Regular languages in NC1
dc.contributor.author | Mix Barrington, David A. | en_US |
dc.contributor.author | Compton, Kevin J. | en_US |
dc.contributor.author | Straubing, Howard | en_US |
dc.contributor.author | Therien, Denis | en_US |
dc.date.accessioned | 2006-04-10T15:12:01Z | |
dc.date.available | 2006-04-10T15:12:01Z | |
dc.date.issued | 1992-06 | en_US |
dc.identifier.citation | Mix Barrington, David A., Compton, Kevin, Straubing, Howard, Therien, Denis (1992/06)."Regular languages in NC1." Journal of Computer and System Sciences 44(3): 478-499. <http://hdl.handle.net/2027.42/30017> | en_US |
dc.identifier.uri | http://www.sciencedirect.com/science/article/B6WJ0-4B4RJ5P-1K/2/78e4de8c07abd4ebdbe4bd15e737a664 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/30017 | |
dc.description.abstract | We give several characterizations, in terms of formal logic, semigroup theory, and operations on languages, of the regular languages in the circuit complexity class AC0, thus answering a question of Chandra, Fortune, and Lipton. As a by-product, we are able to determine effectively whether a given regular language is in AC0 and to solve in part an open problem originally posed by McNaughton. Using recent lower-bound results of Razborov and Smolensky, we obtain similar characterizations of the family of regular languages recognized by constant-depth circuit families that include unbounded fan-in mod p addition gates for a fixed prime p along with unbounded fan-in boolean gates. We also obtain logical characterizations for the class of all languages recognized by nonuniform circuit families in which mod m gates (where m is not necessarily prime) are permitted. Comparison of this characterization with our previous results provides evidence for a conjecture concerning the regular languages in this class. A proof of this conjecture would show that computing the bit sum modulo p, where p is a prime not dividing m, is not AC0-reducible to addition mod m, and thus that MAJORITY is not AC0-reducible to addition mod m. | en_US |
dc.format.extent | 1497199 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 | Regular languages in NC1 | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Philosophy | en_US |
dc.subject.hlbsecondlevel | Computer Science | en_US |
dc.subject.hlbtoplevel | Humanities | en_US |
dc.subject.hlbtoplevel | Engineering | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Computer Science, The University of Michigan, Ann Arbor, Michigan 48109, USA. | en_US |
dc.contributor.affiliationother | Department of Computer and Information Science, The University of Massachusetts,Amherst, Massachusetts 01003, USA. | en_US |
dc.contributor.affiliationother | Computer Science Department, Boston College, Chestnut Hill. Massachusetts 02167, USA. | en_US |
dc.contributor.affiliationother | School of Computer Science, McGill University, MontrPal, Q&bee, Canada H3A 2K6 | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/30017/1/0000385.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1016/0022-0000(92)90014-A | en_US |
dc.identifier.source | Journal of Computer and System Sciences | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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