{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T15:30:45Z","timestamp":1759073445896},"reference-count":28,"publisher":"Elsevier BV","issue":"3","license":[{"start":{"date-parts":[[1992,6,1]],"date-time":"1992-06-01T00:00:00Z","timestamp":707356800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":7716,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Computer and System Sciences"],"published-print":{"date-parts":[[1992,6]]},"DOI":"10.1016\/0022-0000(92)90014-a","type":"journal-article","created":{"date-parts":[[2003,12,4]],"date-time":"2003-12-04T12:01:00Z","timestamp":1070539260000},"page":"478-499","source":"Crossref","is-referenced-by-count":78,"title":["Regular languages in NC1"],"prefix":"10.1016","volume":"44","author":[{"given":"David A.","family":"Mix Barrington","sequence":"first","affiliation":[]},{"given":"Kevin","family":"Compton","sequence":"additional","affiliation":[]},{"given":"Howard","family":"Straubing","sequence":"additional","affiliation":[]},{"given":"Denis","family":"Th\u00e9rien","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/0022-0000(92)90014-A_BIB1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0168-0072(83)90038-6","article-title":"\u03a311 formulae on finite structure","volume":"24","author":"Ajtai","year":"1983","journal-title":"Ann. Pure Appl. Logic"},{"key":"10.1016\/0022-0000(92)90014-A_BIB2","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/0022-0000(89)90037-8","article-title":"Bounded-width polynomial-size branching programs recognize exactly those languages in NC1","volume":"38","author":"Barrington","year":"1989","journal-title":"J. Comput. System Sci."},{"key":"10.1016\/0022-0000(92)90014-A_BIB3","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/0022-0000(90)90022-D","article-title":"On uniformity in NC1","volume":"4","author":"Barrington","year":"1990","journal-title":"J. Comput. System Sci."},{"key":"10.1016\/0022-0000(92)90014-A_BIB4","doi-asserted-by":"crossref","first-page":"941","DOI":"10.1145\/48014.63138","article-title":"Finite monoids and the fine structure of NC1","volume":"35","author":"Barrington","year":"1988","journal-title":"J. Assoc. Comput. Mach."},{"key":"10.1016\/0022-0000(92)90014-A_BIB5","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/0890-5401(90)90007-5","article-title":"Non-uniform automata over groups","volume":"89","author":"Barrington","year":"1990","journal-title":"Inform. Comput."},{"key":"10.1016\/0022-0000(92)90014-A_BIB6","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/0022-0000(78)90049-1","article-title":"The dot-depth hierarchy of star-free events is infinite","volume":"16","author":"Brzozowski","year":"1978","journal-title":"J. Comput. System Sci."},{"key":"10.1016\/0022-0000(92)90014-A_BIB7","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1002\/malq.19600060105","article-title":"Weak second-order arithmetic and finite automata","volume":"6","author":"B\u00fcchi","year":"1960","journal-title":"Z. Math. Logik Grundlagen Math."},{"key":"10.1016\/0022-0000(92)90014-A_BIB8","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1016\/0022-0000(85)90015-7","article-title":"Unbounded fan-in circuits and associative functions","volume":"30","author":"Chandra","year":"1985","journal-title":"J. Comput. System Sci."},{"key":"10.1016\/0022-0000(92)90014-A_BIB9","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1137\/0213028","article-title":"Constant depth reducibility","volume":"13","author":"Chandra","year":"1984","journal-title":"SIAM J. Comput."},{"key":"10.1016\/0022-0000(92)90014-A_BIB10","volume":"Vol. B","author":"Eilenberg","year":"1976"},{"key":"10.1016\/0022-0000(92)90014-A_BIB11","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/BF01744431","article-title":"Parity, circuits, and the polynomial time hierarchy","volume":"17","author":"Furst","year":"1984","journal-title":"Math Systems Theory"},{"key":"10.1016\/0022-0000(92)90014-A_BIB12","series-title":"Proceedings, 28th IEEE FOCS","first-page":"99","article-title":"Threshold circuits of bounded depth","author":"Hajnal","year":"1987"},{"key":"10.1016\/0022-0000(92)90014-A_BIB13","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1137\/0216051","article-title":"Languages that capture complexity classes","volume":"16","author":"Immerman","year":"1987","journal-title":"SIAM J. Comput."},{"key":"10.1016\/0022-0000(92)90014-A_BIB14","series-title":"Proceedings, 12th ACM STOC","first-page":"302","article-title":"Some connections between non-uniform and uniform complexity classes","author":"Karp","year":"1980"},{"key":"10.1016\/0022-0000(92)90014-A_BIB15","series-title":"Semigroups and Combinatorial Applications","author":"Lallement","year":"1979"},{"key":"10.1016\/0022-0000(92)90014-A_BIB16","series-title":"Counter-free Automata","author":"McNaughton","year":"1971"},{"key":"10.1016\/0022-0000(92)90014-A_BIB17","series-title":"Varieties of Formal Languages","author":"Pin","year":"1986"},{"key":"10.1016\/0022-0000(92)90014-A_BIB18_1","first-page":"598","article-title":"Lower bounds for the size of circuits of bounded depth with basis {&, \u22c7}","volume":"41","author":"Razborov","year":"1987","journal-title":"Mat. Zametki"},{"key":"10.1016\/0022-0000(92)90014-A_BIB18_2","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1007\/BF01137685","article-title":"Lower bounds for the size of circuits of bounded depth with basis {&, \u22c7}","volume":"41","author":"Razborov","year":"1987","journal-title":"Math. Notes"},{"key":"10.1016\/0022-0000(92)90014-A_BIB19","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1016\/S0019-9958(65)90108-7","article-title":"On finite monoids having only trivial subgroups","volume":"8","author":"Sch\u00fctzenberger","year":"1965","journal-title":"Inform. Control"},{"key":"10.1016\/0022-0000(92)90014-A_BIB20","series-title":"Proceedings, 15th ACM STOC","first-page":"61","article-title":"Borel sets and circuit complexity","author":"Sipser","year":"1983"},{"key":"10.1016\/0022-0000(92)90014-A_BIB21","series-title":"Proceedings, 19th ACM STOC","first-page":"77","article-title":"Algebraic methods in the theory of lower bounds for boolean circuit complexity","author":"Smolensky","year":"1987"},{"key":"10.1016\/0022-0000(92)90014-A_BIB22","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/0022-4049(79)90024-0","article-title":"Families of recognizable sets corresponding to certain varieties of finite monoids","volume":"15","author":"Straubing","year":"1979","journal-title":"J. Pure Appl. Algebra"},{"key":"10.1016\/0022-0000(92)90014-A_BIB23","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1016\/0022-4049(79)90025-2","article-title":"Aperiodic homomorphisms and the concatenation product of recognizable sets","volume":"15","author":"Straubing","year":"1979","journal-title":"J. Pure Appl. Algebra"},{"key":"10.1016\/0022-0000(92)90014-A_BIB24","series-title":"Proceedings, 15th ICALP","first-page":"561","article-title":"Regular languages defined with generalized quantifiers","author":"Straubing","year":"1988"},{"key":"10.1016\/0022-0000(92)90014-A_BIB25","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1142\/S0218196791000043","article-title":"Constant-Depth Periodic Circuits","volume":"1","author":"Straubing","year":"1991","journal-title":"Internat. J. Algebra Comput."},{"key":"10.1016\/0022-0000(92)90014-A_BIB26","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1016\/0022-0000(82)90016-2","article-title":"Classifying regular events in symbolic logic","volume":"25","author":"Thomas","year":"1982","journal-title":"J. Comput. System Sci."},{"key":"10.1016\/0022-0000(92)90014-A_BIB27","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/0022-4049(87)90108-3","article-title":"Categories as algebra","volume":"48","author":"Tilson","year":"1987","journal-title":"J. Pure Appl. Algebra"}],"container-title":["Journal of Computer and System Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:002200009290014A?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:002200009290014A?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,2,16]],"date-time":"2019-02-16T13:57:08Z","timestamp":1550325428000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/002200009290014A"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,6]]},"references-count":28,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1992,6]]}},"alternative-id":["002200009290014A"],"URL":"https:\/\/doi.org\/10.1016\/0022-0000(92)90014-a","relation":{},"ISSN":["0022-0000"],"issn-type":[{"value":"0022-0000","type":"print"}],"subject":[],"published":{"date-parts":[[1992,6]]}}}