{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,6]],"date-time":"2025-01-06T05:08:36Z","timestamp":1736140116049,"version":"3.32.0"},"publisher-location":"Berlin\/Heidelberg","reference-count":9,"publisher":"Springer-Verlag","isbn-type":[{"type":"print","value":"3540552847"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/bfb0023814","type":"book-chapter","created":{"date-parts":[[2005,11,19]],"date-time":"2005-11-19T06:17:40Z","timestamp":1132381060000},"page":"24-31","source":"Crossref","is-referenced-by-count":4,"title":["Complex polynomials and circuit lower bounds for modular counting"],"prefix":"10.1007","author":[{"given":"David A.","family":"Mix Barrington","sequence":"first","affiliation":[]},{"given":"Howard","family":"Straubing","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"3_CR1","doi-asserted-by":"crossref","unstructured":"J. Aspnes, R. Beigel, M. Furst, and S. Rudich, The expressive power of voting polynomials, Proc. 23rd ACM STOC, 402\u2013409, 1991.","DOI":"10.1145\/103418.103461"},{"key":"3_CR2","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/0890-5401(90)90007-5","volume":"89","author":"D. A. M. Barrington","year":"1990","unstructured":"D. A. Mix Barrington, H. Straubing, and D. Th\u00e9rien, Nonuniform automata over groups, Information and Computation 89 (1990), 109\u2013132.","journal-title":"Information and Computation"},{"key":"3_CR3","unstructured":"R. Beigel, personal communication and presentation at Jan. 1991 DIMACS workshop."},{"key":"3_CR4","doi-asserted-by":"crossref","unstructured":"R. Beigel, N. Reingold, and D. Spielman, The perceptron strikes back, Proc. 6th Structure in Complexity Theory, (1991), 286\u2013293.","DOI":"10.1109\/SCT.1991.160270"},{"key":"3_CR5","doi-asserted-by":"crossref","unstructured":"R. Beigel, N. Reingold, and D. Spielman, PP is closed under intersection, Proc. 23rd ACM STOC, 1\u20139, 1991.","DOI":"10.1145\/103418.103426"},{"key":"3_CR6","doi-asserted-by":"crossref","unstructured":"F. Green, An oracle separating \u2295P from PP PH , Proc. 5th Structure in Complexity Theory, (1990), 295\u2013298.","DOI":"10.1109\/SCT.1990.113977"},{"key":"3_CR7","doi-asserted-by":"crossref","unstructured":"N. Linial, Y. Mansour and N. Nisan, Constant-depth circuits, Fourier transforms and learnability, Proc. 30th IEEE FOCS, (1989), 574\u2013579.","DOI":"10.1109\/SFCS.1989.63537"},{"key":"3_CR8","volume-title":"Perceptrons","author":"M. L. Minsky","year":"1988","unstructured":"M. L. Minsky and S. A. Papert, Perceptrons (Cambridge, MA, MIT Press, 1988). (Expanded edition, original edition was in 1968.)"},{"key":"3_CR9","doi-asserted-by":"crossref","unstructured":"R. Smolensky, Algebraic methods in the theory of lower bounds for Boolean circuit complexity, Proc. 19th ACM STOC, 77\u201382, 1987.","DOI":"10.1145\/28395.28404"}],"container-title":["Lecture Notes in Computer Science","LATIN '92"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BFb0023814.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,5]],"date-time":"2025-01-05T18:53:56Z","timestamp":1736103236000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BFb0023814"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["3540552847"],"references-count":9,"URL":"https:\/\/doi.org\/10.1007\/bfb0023814","relation":{},"subject":[]}}