{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T03:17:42Z","timestamp":1778296662049,"version":"3.51.4"},"reference-count":39,"publisher":"Elsevier BV","issue":"1","license":[{"start":{"date-parts":[[1989,8,1]],"date-time":"1989-08-01T00:00:00Z","timestamp":617932800000},"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":8751,"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":[[1989,8]]},"DOI":"10.1016\/0022-0000(89)90020-2","type":"journal-article","created":{"date-parts":[[2003,12,4]],"date-time":"2003-12-04T12:01:00Z","timestamp":1070539260000},"page":"84-100","source":"Crossref","is-referenced-by-count":64,"title":["Probabilistic complexity classes and lowness"],"prefix":"10.1016","volume":"39","author":[{"given":"Uwe","family":"Sch\u00f6ning","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/0022-0000(89)90020-2_BIB1","series-title":"Proceedings, 9th ACM Symp. Theory of Comput. Sci.","first-page":"151","article-title":"Reducibility, randomness, and intractability","author":"Adleman","year":"1977"},{"key":"10.1016\/0022-0000(89)90020-2_BIB2","series-title":"Proceedings, 17th ACM Symp. Theory of Comput. Sci.","first-page":"421","article-title":"Trading group theory for randomness","author":"Babai","year":"1985"},{"key":"10.1016\/0022-0000(89)90020-2_BIB3","series-title":"Arthur-Merlin games: A randomized proof system and a short hierarchy of complexity classes","author":"Babai","year":"1986"},{"key":"10.1016\/0022-0000(89)90020-2_BIB4","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1137\/0215053","article-title":"Sparse sets, lowness, and highness","volume":"15","author":"Balc\u00e1zar","year":"1986","journal-title":"SIAM J. Comput."},{"key":"10.1016\/0022-0000(89)90020-2_BIB5","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1137\/0210008","article-title":"Relative to a random oracle A, PA \u2260 co-NPA with probability 1","volume":"10","author":"Bennett","year":"1981","journal-title":"SIAM J. Comput."},{"key":"10.1016\/0022-0000(89)90020-2_BIB6","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1137\/0206023","article-title":"On isomorphism and density of NP and other complete sets","volume":"6","author":"Berman","year":"1977","journal-title":"SIAM J. Comput."},{"key":"10.1016\/0022-0000(89)90020-2_BIB7","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/0020-0190(87)90232-8","article-title":"Does co-NP have short interactive proofs?","volume":"25","author":"Boppana","year":"1987","journal-title":"Inform. Process. Lett."},{"key":"10.1016\/0022-0000(89)90020-2_BIB8","series-title":"Proceedings, 2nd Structure in Complexity Theory Conf.","first-page":"132","article-title":"Strong non deterministic Turing reduction\u2014A technique for proving intractability","author":"Chung","year":"1987"},{"key":"10.1016\/0022-0000(89)90020-2_BIB9","doi-asserted-by":"crossref","first-page":"675","DOI":"10.1137\/0206049","article-title":"Computational complexity of probabilistic complexity classes","volume":"6","author":"Gill","year":"1977","journal-title":"SIAM J. Comput."},{"key":"10.1016\/0022-0000(89)90020-2_BIB10_1","series-title":"Math. Found. Comput. Sci. 1986","first-page":"639","article-title":"Proofs that release minimum knowledges","volume":"Vol. 233","author":"Goldreich","year":"1986"},{"key":"10.1016\/0022-0000(89)90020-2_BIB10_2","series-title":"Proc. 27th Ann. Symp. Foundations of Comput. Sci.","first-page":"174","article-title":"Proofs that yield nothing but their validity and a methodology of interactive proof systems","author":"Goldreich","year":"1986"},{"key":"10.1016\/0022-0000(89)90020-2_BIB11","series-title":"Proceedings, 17th ACM Symp. Theory of Comput Sci.","first-page":"291","article-title":"The knowledge complexity of interactive proofsystems","author":"Goldwasser","year":"1985"},{"key":"10.1016\/0022-0000(89)90020-2_BIB12","series-title":"Proceedings 18th ACM Symp. Theory of Comput. Sci.","first-page":"59","article-title":"Private coins versus public coins in interactive proof systems","author":"Goldwasser","year":"1986"},{"key":"10.1016\/0022-0000(89)90020-2_BIB13","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/0304-3975(86)90174-X","article-title":"Random generation of combinatorial structures from a uniform distribution","volume":"43","author":"Jerrum","year":"1986","journal-title":"Theoret. Comput. Sci"},{"key":"10.1016\/0022-0000(89)90020-2_BIB14","series-title":"Proc. 12th ACM Symp. Theory of Comput. Sci.","first-page":"302","article-title":"Some connections between nonuniform and uniform complexity classes","author":"Karp","year":"1980"},{"key":"10.1016\/0022-0000(89)90020-2_BIB15","series-title":"Generalized lowness and highness and probabilistic complexity classes","author":"Klapper","year":"1988"},{"key":"10.1016\/0022-0000(89)90020-2_BIB16","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/0020-0190(82)90139-9","article-title":"Some observations on the probabilistic algorithms and NP-hard problems","volume":"14","author":"Ko","year":"1982","journal-title":"Inform. Process. Lett."},{"key":"10.1016\/0022-0000(89)90020-2_BIB17","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/0304-3975(87)90078-8","article-title":"On helping by robust oracle machines","volume":"52","author":"Ko","year":"1987","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/0022-0000(89)90020-2_BIB18","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1137\/0214003","article-title":"On circuit-size complexity and the low hierarchy in NP","volume":"14","author":"Ko","year":"1985","journal-title":"SIAM J. Comput."},{"key":"10.1016\/0022-0000(89)90020-2_BIB19","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/0020-0190(83)90044-3","article-title":"BPP and the polynomial hierarchy","volume":"14","author":"Lautemann","year":"1983","journal-title":"Inform. Process. Lett."},{"key":"10.1016\/0022-0000(89)90020-2_BIB20","series-title":"Degrees of Unsolvability","author":"Lerman","year":"1983"},{"key":"10.1016\/0022-0000(89)90020-2_BIB21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0304-3975(82)90085-8","article-title":"Strong nondeterministic polynomial-time reducibilities","volume":"21","author":"Long","year":"1982","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/0022-0000(89)90020-2_BIB22","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/0022-0000(83)90027-2","article-title":"A low and a high hierarchy within NP","volume":"27","author":"Sch\u00f6ning","year":"1983","journal-title":"J. Comput. System Sci."},{"key":"10.1016\/0022-0000(89)90020-2_BIB23","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/0304-3975(84)90058-6","article-title":"On small generators","volume":"34","author":"Sch\u00f6ning","year":"1984","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/0022-0000(89)90020-2_BIB24","article-title":"Complexity and Structure","volume":"Vol. 211","author":"Sch\u00f6ning","year":"1986"},{"key":"10.1016\/0022-0000(89)90020-2_BIB25","series-title":"4th Symp. Theor. Aspects of Comput. Sci. 1987","first-page":"114","article-title":"Graph isomorphism is in the low hierarchy","volume":"Vol. 247","author":"Sch\u00f6ning","year":"1987"},{"key":"10.1016\/0022-0000(89)90020-2_BIB26","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1016\/0022-0000(88)90010-4","article-title":"Graph isomorphism is in the low hierarchy","volume":"37","author":"Sch\u00f6ning","year":"1988","journal-title":"J. Comput. System Sci."},{"key":"10.1016\/0022-0000(89)90020-2_BIB27","series-title":"Proceedings, 2nd Structure in Complexity Theory Conf.","first-page":"2","article-title":"Probabilistic complexity classes and lowness","author":"Sch\u00f6ning","year":"1987"},{"key":"10.1016\/0022-0000(89)90020-2_BIB28","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/0304-3975(82)90039-1","article-title":"Reductions on NP and p-selective sets","volume":"19","author":"Selman","year":"1982","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/0022-0000(89)90020-2_BIB29","series-title":"Proceedings, 15th ACM Symp. Theory of Comput. Sci.","first-page":"330","article-title":"A complexity theoretic approach to randomness","author":"Sipser","year":"1983"},{"key":"10.1016\/0022-0000(89)90020-2_BIB30","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."},{"key":"10.1016\/0022-0000(89)90020-2_BIB31","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1137\/0214060","article-title":"On approximation algorithms for \u2260 P","volume":"14","author":"Stockmeyer","year":"1985","journal-title":"SIAM J. Comput."},{"key":"10.1016\/0022-0000(89)90020-2_BIB32","series-title":"Proceedings, 3rd Structure in Complexity Conf. 1988","article-title":"On tally relativizations of BP-complexity classes","author":"Tang","year":"1988"},{"key":"10.1016\/0022-0000(89)90020-2_BIB33","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/0304-3975(76)90062-1","article-title":"Complete sets and the polynomial-time hierarchy","volume":"3","author":"Wrathall","year":"1977","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/0022-0000(89)90020-2_BIB34","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1016\/0304-3975(83)90020-8","article-title":"Some consequences of non-uniform conditions on uniform classes","volume":"26","author":"Yap","year":"1983","journal-title":"Theoret. Comput. Sci."},{"key":"10.1016\/0022-0000(89)90020-2_BIB35","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/S0019-9958(82)80019-3","article-title":"Robustness of probabilistic complexity classes under definitional perturbations","volume":"54","author":"Zachos","year":"1982","journal-title":"Inform. and Control."},{"key":"10.1016\/0022-0000(89)90020-2_BIB36","series-title":"Proceedings, Ist Structure in Complexity Theory Conf. 1986","first-page":"383","article-title":"Probabilistic quantifiers, adversaries, and complexity classes","volume":"Vol. 223","author":"Zachos","year":"1986"},{"key":"10.1016\/0022-0000(89)90020-2_BIB37","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/S0019-9958(86)80044-4","article-title":"A decisive characterization of BPP","volume":"69","author":"Zachos","year":"1986","journal-title":"Inform. and Control."},{"key":"10.1016\/0022-0000(89)90020-2_BIB38","series-title":"Probabilistic quantifiers vs distrustful adversaries","author":"Zachos","year":"1985"}],"container-title":["Journal of Computer and System Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0022000089900202?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:0022000089900202?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,2,16]],"date-time":"2019-02-16T13:55:05Z","timestamp":1550325305000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/0022000089900202"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,8]]},"references-count":39,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1989,8]]}},"alternative-id":["0022000089900202"],"URL":"https:\/\/doi.org\/10.1016\/0022-0000(89)90020-2","relation":{},"ISSN":["0022-0000"],"issn-type":[{"value":"0022-0000","type":"print"}],"subject":[],"published":{"date-parts":[[1989,8]]}}}