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| Content Provider | Springer Nature Link |
|---|---|
| Author | Gutoski, Gus Wu, Xiaodi |
| Copyright Year | 2013 |
| Abstract | This paper presents an efficient parallel approximation scheme for a new class of min-max problems. The algorithm is derived from the matrix multiplicative weights update method and can be used to find near-optimal strategies for competitive two-party classical or quantum interactions in which a referee exchanges any number of messages with one party followed by any number of additional messages with the other. It considerably extends the class of interactions which admit parallel solutions, demonstrating for the first time the existence of a parallel algorithm for an interaction in which one party reacts adaptively to the other. As a consequence, we prove that several competing-provers complexity classes collapse to PSPACE, such as QRG(2), SQG and two new classes called DIP and DQIP. A special case of our result is a parallel approximation scheme for a specific class of semidefinite programs whose feasible region consists of lists of semidefinite matrices that satisfy a transcript-like consistency condition. Applied to this special case, our algorithm yields a direct polynomial-space simulation of multi-message quantum interactive proofs resulting in a first-principles proof of QIP =PSPACE. |
| Ending Page | 428 |
| Page Count | 44 |
| Starting Page | 385 |
| File Format | |
| ISSN | 10163328 |
| e-ISSN | 14208954 |
| Journal | Computational complexity |
| Issue Number | 2 |
| Volume Number | 22 |
| Language | English |
| Publisher | SP Birkhäuser Verlag Basel |
| Publisher Date | 2013-05-03 |
| Publisher Place | Basel |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Complexity classes (hierarchies, relations among complexity classes, etc.) Semidefinite programming Computational Mathematics and Numerical Analysis Quantum algorithms and complexity Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) Parallel algorithms Models of computation (Turing machines, etc.) Parallel approximation algorithm semidefinite programming zero-sum games quantum interactive proofs with competing provers Approximation algorithms Minimax problems Algorithm Analysis and Problem Complexity |
| Content Type | Text |
| Resource Type | Article |
| Subject | Theoretical Computer Science Computational Theory and Mathematics Computational Mathematics |
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