Amir Yehudayoff's Books

Communication Complexity

and Applications

By: Anup Rao,Amir Yehudayoff

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Communication Complexity

and Applications

By: Anup Rao,Amir Yehudayoff

Presents basic theory for graduate students and researchers with applications in circuit and proof complexity, streaming algorithms and distributed computing.

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Page Count

271

Publisher

Cambridge University Press

Published Date

ISBN 10

1108497985

ISBN 13

9781108497985

Arithmetic Circuits

A Survey of Recent Results and Open Questions

By: Amir Shpilka,Amir Yehudayoff

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Arithmetic Circuits

A Survey of Recent Results and Open Questions

By: Amir Shpilka,Amir Yehudayoff

A large class of problems in symbolic computation can be expressed as the task of computing some polynomials; and arithmetic circuits form the most standard model for studying the complexity of such computations. This algebraic model of computation attracted a large amount of research in the last five decades, partially due to its simplicity and elegance. Being a more structured model than Boolean circuits, one could hope that the fundamental problems of theoretical computer science, such as separating P from NP, will be easier to solve for arithmetic circuits. However, in spite of the appearing simplicity and the vast amount of mathematical tools available, no major breakthrough has been seen. In fact, all the fundamental questions are still open for this model as well. Nevertheless, there has been a lot of progress in the area and beautiful results have been found, some in the last few years. As examples we mention the connection between polynomial identity testing and lower bounds of Kabanets and Impagliazzo, the lower bounds of Raz for multilinear formulas, and two new approaches for proving lower bounds: Geometric Complexity Theory and Elusive Functions. The goal of this monograph is to survey the field of arithmetic circuit complexity, focusing mainly on what we find to be the most interesting and accessible research directions. We aim to cover the main results and techniques, with an emphasis on works from the last two decades. In particular, we discuss the recent lower bounds for multilinear circuits and formulas, the advances in the question of deterministically checking polynomial identities, and the results regarding reconstruction of arithmetic circuits. We do, however, also cover part of the classical works on arithmetic circuits. In order to keep this monograph at a reasonable length, we do not give full proofs of most theorems, but rather try to convey the main ideas behind each proof and demonstrate it, where possible, by proving some special cases.

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Page Count

193

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Now Publishers Inc

Published Date

ISBN 10

1601984006

ISBN 13

9781601984005

Communication Complexity

and Applications

By: Anup Rao,Amir Yehudayoff

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Communication Complexity

and Applications

By: Anup Rao,Amir Yehudayoff

Communication complexity is the mathematical study of scenarios where several parties need to communicate to achieve a common goal, a situation that naturally appears during computation. This introduction presents the most recent developments in an accessible form, providing the language to unify several disjoint research subareas. Written as a guide for a graduate course on communication complexity, it will interest a broad audience in computer science, from advanced undergraduates to researchers in areas ranging from theory to algorithm design to distributed computing. The first part presents basic theory in a clear and illustrative way, offering beginners an entry into the field. The second part describes applications including circuit complexity, proof complexity, streaming algorithms, extension complexity of polytopes, and distributed computing. Proofs throughout the text use ideas from a wide range of mathematics, including geometry, algebra, and probability. Each chapter contains numerous examples, figures, and exercises to aid understanding.

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Page Count

271

Publisher

Cambridge University Press

Published Date

ISBN 10

1108776019

ISBN 13

9781108776011

Arithmetic Circuits

A Survey of Recent Results and Open Questions

By: Amir Shpilka,Amir Yehudayoff

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Arithmetic Circuits

A Survey of Recent Results and Open Questions

By: Amir Shpilka,Amir Yehudayoff

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

193

Publisher

Now Publishers Inc

Published Date

ISBN 10

1601984006

ISBN 13

9781601984005

Book's by Amir Yehudayoff

Communication Complexity

Communication Complexity

Arithmetic Circuits

Arithmetic Circuits

Communication Complexity

Communication Complexity

Arithmetic Circuits

Arithmetic Circuits

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