{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T11:12:16Z","timestamp":1778497936404,"version":"3.51.4"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2009,4,29]],"date-time":"2009-04-29T00:00:00Z","timestamp":1240963200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Found Comput Math"],"published-print":{"date-parts":[[2009,10]]},"DOI":"10.1007\/s10208-009-9048-2","type":"journal-article","created":{"date-parts":[[2009,4,28]],"date-time":"2009-04-28T15:26:21Z","timestamp":1240932381000},"page":"599-609","source":"Crossref","is-referenced-by-count":4,"title":["Real Computational Universality: The Word Problem for a Class of Groups with Infinite Presentation"],"prefix":"10.1007","volume":"9","author":[{"given":"Klaus","family":"Meer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Ziegler","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,4,29]]},"reference":[{"key":"9048_CR1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0273-0979-1989-15750-9","volume":"21","author":"L. Blum","year":"1989","unstructured":"L. Blum, M. Shub, S. Smale, On a theory of computation and complexity over the real numbers: $\\protect\\mathcal{NP}$ -completeness, recursive functions, and universal machines, Bull. Am. Math. Soc. 21, 1\u201346 (1989).","journal-title":"Bull. Am. Math. Soc."},{"key":"9048_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0701-6","volume-title":"Complexity and Real Computation","author":"L. Blum","year":"1998","unstructured":"L. Blum, F. Cucker, M. Shub, S. Smale, Complexity and Real Computation (Springer, New York, 1998)."},{"key":"9048_CR3","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1073\/pnas.44.10.1061","volume":"44","author":"W.W. Boone","year":"1958","unstructured":"W.W. Boone, The word problem, Proc. Natl. Acad. Sci. U.S.A. 44, 265\u2013269 (1958).","journal-title":"Proc. Natl. Acad. Sci. U.S.A."},{"key":"9048_CR4","doi-asserted-by":"crossref","first-page":"493","DOI":"10.1002\/1521-3870(200111)47:4<493::AID-MALQ493>3.0.CO;2-S","volume":"47","author":"M. Bourgade","year":"2001","unstructured":"M. Bourgade, Separations et transferts dans la hi\u00e9rarchie polynomiale des groupes ab\u00e9liens infinis, Math. Log. Q. 47, 493\u2013502 (2001).","journal-title":"Math. Log. Q."},{"key":"9048_CR5","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/S0166-8641(99)00103-0","volume":"106","author":"J.W. Cannon","year":"2000","unstructured":"J.W. Cannon, G.R. Conner, The combinatorial structure of the Hawaiian earring group, Topology Appl. 106, 225\u2013271 (2000).","journal-title":"Topology Appl."},{"issue":"3","key":"9048_CR6","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1093\/logcom\/2.3.375","volume":"2","author":"F. Cucker","year":"1992","unstructured":"F. Cucker, The arithmetical hierarchy over the reals, J. Log. Comput. 2(3), 375\u2013395 (1992).","journal-title":"J. Log. Comput."},{"key":"9048_CR7","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/j.jsc.2004.11.008","volume":"39","author":"H. Derksen","year":"2005","unstructured":"H. Derksen, E. Jeandel, P. Koiran, Quantum automata and algebraic groups, J. Symb. Comput. 39, 357\u2013371 (2005).","journal-title":"J. Symb. Comput."},{"key":"9048_CR8","doi-asserted-by":"crossref","first-page":"574","DOI":"10.1006\/jcom.2001.0583","volume":"17","author":"C. Ga\u00dfner","year":"2001","unstructured":"C. Ga\u00dfner, The $\\mathcal{P}=\\mathcal{DNP}$ problem for infinite abelian groups, J. Complex. 17, 574\u2013583 (2001).","journal-title":"J. Complex."},{"key":"9048_CR9","doi-asserted-by":"crossref","first-page":"92","DOI":"10.2307\/2275252","volume":"59","author":"J.B. Goode","year":"1994","unstructured":"J.B. Goode, Accessible telephone directories, J. Symb. Log. 59, 92\u2013105 (1994).","journal-title":"J. Symb. Log."},{"key":"9048_CR10","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1112\/jlms\/s1-24.4.247","volume":"24","author":"G. Higman","year":"1949","unstructured":"G. Higman, B.H. Neumann, H. Neumann, Embedding theorems for groups, J. Lond. Math. Soc. 24, 247\u2013254 (1949).","journal-title":"J. Lond. Math. Soc."},{"issue":"3","key":"9048_CR11","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1112\/S002461070500654X","volume":"71","author":"D.F. Holt","year":"2005","unstructured":"D.F. Holt, S. Rees, C.E. R\u00f6ver, R.M. Thomas, Groups with context-free co-word problem, J. Lond. Math. Soc. 71(3), 643\u2013657 (2005).","journal-title":"J. Lond. Math. Soc."},{"key":"9048_CR12","volume-title":"SL\u20092(\u211d)","author":"S. Lang","year":"1985","unstructured":"S. Lang, SL\u20092(\u211d) (Springer, New York, 1985)."},{"key":"9048_CR13","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-61896-3","volume-title":"Combinatorial Group Theory","author":"R.C. Lyndon","year":"1977","unstructured":"R.C. Lyndon, P.E. Schupp, Combinatorial Group Theory (Springer, Berlin, 1977)."},{"issue":"1","key":"9048_CR14","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.jco.2006.09.004","volume":"24","author":"K. Meer","year":"2008","unstructured":"K. Meer, M. Ziegler, An explicit solution to Post\u2019s problem over the reals, J. Complex. 24(1), 3\u201315 (2008).","journal-title":"J. Complex."},{"key":"9048_CR15","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1090\/S0002-9939-1991-1041016-9","volume":"112","author":"C. Michaux","year":"1991","unstructured":"C. Michaux, Ordered rings over which output sets are recursively enumerable, Proc. Am. Math. Soc. 112, 569\u2013575 (1991).","journal-title":"Proc. Am. Math. Soc."},{"key":"9048_CR16","series-title":"Math. Sci. Res. Inst. Publ.","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-1-4613-9730-4_1","volume-title":"Algorithms and Classification in Combinatorial Group Theory","author":"C.F. Miller III","year":"1992","unstructured":"C.F. Miller III, Decision problems for groups\u2014survey and reflections, in Algorithms and Classification in Combinatorial Group Theory, ed. by G. Baumslag, C.F. Miller III. Math. Sci. Res. Inst. Publ., vol.\u00a01 (Springer, New York, 1992), pp. 1\u201359."},{"key":"9048_CR17","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/0022-0000(83)90003-X","volume":"26","author":"D.E. Muller","year":"1983","unstructured":"D.E. Muller, P.E. Schupp, Groups, the theory of ends, and context-free languages, J. Comput. Syst. Sci. 26, 295\u2013310 (1983).","journal-title":"J. Comput. Syst. Sci."},{"key":"9048_CR18","unstructured":"P.S. Novikov, On the algorithmic unsolvability of the word problem in group theory. Tr. Mat. Inst. Steklov 44 (1955)."},{"key":"9048_CR19","volume-title":"Les Petits Cailloux","author":"B. Poizat","year":"1995","unstructured":"B. Poizat, Les Petits Cailloux (Al\u00e9as, Lyon, 1995)."},{"key":"9048_CR20","doi-asserted-by":"crossref","first-page":"235","DOI":"10.2178\/jsl\/1190150041","volume":"67","author":"M. Prunescu","year":"2002","unstructured":"M. Prunescu, A model-theoretic proof for $\\mathcal{P}\\neq\\mathcal{NP}$ over all infinite abelian groups, J. Symb. Log. 67, 235\u2013238 (2002).","journal-title":"J. Symb. Log."},{"key":"9048_CR21","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4176-8","volume-title":"An Introduction to the Theory of Groups","author":"J.J. Rotman","year":"1995","unstructured":"J.J. Rotman, An Introduction to the Theory of Groups, 4th edn. (Springer, Berlin, 1995).","edition":"4"},{"key":"9048_CR22","doi-asserted-by":"crossref","first-page":"103","DOI":"10.2307\/2273358","volume":"45","author":"J.V. Tucker","year":"1980","unstructured":"J.V. Tucker, Computability and the algebra of fields, J. Symb. Log. 45, 103\u2013120 (1980).","journal-title":"J. Symb. Log."}],"container-title":["Foundations of Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-009-9048-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10208-009-9048-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-009-9048-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T11:05:10Z","timestamp":1559127910000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10208-009-9048-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,4,29]]},"references-count":22,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2009,10]]}},"alternative-id":["9048"],"URL":"https:\/\/doi.org\/10.1007\/s10208-009-9048-2","relation":{},"ISSN":["1615-3375","1615-3383"],"issn-type":[{"value":"1615-3375","type":"print"},{"value":"1615-3383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,4,29]]}}}