{"id":"https://openalex.org/W2996645849","doi":"https://doi.org/10.1145/3369935","title":"Pattern Matching with Variables","display_name":"Pattern Matching with Variables","publication_year":2020,"publication_date":"2020-02-11","ids":{"openalex":"https://openalex.org/W2996645849","doi":"https://doi.org/10.1145/3369935","mag":"2996645849"},"language":"en","primary_location":{"id":"doi:10.1145/3369935","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3369935","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computation Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://resolver.sub.uni-goettingen.de/purl?gro-2/136236","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015688812","display_name":"Henning Fernau","orcid":"https://orcid.org/0000-0002-4444-3220"},"institutions":[{"id":"https://openalex.org/I89864525","display_name":"Universit\u00e4t Trier","ror":"https://ror.org/02778hg05","country_code":"DE","type":"education","lineage":["https://openalex.org/I89864525"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Henning Fernau","raw_affiliation_strings":["Fachbereich IV\u2013Abteilung Informatikwissenschaften, Universit\u00e4t Trier, Trier, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich IV\u2013Abteilung Informatikwissenschaften, Universit\u00e4t Trier, Trier, Germany","institution_ids":["https://openalex.org/I89864525"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5006548981","display_name":"Flor\u00edn Manea","orcid":"https://orcid.org/0000-0001-6094-3324"},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Florin Manea","raw_affiliation_strings":["G\u00f6ttingen University, Institute of Computer Science, Goettingen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"G\u00f6ttingen University, Institute of Computer Science, Goettingen, Germany","institution_ids":["https://openalex.org/I74656192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049507611","display_name":"Robert Merca\u015f","orcid":"https://orcid.org/0000-0001-6034-433X"},"institutions":[{"id":"https://openalex.org/I143804889","display_name":"Loughborough University","ror":"https://ror.org/04vg4w365","country_code":"GB","type":"education","lineage":["https://openalex.org/I143804889"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Robert Merca\u015f","raw_affiliation_strings":["Loughborough University, Department of Computer Science, Leicestershire, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Loughborough University, Department of Computer Science, Leicestershire, United Kingdom","institution_ids":["https://openalex.org/I143804889"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038601790","display_name":"Markus L. Schmid","orcid":"https://orcid.org/0000-0001-5137-1504"},"institutions":[{"id":"https://openalex.org/I89864525","display_name":"Universit\u00e4t Trier","ror":"https://ror.org/02778hg05","country_code":"DE","type":"education","lineage":["https://openalex.org/I89864525"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Markus L. Schmid","raw_affiliation_strings":["Fachbereich IV\u2013Abteilung Informatikwissenschaften, Universit\u00e4t Trier, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich IV\u2013Abteilung Informatikwissenschaften, Universit\u00e4t Trier, Berlin, Germany","institution_ids":["https://openalex.org/I89864525"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7823,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.77511163,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"12","issue":"1","first_page":"1","last_page":"37"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11269","display_name":"Algorithms and Data Compression","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9991000294685364,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7509257197380066},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.6980462670326233},{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.662032961845398},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.636883020401001},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.6216039657592773},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6105890870094299},{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.5394618511199951},{"id":"https://openalex.org/keywords/pattern-matching","display_name":"Pattern matching","score":0.5221786499023438},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4647570848464966},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.42869019508361816},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3830963969230652},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16811314225196838},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14086699485778809},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11316749453544617}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7509257197380066},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.6980462670326233},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.662032961845398},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.636883020401001},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.6216039657592773},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6105890870094299},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.5394618511199951},{"id":"https://openalex.org/C68859911","wikidata":"https://www.wikidata.org/wiki/Q1503724","display_name":"Pattern matching","level":2,"score":0.5221786499023438},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4647570848464966},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.42869019508361816},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3830963969230652},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16811314225196838},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14086699485778809},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11316749453544617},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3369935","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3369935","pdf_url":null,"source":{"id":"https://openalex.org/S205019203","display_name":"ACM Transactions on Computation Theory","issn_l":"1942-3454","issn":["1942-3454","1942-3462"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Computation Theory","raw_type":"journal-article"},{"id":"pmh:oai:publications.goettingen-research-online.de:2/136236","is_oa":true,"landing_page_url":"https://resolver.sub.uni-goettingen.de/purl?gro-2/136236","pdf_url":null,"source":{"id":"https://openalex.org/S4306401634","display_name":"GoeScholar  The Publication Server of the Georg-August-Universit\u00e4t G\u00f6ttingen (Georg-August-Universit\u00e4t G\u00f6ttingen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210122495","host_organization_name":"Asklepios Klinik St. Georg","host_organization_lineage":["https://openalex.org/I4210122495"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:publications.goettingen-research-online.de:2/136236","is_oa":true,"landing_page_url":"https://resolver.sub.uni-goettingen.de/purl?gro-2/136236","pdf_url":null,"source":{"id":"https://openalex.org/S4306401634","display_name":"GoeScholar  The Publication Server of the Georg-August-Universit\u00e4t G\u00f6ttingen (Georg-August-Universit\u00e4t G\u00f6ttingen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210122495","host_organization_name":"Asklepios Klinik St. Georg","host_organization_lineage":["https://openalex.org/I4210122495"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.5099999904632568}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W38743098","https://openalex.org/W58759770","https://openalex.org/W797346804","https://openalex.org/W938539187","https://openalex.org/W1553958932","https://openalex.org/W1558603395","https://openalex.org/W1601674470","https://openalex.org/W1791665180","https://openalex.org/W1964169783","https://openalex.org/W1965415591","https://openalex.org/W1968517468","https://openalex.org/W1970263043","https://openalex.org/W1972596784","https://openalex.org/W1990061958","https://openalex.org/W2017793853","https://openalex.org/W2053013024","https://openalex.org/W2067443406","https://openalex.org/W2067656180","https://openalex.org/W2067787802","https://openalex.org/W2067974452","https://openalex.org/W2078042165","https://openalex.org/W2080175276","https://openalex.org/W2083735143","https://openalex.org/W2166265158","https://openalex.org/W2173960414","https://openalex.org/W2238855891","https://openalex.org/W2377412172","https://openalex.org/W2741656747","https://openalex.org/W2796857528","https://openalex.org/W2913904462","https://openalex.org/W2949583843","https://openalex.org/W2950254397"],"related_works":["https://openalex.org/W2655188380","https://openalex.org/W1492157759","https://openalex.org/W2034514454","https://openalex.org/W2905880134","https://openalex.org/W1601661462","https://openalex.org/W3188841602","https://openalex.org/W1490327274","https://openalex.org/W2555024370","https://openalex.org/W3096721441","https://openalex.org/W2811433520"],"abstract_inverted_index":{"A":[0],"pattern":[1,41],"\u0251":[2,26],"(i.e.,":[3,129],"a":[4,11,39,43,73,82,100,105],"string":[5],"of":[6,25,58,76,88,122,137,148],"variables":[7,24,78,131],"and":[8,79,104],"terminals)":[9],"matches":[10,42],"word":[12,106],"w":[13,16,107,110],",":[14,108],"if":[15],"can":[17,50,111],"be":[18,51,112],"obtained":[19],"by":[20,27,134],"uniformly":[21],"replacing":[22],"the":[23,65,86,126,138],"terminal":[28],"words.":[29],"The":[30],"respective":[31],"matching":[32,66,139],"problem,":[33],"i.e.,":[34],"deciding":[35],"whether":[36,109],"or":[37],"not":[38],"given":[40,44,101],"word,":[45],"is":[46,95,141],"generally":[47],"NP-complete,":[48],"but":[49],"solved":[52],"in":[53],"polynomial-time":[54],"for":[55,64,99,144],"restricted":[56,146],"classes":[57,147],"patterns.":[59,149],"We":[60],"present":[61],"efficient":[62],"algorithms":[63],"problem":[67,140],"with":[68,72,81],"respect":[69],"to":[70,97],"patterns":[71,80],"bounded":[74],"number":[75,102],"repeated":[77],"structural":[83],"restriction":[84],"on":[85],"order":[87],"variables.":[89],"Furthermore,":[90],"we":[91],"show":[92],"that":[93],"it":[94],"NP-complete":[96,142],"decide,":[98],"k":[103,115],"factorised":[113],"into":[114],"distinct":[116],"factors.":[117],"As":[118],"an":[119],"immediate":[120],"consequence":[121],"this":[123],"hardness":[124],"result,":[125],"injective":[127],"version":[128],"different":[130,135],"are":[132],"replaced":[133],"words)":[136],"even":[143],"very":[145]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}