The Minimum Oracle Circuit Size Problem
We consider variants of the minimum circuit size problem MCSP, where the goal is to minimize the size of oracle circuits computing a given function. When the oracle is QBF, the resulting problem MSCP[superscript QBF] is known to be complete for PSPACE under ZPP reductions. We show that it is not com...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer International Publishing
2017
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| Online Access: | http://hdl.handle.net/1721.1/106913 |
| _version_ | 1811073148444999680 |
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| author | Allender, Eric Holden, Dhiraj Kabanets, Valentine |
| author2 | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory |
| author_facet | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Allender, Eric Holden, Dhiraj Kabanets, Valentine |
| author_sort | Allender, Eric |
| collection | MIT |
| description | We consider variants of the minimum circuit size problem MCSP, where the goal is to minimize the size of oracle circuits computing a given function. When the oracle is QBF, the resulting problem MSCP[superscript QBF] is known to be complete for PSPACE under ZPP reductions. We show that it is not complete under logspace reductions, and indeed it is not even hard for TC[superscript 0] under uniform AC[superscript 0] reductions. We obtain a variety of consequences that follow if oracle versions of MCSP are hard for various complexity classes under different types of reductions. We also prove analogous results for the problem of determining the resource-bounded Kolmogorov complexity of strings, for certain types of Kolmogorov complexity measures. |
| first_indexed | 2024-09-23T09:29:12Z |
| format | Article |
| id | mit-1721.1/106913 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:29:12Z |
| publishDate | 2017 |
| publisher | Springer International Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1069132022-09-30T14:44:48Z The Minimum Oracle Circuit Size Problem Allender, Eric Holden, Dhiraj Kabanets, Valentine Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Holden, Dhiraj We consider variants of the minimum circuit size problem MCSP, where the goal is to minimize the size of oracle circuits computing a given function. When the oracle is QBF, the resulting problem MSCP[superscript QBF] is known to be complete for PSPACE under ZPP reductions. We show that it is not complete under logspace reductions, and indeed it is not even hard for TC[superscript 0] under uniform AC[superscript 0] reductions. We obtain a variety of consequences that follow if oracle versions of MCSP are hard for various complexity classes under different types of reductions. We also prove analogous results for the problem of determining the resource-bounded Kolmogorov complexity of strings, for certain types of Kolmogorov complexity measures. National Science Foundation (U.S.) (grants CCF-1064785, CCF-1423544, and CCF-1555409) Natural Sciences and Engineering Research Council of Canada (Discovery Grant) 2017-02-10T20:58:59Z 2017-02-10T20:58:59Z 2016-02 2016-08-18T15:40:13Z Article http://purl.org/eprint/type/JournalArticle 1016-3328 1420-8954 http://hdl.handle.net/1721.1/106913 Allender, Eric, Dhiraj Holden, and Valentine Kabanets. “The Minimum Oracle Circuit Size Problem.” Comput. Complex. (February 17, 2016). en http://dx.doi.org/10.1007/s00037-016-0124-0 computational complexity Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer International Publishing application/pdf Springer International Publishing Springer International Publishing |
| spellingShingle | Allender, Eric Holden, Dhiraj Kabanets, Valentine The Minimum Oracle Circuit Size Problem |
| title | The Minimum Oracle Circuit Size Problem |
| title_full | The Minimum Oracle Circuit Size Problem |
| title_fullStr | The Minimum Oracle Circuit Size Problem |
| title_full_unstemmed | The Minimum Oracle Circuit Size Problem |
| title_short | The Minimum Oracle Circuit Size Problem |
| title_sort | minimum oracle circuit size problem |
| url | http://hdl.handle.net/1721.1/106913 |
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