{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T14:04:13Z","timestamp":1770818653314,"version":"3.50.1"},"reference-count":44,"publisher":"Elsevier BV","issue":"3","license":[{"start":{"date-parts":[[1990,12,1]],"date-time":"1990-12-01T00:00:00Z","timestamp":660009600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[1990,12,1]],"date-time":"1990-12-01T00:00:00Z","timestamp":660009600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2013,7,17]],"date-time":"2013-07-17T00:00:00Z","timestamp":1374019200000},"content-version":"vor","delay-in-days":8264,"URL":"http:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCR-8714714"],"award-info":[{"award-number":["CCR-8714714"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCR-8700700"],"award-info":[{"award-number":["CCR-8700700"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DCR-8603346"],"award-info":[{"award-number":["DCR-8603346"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["CCR-8806308"],"award-info":[{"award-number":["CCR-8806308"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computer and System Sciences"],"published-print":{"date-parts":[[1990,12]]},"DOI":"10.1016\/0022-0000(90)90022-d","type":"journal-article","created":{"date-parts":[[2003,12,4]],"date-time":"2003-12-04T07:01:00Z","timestamp":1070521260000},"page":"274-306","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":334,"title":["On uniformity within NC1"],"prefix":"10.1016","volume":"41","author":[{"given":"David A.","family":"Mix Barrington","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Neil","family":"Immerman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Howard","family":"Straubing","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/0022-0000(90)90022-D_BIB1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0168-0072(83)90038-6","article-title":"\u03a31i formulae on finite structures","volume":"24","author":"Ajtai","year":"1983","journal-title":"Ann. Pure Appl. Logic"},{"issue":"No. 4","key":"10.1016\/0022-0000(90)90022-D_BIB2","doi-asserted-by":"crossref","first-page":"912","DOI":"10.1145\/76359.76370","article-title":"P-uniform circuit complexity","volume":"36","author":"Allender","year":"1989","journal-title":"J. Assoc. Comput. Mach."},{"key":"10.1016\/0022-0000(90)90022-D_BIB3","article-title":"Bounded-Width Branching Programs","author":"Barrington","year":"1986"},{"issue":"No. 1","key":"10.1016\/0022-0000(90)90022-D_BIB4","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/0022-0000(89)90037-8","article-title":"Bounded-width polynomial-size branching recognize exactly those languages in NC1","volume":"38","author":"Barrington","year":"1989","journal-title":"J. Comput. System Sci."},{"key":"10.1016\/0022-0000(90)90022-D_BIB5","series-title":"Structure in Complexity Theory: Third Annual Conference","first-page":"47","article-title":"On uniformity within NC1","author":"Barrington","year":"1988"},{"key":"10.1016\/0022-0000(90)90022-D_BIB6","article-title":"Regular languages in NO1","author":"Barrington","year":"1988"},{"issue":"No. 4","key":"10.1016\/0022-0000(90)90022-D_BIB7","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(90)90022-D_BIB8","doi-asserted-by":"crossref","first-page":"994","DOI":"10.1137\/0215070","article-title":"Log-depth circuits for division and related problems","volume":"15","author":"Beame","year":"1986","journal-title":"SIAM J. Comput."},{"key":"10.1016\/0022-0000(90)90022-D_BIB9","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1137\/0206023","article-title":"On isomorphisms and density of NP and other complete sets","volume":"6","author":"Berman","year":"1977","journal-title":"SIAM J. Comput."},{"key":"10.1016\/0022-0000(90)90022-D_BIB10","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 Grundl. Math."},{"key":"10.1016\/0022-0000(90)90022-D_BIB11","series-title":"19th ACM STOC Symp.","first-page":"123","article-title":"The Boolean formula value problem is in ALOGTIME","author":"Buss","year":"1987"},{"key":"10.1016\/0022-0000(90)90022-D_BIB12","series-title":"An optimal parallel algorithm for formula evaluation","author":"Buss","year":"1989"},{"key":"10.1016\/0022-0000(90)90022-D_BIB13","series-title":"15th ACM STOC Symp.","first-page":"52","article-title":"Unbounded fan-in circuits and associative functions","author":"Chandra","year":"1983"},{"key":"10.1016\/0022-0000(90)90022-D_BIB14","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1145\/322234.322243","article-title":"Alternation","volume":"28","author":"Chandra","year":"1981","journal-title":"J. Assoc. Comput. Mach."},{"issue":"No. 2","key":"10.1016\/0022-0000(90)90022-D_BIB15","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(90)90022-D_BIB16","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1016\/S0019-9958(85)80041-3","article-title":"A taxonomy of problems with fast parallel algorithms","volume":"64","author":"Cook","year":"1985","journal-title":"Inform. and Control"},{"key":"10.1016\/0022-0000(90)90022-D_BIB17","volume":"Vol. B","author":"Eilenberg","year":"1976"},{"key":"10.1016\/0022-0000(90)90022-D_BIB18","series-title":"A Mathematical Introduction to Logic","author":"Enderton","year":"1972"},{"key":"10.1016\/0022-0000(90)90022-D_BIB19","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(90)90022-D_BIB20","series-title":"28th IEEE FOCS Symp.","first-page":"99","article-title":"Threshold circuits of bounded depth","author":"Hajnal","year":"1987"},{"key":"10.1016\/0022-0000(90)90022-D_BIB21","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/S0019-9958(86)80029-8","article-title":"Relational queries computable in polynomial time","volume":"68","author":"Immerman","year":"1986","journal-title":"Inform. and Control"},{"issue":"No. 4","key":"10.1016\/0022-0000(90)90022-D_BIB22","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1137\/0216051","article-title":"Languages which capture complexity classes","volume":"16","author":"Immerman","year":"1987","journal-title":"SIAM J. Comput."},{"key":"10.1016\/0022-0000(90)90022-D_BIB23","series-title":"Second Structure in Complexity Theory Conf.","first-page":"194","article-title":"Expressibility as a complexity measure: Results and directions","author":"Immerman","year":"1987"},{"issue":"No. 5","key":"10.1016\/0022-0000(90)90022-D_BIB24","doi-asserted-by":"crossref","first-page":"935","DOI":"10.1137\/0217058","article-title":"Nondeterministic space is closed under complementation","volume":"17","author":"Immerman","year":"1988","journal-title":"SIAM J. Comput."},{"key":"10.1016\/0022-0000(90)90022-D_BIB25","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1137\/0218043","article-title":"Expressibility and parallel complexity","volume":"18","author":"Immerman","year":"1989","journal-title":"SIAM J. Comput."},{"key":"10.1016\/0022-0000(90)90022-D_BIB26","series-title":"The Algebraic Theory of Machines, Languages, and Semigroups","author":"Krohn","year":"1968"},{"key":"10.1016\/0022-0000(90)90022-D_BIB27","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/S0019-9958(77)90443-0","article-title":"Application of model-theoretic games to discrete linear orders and finite automata","volume":"33","author":"Ladner","year":"1977","journal-title":"Inform. and Control"},{"key":"10.1016\/0022-0000(90)90022-D_BIB28","series-title":"Semigroups and Combinatorial Applications","author":"Lallement","year":"1979"},{"key":"10.1016\/0022-0000(90)90022-D_BIB29","series-title":"19th IEEE FOCS Symp.","first-page":"193","article-title":"Model theoretic aspects of computational complexity","author":"Lipton","year":"1978"},{"key":"10.1016\/0022-0000(90)90022-D_BIB30","series-title":"Counter-Free Automata","author":"McNaughton","year":"1971"},{"issue":"No. 3","key":"10.1016\/0022-0000(90)90022-D_BIB31","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1016\/0022-0000(88)90030-X","article-title":"Parallel computation with threshold functions","volume":"36","author":"Parberry","year":"1988","journal-title":"J. Comput. System Sci."},{"key":"10.1016\/0022-0000(90)90022-D_BIB32","series-title":"Varieties of Formal Languages","author":"Pin","year":"1986"},{"issue":"No. 4","key":"10.1016\/0022-0000(90)90022-D_BIB33_1","first-page":"598","article-title":"Lower bounds for the size of circuits of bounded depth with basis {&,\u2295}","volume":"41","author":"Razborov","year":"1987","journal-title":"Math. Zametki"},{"issue":"No. 4","key":"10.1016\/0022-0000(90)90022-D_BIB33_2","first-page":"333","volume":"41","author":"Razborov","year":"1987","journal-title":"Math. Notes Acad. Sci. USSR"},{"key":"10.1016\/0022-0000(90)90022-D_BIB34","series-title":"Second Structure in Complexity Theory Conference","first-page":"118","article-title":"On threshold circuits and polynomial computation","author":"Reif","year":"1987"},{"issue":"No. 2","key":"10.1016\/0022-0000(90)90022-D_BIB35","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/0022-0000(81)90038-6","article-title":"On uniform circuit complexity","volume":"21","author":"Ruzzo","year":"1981","journal-title":"J. Comput. System Sci."},{"key":"10.1016\/0022-0000(90)90022-D_BIB36","series-title":"19th ACM STOC Symp.","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(90)90022-D_BIB37","series-title":"Proceedings, 4th Hawaii Symposium on System Sciences","first-page":"525","article-title":"On time-hardware complexity tradeoffs for Boolean functions","author":"Spira","year":"1971"},{"key":"10.1016\/0022-0000(90)90022-D_BIB38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0304-3975(76)90061-X","article-title":"The polynomial-time hierarchy","volume":"3","author":"Stockmeyer","year":"1977","journal-title":"Theoret. Comput. Sci."},{"issue":"No. 2","key":"10.1016\/0022-0000(90)90022-D_BIB39","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1137\/0213027","article-title":"Simulation of parallel random access machines by circuits","volume":"13","author":"Stockmeyer","year":"1984","journal-title":"SIAM J. Comput."},{"key":"10.1016\/0022-0000(90)90022-D_BIB40","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":"18","author":"Straubing","year":"1979","journal-title":"J. Pure Appl. Algebra"},{"key":"10.1016\/0022-0000(90)90022-D_BIB41","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(90)90022-D_BIB42","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(90)90022-D_BIB43","series-title":"14th ACM STOC Symp.","first-page":"137","article-title":"Complexity of relational query languages","author":"Vardi","year":"1982"}],"container-title":["Journal of Computer and System Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:002200009090022D?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:002200009090022D?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T18:11:07Z","timestamp":1757095867000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/002200009090022D"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,12]]},"references-count":44,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1990,12]]}},"alternative-id":["002200009090022D"],"URL":"https:\/\/doi.org\/10.1016\/0022-0000(90)90022-d","relation":{},"ISSN":["0022-0000"],"issn-type":[{"value":"0022-0000","type":"print"}],"subject":[],"published":{"date-parts":[[1990,12]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"On uniformity within NC1","name":"articletitle","label":"Article Title"},{"value":"Journal of Computer and System Sciences","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/0022-0000(90)90022-D","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"converted-article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 1990 Published by Elsevier Inc.","name":"copyright","label":"Copyright"}]}}