{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T18:26:42Z","timestamp":1773080802054,"version":"3.50.1"},"reference-count":21,"publisher":"Elsevier BV","issue":"1","license":[{"start":{"date-parts":[[2003,10,1]],"date-time":"2003-10-01T00:00:00Z","timestamp":1064966400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2013,8,22]],"date-time":"2013-08-22T00:00:00Z","timestamp":1377129600000},"content-version":"vor","delay-in-days":3613,"URL":"https:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information and Computation"],"published-print":{"date-parts":[[2003,10]]},"DOI":"10.1016\/s0890-5401(03)00118-4","type":"journal-article","created":{"date-parts":[[2003,6,2]],"date-time":"2003-06-02T23:15:45Z","timestamp":1054595745000},"page":"78-89","source":"Crossref","is-referenced-by-count":11,"title":["A lower bound for integer multiplication on randomized ordered read-once branching programs"],"prefix":"10.1016","volume":"186","author":[{"given":"Farid","family":"Ablayev","sequence":"first","affiliation":[]},{"given":"Marek","family":"Karpinski","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0890-5401(03)00118-4_BIB1","series-title":"Proceedings of the ICALP\u201993","first-page":"241","article-title":"Lower bounds for one-way probabilistic communication complexity","volume":"vol. 700","author":"Ablayev","year":"1993"},{"key":"10.1016\/S0890-5401(03)00118-4_BIB2","series-title":"Proceedings of the ICALP\u201997","first-page":"195","article-title":"Randomization and nondeterminism are incomparable for ordered read-once branching programs","volume":"vol. 1256","author":"Ablayev","year":"1997"},{"key":"10.1016\/S0890-5401(03)00118-4_BIB3","unstructured":"F. Ablayev, M. Karpinski, On the power of randomized ordered branching programs, Research Report 85181-CS, University of Bonn, 1997"},{"key":"10.1016\/S0890-5401(03)00118-4_BIB4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF01200404","article-title":"On lower bounds for read-k-times branching programs","volume":"3","author":"Borodin","year":"1993","journal-title":"Comput. Complex."},{"issue":"8","key":"10.1016\/S0890-5401(03)00118-4_BIB5","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1109\/TC.1986.1676819","article-title":"Graph-based algorithms for boolean function manipulation","volume":"C-35","author":"Bryant","year":"1986","journal-title":"IEEE Trans. Comput."},{"issue":"2","key":"10.1016\/S0890-5401(03)00118-4_BIB6","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1109\/12.73590","article-title":"On the complexity of VLSI implementations and graph representations of Boolean functions with applications to integer multiplication","volume":"40","author":"Bryant","year":"1991","journal-title":"IEEE Trans. Comput."},{"issue":"3","key":"10.1016\/S0890-5401(03)00118-4_BIB7","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1145\/136035.136043","article-title":"Symbolic boolean manipulation with ordered binary decision diagrams","volume":"24","author":"Bryant","year":"1992","journal-title":"ACM Comput. Surv."},{"key":"10.1016\/S0890-5401(03)00118-4_BIB8","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0020-0190(92)90180-4","article-title":"The graph of multiplication is equivalent to counting","volume":"41","author":"Buss","year":"1992","journal-title":"Inf. Process. Lett."},{"key":"10.1016\/S0890-5401(03)00118-4_BIB9","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/0020-0190(94)00094-8","article-title":"Time-space tradeoffs for integer multiplication on various types of input oblivious sequential machines","volume":"51","author":"Gergov","year":"1994","journal-title":"Inf. Process. Lett."},{"key":"10.1016\/S0890-5401(03)00118-4_BIB10","unstructured":"S. Jukna, The graph of integer multiplication is hard for read-k-times networks, TR 95-10 Mathematik\/Informatik University of Trier, 1995"},{"key":"10.1016\/S0890-5401(03)00118-4_BIB11","series-title":"Communication Complexity and Parallel Computing","author":"Hromkovic","year":"1997"},{"key":"10.1016\/S0890-5401(03)00118-4_BIB12","series-title":"Communication Complexity","author":"Kushilevitz","year":"1997"},{"key":"10.1016\/S0890-5401(03)00118-4_BIB13","doi-asserted-by":"crossref","unstructured":"S. Ponzio, A lower bound for integer multiplication with read-once branching programs, in: Proceedings of the 27-th STOC, 1995, pp. 130\u2013139","DOI":"10.1145\/225058.225098"},{"key":"10.1016\/S0890-5401(03)00118-4_BIB14","unstructured":"S. Ponzio, Restricted branching programs and hardware verification, Technical Report, MIT\/LCS-TR-633, MIT, 1995"},{"key":"10.1016\/S0890-5401(03)00118-4_BIB15","series-title":"Proceedings of the FCT\u201991","first-page":"47","article-title":"Lower bounds for deterministic and nondeterministic branching programs","volume":"vol. 529","author":"Razborov","year":"1991"},{"key":"10.1016\/S0890-5401(03)00118-4_BIB16","unstructured":"P. Savicky, S. Zak, A large lower bound for 1-branching programs, Electronic Colloquium on Computational Complexity, Revision 01 of TR96-036 (1996). Available From http:\/\/www.eccc.uni-trier.de\/eccc\/"},{"key":"10.1016\/S0890-5401(03)00118-4_BIB17","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/0012-365X(95)90790-R","article-title":"Efficient data structure for Boolean functions","volume":"136","author":"Wegener","year":"1994","journal-title":"Discrete Math."},{"key":"10.1016\/S0890-5401(03)00118-4_BIB18","doi-asserted-by":"crossref","unstructured":"I. Wegener, Branching programs and binary decision diagrams. Theory and applications, SIAM Monographs on Discrete Mathematics and Applications, 2000","DOI":"10.1137\/1.9780898719789"},{"key":"10.1016\/S0890-5401(03)00118-4_BIB19","doi-asserted-by":"crossref","unstructured":"A.C. Yao, Some complexity questions related to distributive computing, in: Proceedings of the 11th Annual ACM Symposium on the Theory of Computing 1979, pp. 209\u2013213","DOI":"10.1145\/800135.804414"},{"key":"10.1016\/S0890-5401(03)00118-4_BIB20","doi-asserted-by":"crossref","unstructured":"A.C. Yao, Lower bounds by probabilistic arguments, in: Proceedings of the 27th Annual IEEE Symposium on Foundations of Computer Science, 1983, pp. 420\u2013428","DOI":"10.1109\/SFCS.1983.30"},{"key":"10.1016\/S0890-5401(03)00118-4_FR1","series-title":"Proceedings of the ICALP\u201996","first-page":"348","article-title":"On the power of randomized branching programs","volume":"vol. 1099","author":"Ablayev","year":"1996"}],"container-title":["Information and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0890540103001184?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0890540103001184?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2020,3,20]],"date-time":"2020-03-20T19:35:44Z","timestamp":1584732944000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0890540103001184"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,10]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2003,10]]}},"alternative-id":["S0890540103001184"],"URL":"https:\/\/doi.org\/10.1016\/s0890-5401(03)00118-4","relation":{},"ISSN":["0890-5401"],"issn-type":[{"value":"0890-5401","type":"print"}],"subject":[],"published":{"date-parts":[[2003,10]]}}}