computational trade-offs in those problems. In the first chapter, we prove a useful variant of the well-known Davis{Kahan theorem, which is a spectral perturbation result that allows us to bound of the distance between population eigenspaces and …
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New error correcting codes from lifting
… used for protecting information from noise. The theory of error correcting codes studies the range of parameters achievable by such codes, as well as the efficiency with which one can encode and decode them. In recent years, attention has focused on the study of sublinear-time algorithms for …
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The space around BQP
This thesis explores the computational power of quantum devices from the perspective of computational complexity theory. Quantum computers hold the promise of solving many problems exponentially faster than classical computers. The computational power of universal quantum devices is captured by the …
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PCPs for Arthur-Merlin games and communication protocols
… of proof systems that have played a key role in computational complexity theory. In this thesis we study the power of PCPs in two new settings: Arthur-Merlin games and communication protocols. In the first part of the thesis, we give a 'PCP characterization' of AM analogous to the PCP Theorem for …
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A Hybrid multi-agent architecture and heuristics generation for solving meeting scheduling problem
… centralised and distributed architectures. In computational complexity theory, researchers have classified the problems into the followings categories: (i) P problems, (ii) NP problems, (iii) NP-complete problems, and (iv) NP-hard problems. A method for computing the solution to NP-hard …
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Complexity in physical, living and mathematical systems
… the phase transition. Some connections between Computational complexity theory, Statistical physics, Number theory and Network theory are also outlined. In the same spirit, the second part of the chapter focuses on a simple algorithm whose dynamics evidence Self-Organized Criticality (SOC). We …