{"id":"https://openalex.org/W2808995689","doi":"https://doi.org/10.1142/s0218196718500431","title":"Parallel identity testing for skew circuits with big powers and applications","display_name":"Parallel identity testing for skew circuits with big powers and applications","publication_year":2018,"publication_date":"2018-06-19","ids":{"openalex":"https://openalex.org/W2808995689","doi":"https://doi.org/10.1142/s0218196718500431","mag":"2808995689"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196718500431","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196718500431","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","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/A5090872841","display_name":"Daniel K\u00f6nig","orcid":null},"institutions":[{"id":"https://openalex.org/I206895457","display_name":"University of Siegen","ror":"https://ror.org/02azyry73","country_code":"DE","type":"education","lineage":["https://openalex.org/I206895457"]},{"id":"https://openalex.org/I2800742272","display_name":"Folkwang University of the Arts","ror":"https://ror.org/03gf02c22","country_code":"DE","type":"education","lineage":["https://openalex.org/I2800742272"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Daniel K\u00f6nig","raw_affiliation_strings":["Department f\u00fcr Elektrotechnik und Informatik, Universit\u00e4t Siegen, Germany"],"affiliations":[{"raw_affiliation_string":"Department f\u00fcr Elektrotechnik und Informatik, Universit\u00e4t Siegen, Germany","institution_ids":["https://openalex.org/I2800742272","https://openalex.org/I206895457"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005500210","display_name":"Markus Lohrey","orcid":"https://orcid.org/0000-0002-4680-7198"},"institutions":[{"id":"https://openalex.org/I206895457","display_name":"University of Siegen","ror":"https://ror.org/02azyry73","country_code":"DE","type":"education","lineage":["https://openalex.org/I206895457"]},{"id":"https://openalex.org/I2800742272","display_name":"Folkwang University of the Arts","ror":"https://ror.org/03gf02c22","country_code":"DE","type":"education","lineage":["https://openalex.org/I2800742272"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Markus Lohrey","raw_affiliation_strings":["Department f\u00fcr Elektrotechnik und Informatik, Universit\u00e4t Siegen, Germany"],"affiliations":[{"raw_affiliation_string":"Department f\u00fcr Elektrotechnik und Informatik, Universit\u00e4t Siegen, Germany","institution_ids":["https://openalex.org/I2800742272","https://openalex.org/I206895457"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5090872841"],"corresponding_institution_ids":["https://openalex.org/I206895457","https://openalex.org/I2800742272"],"apc_list":null,"apc_paid":null,"fwci":0.4039,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.6294808,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"28","issue":"06","first_page":"979","last_page":"1004"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9994999766349792,"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/T11567","display_name":"semigroups and automata theory","score":0.9969000220298767,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7818201780319214},{"id":"https://openalex.org/keywords/skew","display_name":"Skew","score":0.655363142490387},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.48734554648399353},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.48690807819366455},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.4835069477558136},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4232589602470398},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3466702401638031},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17444998025894165}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7818201780319214},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.655363142490387},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.48734554648399353},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.48690807819366455},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.4835069477558136},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4232589602470398},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3466702401638031},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17444998025894165},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","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},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196718500431","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196718500431","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W41330591","https://openalex.org/W636399398","https://openalex.org/W987035227","https://openalex.org/W1527197079","https://openalex.org/W2011758726","https://openalex.org/W2015676876","https://openalex.org/W2017205387","https://openalex.org/W2024091095","https://openalex.org/W2024522546","https://openalex.org/W2026036943","https://openalex.org/W2043641704","https://openalex.org/W2043667326","https://openalex.org/W2045427051","https://openalex.org/W2051521505","https://openalex.org/W2052653988","https://openalex.org/W2052788392","https://openalex.org/W2066012259","https://openalex.org/W2078460168","https://openalex.org/W2261634751","https://openalex.org/W2332837831","https://openalex.org/W2725306094","https://openalex.org/W3138321435","https://openalex.org/W3157585079","https://openalex.org/W4298227433"],"related_works":["https://openalex.org/W4290802965","https://openalex.org/W97789383","https://openalex.org/W3087516072","https://openalex.org/W2727156679","https://openalex.org/W4289406402","https://openalex.org/W2364071303","https://openalex.org/W1483053255","https://openalex.org/W2896097814","https://openalex.org/W20221657","https://openalex.org/W2321648686"],"abstract_inverted_index":{"Powerful":[0],"skew":[1,8,40,55],"arithmetic":[2,9,41],"circuits":[3,10,42],"are":[4,7,62],"introduced.":[5],"These":[6],"with":[11,19],"variables,":[12],"where":[13,86],"input":[14],"gates":[15],"can":[16,70],"be":[17,71],"labeled":[18],"powers":[20],"[Formula:":[21,28,45,74,112,133],"see":[22,29,46,75,113,134],"text]":[23],"for":[24,38,53,101,126],"binary":[25],"encoded":[26],"numbers":[27],"text].":[30,114,135],"It":[31],"is":[32,79],"shown":[33],"that":[34,121],"polynomial":[35],"identity":[36],"testing":[37],"powerful":[39],"belongs":[43,110,131],"to":[44,111,132],"text],":[47],"which":[48],"generalizes":[49],"a":[50,127],"corresponding":[51],"result":[52,61,78],"(standard)":[54],"circuits.":[56],"Two":[57],"applications":[58],"of":[59,66,105],"this":[60,77],"presented:":[63],"(i)":[64],"Equivalence":[65],"higher-dimensional":[67],"straight-line":[68,88],"programs":[69,89],"tested":[72],"in":[73,82],"text];":[76],"even":[80],"new":[81],"the":[83,87,116,122],"one-dimensional":[84],"case,":[85],"produce":[90],"words.":[91],"(ii)":[92],"The":[93],"compressed":[94,123],"word":[95,124],"problem":[96,125],"(or":[97],"circuit":[98],"evaluation":[99],"problem)":[100],"certain":[102],"wreath":[103],"products":[104],"finitely":[106],"generated":[107],"abelian":[108],"groups":[109],"Using":[115],"Magnus":[117],"embedding,":[118],"it":[119],"follows":[120],"free":[128],"metabelian":[129],"group":[130]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
