Definability by constant-depth polynomial-size circuits
dc.contributor.author | Denenberg, Larry | en_US |
dc.contributor.author | Gurevich, Yuri | en_US |
dc.contributor.author | Shelah, Saharon | en_US |
dc.date.accessioned | 2006-04-07T19:27:58Z | |
dc.date.available | 2006-04-07T19:27:58Z | |
dc.date.issued | 1986 | en_US |
dc.identifier.citation | Denenberg, Larry, Gurevich, Yuri, Shelah, Saharon (1986)."Definability by constant-depth polynomial-size circuits." Information and Control 70(2-3): 216-240. <http://hdl.handle.net/2027.42/26084> | en_US |
dc.identifier.uri | http://www.sciencedirect.com/science/article/B7MFM-4G3DGHT-32/2/4dfbaa4efc717c9117e3e98ee9e46945 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/26084 | |
dc.description.abstract | A function of boolean arguments is symmetric if its value depends solely on the number of 1's among its arguments. In the first part of this paper we partially characterize those symmetric functions that can be computed by constant-depth polynomial-size sequences of boolean circuits, and discuss the complete characterization. (We treat both uniform and non-uniform sequences of circuits.) Our results imply that these circuits can compute functions that are not definable in first-order logic. In the second part of the paper we generalize from circuits computing symmetric functions to circuits recognizing first-order structures. By imposing fairly natural restrictions we develop a circuit model with precisely the power of first-order logic: a class of structures is first-order definable if and only if it can be recognized by a constant-depth polynomial-time sequence of such circuits. | en_US |
dc.format.extent | 1457745 bytes | |
dc.format.extent | 3118 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Elsevier | en_US |
dc.title | Definability by constant-depth polynomial-size circuits | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Science (General) | en_US |
dc.subject.hlbsecondlevel | Information and Library Science | en_US |
dc.subject.hlbsecondlevel | Computer Science | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.subject.hlbtoplevel | Social Sciences | en_US |
dc.subject.hlbtoplevel | Engineering | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | University of Michigan, Ann Arbor, Michigan USA | en_US |
dc.contributor.affiliationother | Harvard University, Cambridge, Massachusetts USA | en_US |
dc.contributor.affiliationother | Hebrew University, Tel-Aviv, Israel | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/26084/1/0000160.pdf | en_US |
dc.identifier.source | Information and Control | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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