{"id":"https://openalex.org/W2047947448","doi":"https://doi.org/10.1007/s10208-009-9048-2","title":"Real Computational Universality: The Word Problem for a Class of Groups with Infinite Presentation","display_name":"Real Computational Universality: The Word Problem for a Class of Groups with Infinite Presentation","publication_year":2009,"publication_date":"2009-04-28","ids":{"openalex":"https://openalex.org/W2047947448","doi":"https://doi.org/10.1007/s10208-009-9048-2","mag":"2047947448"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-009-9048-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-009-9048-2","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084382636","display_name":"Klaus Meer","orcid":null},"institutions":[{"id":"https://openalex.org/I51783024","display_name":"Brandenburg University of Technology Cottbus-Senftenberg","ror":"https://ror.org/02wxx3e24","country_code":"DE","type":"education","lineage":["https://openalex.org/I51783024"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Klaus Meer","raw_affiliation_strings":["Theoretical Computer Science, BTU Cottbus, Konrad-Wachsmann-Allee 1, 03046, Cottbus, Germany","BTU Cottbus, Theoretical Computer Science, Konrad-Wachsmann-Allee 1, 03046, Cottbus, Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Theoretical Computer Science, BTU Cottbus, Konrad-Wachsmann-Allee 1, 03046, Cottbus, Germany","institution_ids":["https://openalex.org/I51783024"]},{"raw_affiliation_string":"BTU Cottbus, Theoretical Computer Science, Konrad-Wachsmann-Allee 1, 03046, Cottbus, Germany#TAB#","institution_ids":["https://openalex.org/I51783024"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101546631","display_name":"Martin Ziegler","orcid":"https://orcid.org/0000-0001-6734-7875"},"institutions":[{"id":"https://openalex.org/I206945453","display_name":"Paderborn University","ror":"https://ror.org/058kzsd48","country_code":"DE","type":"education","lineage":["https://openalex.org/I206945453"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Ziegler","raw_affiliation_strings":["Faculty of Computer Science, Electrical Engineering and Mathematics, University of Paderborn, 33095, Paderborn, Germany","University of Paderborn, Faculty of Computer Science, Electrical Engineering and Mathematics, 33095, Paderborn, Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Computer Science, Electrical Engineering and Mathematics, University of Paderborn, 33095, Paderborn, Germany","institution_ids":["https://openalex.org/I206945453"]},{"raw_affiliation_string":"University of Paderborn, Faculty of Computer Science, Electrical Engineering and Mathematics, 33095, Paderborn, Germany#TAB#","institution_ids":["https://openalex.org/I206945453"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5084382636"],"corresponding_institution_ids":["https://openalex.org/I51783024"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.12618579,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"9","issue":"5","first_page":"599","last_page":"609"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/undecidable-problem","display_name":"Undecidable problem","score":0.779128909111023},{"id":"https://openalex.org/keywords/word-problem","display_name":"Word problem (mathematics education)","score":0.7316439151763916},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6895549297332764},{"id":"https://openalex.org/keywords/halting-problem","display_name":"Halting problem","score":0.6463125944137573},{"id":"https://openalex.org/keywords/turing-machine","display_name":"Turing machine","score":0.5900084376335144},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.506653368473053},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.48758262395858765},{"id":"https://openalex.org/keywords/universality","display_name":"Universality (dynamical systems)","score":0.4739037752151489},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4407604932785034},{"id":"https://openalex.org/keywords/p","display_name":"P","score":0.4391731917858124},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.42870983481407166},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.42311325669288635},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.30134880542755127},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.22566398978233337},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.18417468667030334},{"id":"https://openalex.org/keywords/decidability","display_name":"Decidability","score":0.18407556414604187},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.11891257762908936}],"concepts":[{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.779128909111023},{"id":"https://openalex.org/C90988201","wikidata":"https://www.wikidata.org/wiki/Q255912","display_name":"Word problem (mathematics education)","level":2,"score":0.7316439151763916},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6895549297332764},{"id":"https://openalex.org/C137343475","wikidata":"https://www.wikidata.org/wiki/Q622849","display_name":"Halting problem","level":4,"score":0.6463125944137573},{"id":"https://openalex.org/C29248071","wikidata":"https://www.wikidata.org/wiki/Q163310","display_name":"Turing machine","level":3,"score":0.5900084376335144},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.506653368473053},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.48758262395858765},{"id":"https://openalex.org/C183992945","wikidata":"https://www.wikidata.org/wiki/Q2495574","display_name":"Universality (dynamical systems)","level":2,"score":0.4739037752151489},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4407604932785034},{"id":"https://openalex.org/C134026603","wikidata":"https://www.wikidata.org/wiki/Q846354","display_name":"P","level":3,"score":0.4391731917858124},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.42870983481407166},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.42311325669288635},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30134880542755127},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.22566398978233337},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18417468667030334},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.18407556414604187},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.11891257762908936},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10208-009-9048-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-009-9048-2","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W199556903","https://openalex.org/W567605243","https://openalex.org/W631909126","https://openalex.org/W1492288613","https://openalex.org/W1505284964","https://openalex.org/W1514578557","https://openalex.org/W1516116134","https://openalex.org/W1541824250","https://openalex.org/W1550331971","https://openalex.org/W1590722750","https://openalex.org/W1708892819","https://openalex.org/W1993901943","https://openalex.org/W2005996473","https://openalex.org/W2007166036","https://openalex.org/W2008023303","https://openalex.org/W2020692304","https://openalex.org/W2025395116","https://openalex.org/W2032923775","https://openalex.org/W2034460536","https://openalex.org/W2047734040","https://openalex.org/W2049710581","https://openalex.org/W2063091737","https://openalex.org/W2071846104","https://openalex.org/W2074794353","https://openalex.org/W2092986484","https://openalex.org/W2096478770","https://openalex.org/W2111235650","https://openalex.org/W2126160338","https://openalex.org/W2146132580","https://openalex.org/W2607673258","https://openalex.org/W4230191592","https://openalex.org/W4292101339","https://openalex.org/W4301168154"],"related_works":["https://openalex.org/W2468382602","https://openalex.org/W2158086683","https://openalex.org/W1492906489","https://openalex.org/W1511851241","https://openalex.org/W2282186771","https://openalex.org/W2098148669","https://openalex.org/W118811066","https://openalex.org/W91167006","https://openalex.org/W1995628728","https://openalex.org/W2740781308"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-11T08:15:01.531666","created_date":"2025-10-10T00:00:00"}
