{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T13:41:50Z","timestamp":1790257310444,"version":"4.1.0"},"publisher-location":"Berlin, Heidelberg","reference-count":16,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642220050","type":"print"},{"value":"9783642220067","type":"electronic"}],"license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011]]},"DOI":"10.1007\/978-3-642-22006-7_59","type":"book-chapter","created":{"date-parts":[[2011,6,20]],"date-time":"2011-06-20T03:44:05Z","timestamp":1308541445000},"page":"700-711","source":"Crossref","is-referenced-by-count":6,"title":["Characterizing Arithmetic Circuit Classes by Constraint Satisfaction Problems"],"prefix":"10.1007","author":[{"given":"Stefan","family":"Mengel","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"issue":"3","key":"59_CR1","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1145\/2402.322389","volume":"30","author":"C. Beeri","year":"1983","unstructured":"Beeri, C., Fagin, R., Maier, D., Yannakakis, M.: On the desirability of acyclic database schemes. J. ACM\u00a030(3), 479\u2013513 (1983)","journal-title":"J. ACM"},{"issue":"1","key":"59_CR2","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1137\/0221006","volume":"21","author":"M. Ben-Or","year":"1992","unstructured":"Ben-Or, M., Cleve, R.: Computing algebraic formulas using a constant number of registers. SIAM J. Comput.\u00a021(1), 54\u201358 (1992)","journal-title":"SIAM J. Comput."},{"key":"59_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/3-540-50728-0_32","volume-title":"Graph-Theoretic Concepts in Computer Science","author":"H.L. Bodlaender","year":"1989","unstructured":"Bodlaender, H.L.: NC-algorithms for graphs with small treewidth. In: van Leeuwen, J. (ed.) WG 1988. LNCS, vol.\u00a0344, pp. 1\u201310. Springer, Heidelberg (1989)"},{"key":"59_CR4","unstructured":"Brent, R.P.: The complexity of multiple-precision arithmetic. In: Brent, R.P., Andersson, R.S. (eds.) The Complexity of Computational Problem Solving, pp. 126\u2013165. Univ. of Queensland Press (1976)"},{"key":"59_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/978-3-642-03816-7_17","volume-title":"Mathematical Foundations of Computer Science 2009","author":"I. Briquel","year":"2009","unstructured":"Briquel, I., Koiran, P.: A dichotomy theorem for polynomial evaluation. In: Kr\u00e1lovi\u010d, R., Niwi\u0144ski, D. (eds.) MFCS 2009. LNCS, vol.\u00a05734, pp. 187\u2013198. Springer, Heidelberg (2009)"},{"issue":"1","key":"59_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.dam.2010.09.007","volume":"159","author":"I. Briquel","year":"2011","unstructured":"Briquel, I., Koiran, P., Meer, K.: On the expressive power of cnf formulas of bounded tree- and clique-width. Discrete Applied Mathematics\u00a0159(1), 1\u201314 (2011)","journal-title":"Discrete Applied Mathematics"},{"key":"59_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04179-6","volume-title":"Completeness and reduction in algebraic complexity theory","author":"P. B\u00fcrgisser","year":"2000","unstructured":"B\u00fcrgisser, P.: Completeness and reduction in algebraic complexity theory. Springer, Heidelberg (2000)"},{"issue":"1-2","key":"59_CR8","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1016\/S0166-218X(00)00221-3","volume":"108","author":"B. Courcelle","year":"2001","unstructured":"Courcelle, B., Makowsky, J.A., Rotics, U.: On the fixed parameter complexity of graph enumeration problems definable in monadic second-order logic. Discrete Applied Mathematics\u00a0108(1-2), 23\u201352 (2001)","journal-title":"Discrete Applied Mathematics"},{"issue":"4","key":"59_CR9","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1016\/j.dam.2006.06.020","volume":"156","author":"E. Fischer","year":"2008","unstructured":"Fischer, E., Makowsky, J.A., Ravve, E.V.: Counting truth assignments of formulas of bounded tree-width or clique-width. Discrete Applied Mathematics\u00a0156(4), 511\u2013529 (2008)","journal-title":"Discrete Applied Mathematics"},{"key":"59_CR10","volume-title":"Parameterized complexity theory","author":"J. Flum","year":"2006","unstructured":"Flum, J., Grohe, M.: Parameterized complexity theory. Springer-Verlag New York Inc., New York (2006)"},{"issue":"3","key":"59_CR11","doi-asserted-by":"publisher","first-page":"431","DOI":"10.1145\/382780.382783","volume":"48","author":"G. Gottlob","year":"2001","unstructured":"Gottlob, G., Leone, N., Scarcello, F.: The complexity of acyclic conjunctive queries. J. ACM\u00a048(3), 431\u2013498 (2001)","journal-title":"J. ACM"},{"key":"59_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"252","DOI":"10.1007\/978-3-540-92248-3_23","volume-title":"Graph-Theoretic Concepts in Computer Science","author":"P. Koiran","year":"2008","unstructured":"Koiran, P., Meer, K.: On the expressive power of CNF formulas of bounded tree- and clique-width. In: Broersma, H., Erlebach, T., Friedetzky, T., Paulusma, D. (eds.) WG 2008. LNCS, vol.\u00a05344, pp. 252\u2013263. Springer, Heidelberg (2008)"},{"key":"59_CR13","doi-asserted-by":"crossref","unstructured":"Flarup, U., Koiran, P., Lyaudet, L.: On the Expressive Power of Planar Perfect Matching and Permanents of Bounded Treewidth Matrices. In: Tokuyama, T. (ed.) ISAAC 2007. LNCS, vol.\u00a04835, pp. 124\u2013136. Springer, Heidelberg (2007), \n                    \n                      http:\/\/dx.doi.org\/10.1007\/978-3-540-77120-3_13","DOI":"10.1007\/978-3-540-77120-3_13"},{"issue":"1","key":"59_CR14","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1016\/j.jco.2006.09.006","volume":"24","author":"G. Malod","year":"2008","unstructured":"Malod, G., Portier, N.: Characterizing Valiant\u2019s algebraic complexity classes. J. Complexity\u00a024(1), 16\u201338 (2008)","journal-title":"J. Complexity"},{"key":"59_CR15","doi-asserted-by":"crossref","unstructured":"Schaefer, T.J.: The complexity of satisfiability problems. In: STOC 1978, pp. 216\u2013226 (1978)","DOI":"10.1145\/800133.804350"},{"issue":"4","key":"59_CR16","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1137\/0212043","volume":"12","author":"L.G. Valiant","year":"1983","unstructured":"Valiant, L.G., Skyum, S., Berkowitz, S., Rackoff, C.: Fast parallel computation of polynomials using few processors. SIAM J. Comput.\u00a012(4), 641\u2013644 (1983)","journal-title":"SIAM J. Comput."}],"container-title":["Lecture Notes in Computer Science","Automata, Languages and Programming"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-22006-7_59","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,29]],"date-time":"2019-03-29T02:18:34Z","timestamp":1553825914000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-22006-7_59"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9783642220050","9783642220067"],"references-count":16,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-22006-7_59","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011]]}}}