{"id":"https://openalex.org/W2024522546","doi":"https://doi.org/10.1137/s0097539704445950","title":"Word Problems and Membership Problems on Compressed Words","display_name":"Word Problems and Membership Problems on Compressed Words","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2024522546","doi":"https://doi.org/10.1137/s0097539704445950","mag":"2024522546"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539704445950","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539704445950","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5005500210","display_name":"Markus Lohrey","orcid":"https://orcid.org/0000-0002-4680-7198"},"institutions":[{"id":"https://openalex.org/I100066346","display_name":"University of Stuttgart","ror":"https://ror.org/04vnq7t77","country_code":"DE","type":"education","lineage":["https://openalex.org/I100066346"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Markus Lohrey","raw_affiliation_strings":["Institut f\u00fcr Formale Methoden der Informatik, Universit\u00e4t Stuttgart, Universit\u00e4tsstr. 38, 70569 Stuttgart, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Formale Methoden der Informatik, Universit\u00e4t Stuttgart, Universit\u00e4tsstr. 38, 70569 Stuttgart, Germany","institution_ids":["https://openalex.org/I100066346"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005500210"],"corresponding_institution_ids":["https://openalex.org/I100066346"],"apc_list":null,"apc_paid":null,"fwci":6.0666,"has_fulltext":false,"cited_by_count":65,"citation_normalized_percentile":{"value":0.96723414,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"35","issue":"5","first_page":"1210","last_page":"1240"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9998999834060669,"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/T11567","display_name":"semigroups and automata theory","score":0.9998999834060669,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9994000196456909,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9926999807357788,"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/monoid","display_name":"Monoid","score":0.8223527669906616},{"id":"https://openalex.org/keywords/word-problem","display_name":"Word problem (mathematics education)","score":0.6981968283653259},{"id":"https://openalex.org/keywords/completeness","display_name":"Completeness (order theory)","score":0.5969217419624329},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.5743597745895386},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5574074983596802},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5152788162231445},{"id":"https://openalex.org/keywords/context-free-language","display_name":"Context-free language","score":0.4839501678943634},{"id":"https://openalex.org/keywords/regular-language","display_name":"Regular language","score":0.48286062479019165},{"id":"https://openalex.org/keywords/rule-based-machine-translation","display_name":"Rule-based machine translation","score":0.42494070529937744},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3871365189552307},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3783133029937744},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.2697892189025879},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.22083958983421326},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17695340514183044},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.14591005444526672}],"concepts":[{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.8223527669906616},{"id":"https://openalex.org/C90988201","wikidata":"https://www.wikidata.org/wiki/Q255912","display_name":"Word problem (mathematics education)","level":2,"score":0.6981968283653259},{"id":"https://openalex.org/C17231256","wikidata":"https://www.wikidata.org/wiki/Q5156540","display_name":"Completeness (order theory)","level":2,"score":0.5969217419624329},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.5743597745895386},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5574074983596802},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5152788162231445},{"id":"https://openalex.org/C198838072","wikidata":"https://www.wikidata.org/wiki/Q729271","display_name":"Context-free language","level":3,"score":0.4839501678943634},{"id":"https://openalex.org/C52370388","wikidata":"https://www.wikidata.org/wiki/Q752532","display_name":"Regular language","level":3,"score":0.48286062479019165},{"id":"https://openalex.org/C53893814","wikidata":"https://www.wikidata.org/wiki/Q7378909","display_name":"Rule-based machine translation","level":2,"score":0.42494070529937744},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3871365189552307},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3783133029937744},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2697892189025879},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.22083958983421326},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17695340514183044},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.14591005444526672},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0097539704445950","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539704445950","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.67.6712","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.67.6712","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://inf.informatik.uni-stuttgart.de/fmi/ti/personen/Lohrey/04-SIAM.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":69,"referenced_works":["https://openalex.org/W128453691","https://openalex.org/W147871093","https://openalex.org/W190006957","https://openalex.org/W1491846504","https://openalex.org/W1496412704","https://openalex.org/W1497287285","https://openalex.org/W1497949336","https://openalex.org/W1510722254","https://openalex.org/W1538868153","https://openalex.org/W1553048644","https://openalex.org/W1557759443","https://openalex.org/W1565623053","https://openalex.org/W1568478997","https://openalex.org/W1584818251","https://openalex.org/W1591640628","https://openalex.org/W1592405134","https://openalex.org/W1597956802","https://openalex.org/W1599548286","https://openalex.org/W1859318703","https://openalex.org/W1955766098","https://openalex.org/W1970755596","https://openalex.org/W1973608346","https://openalex.org/W1979254690","https://openalex.org/W1979328074","https://openalex.org/W1982347904","https://openalex.org/W1982538209","https://openalex.org/W1986736553","https://openalex.org/W1990870868","https://openalex.org/W1991636160","https://openalex.org/W1996184580","https://openalex.org/W2004459113","https://openalex.org/W2009571139","https://openalex.org/W2011039300","https://openalex.org/W2016550752","https://openalex.org/W2017205387","https://openalex.org/W2019724649","https://openalex.org/W2021380921","https://openalex.org/W2024730357","https://openalex.org/W2027501230","https://openalex.org/W2031613223","https://openalex.org/W2033323875","https://openalex.org/W2043641704","https://openalex.org/W2045583484","https://openalex.org/W2051521505","https://openalex.org/W2061161327","https://openalex.org/W2065251436","https://openalex.org/W2065939997","https://openalex.org/W2066012259","https://openalex.org/W2072181151","https://openalex.org/W2078130239","https://openalex.org/W2090186445","https://openalex.org/W2094939442","https://openalex.org/W2100338689","https://openalex.org/W2104952158","https://openalex.org/W2107745473","https://openalex.org/W2108112890","https://openalex.org/W2115990355","https://openalex.org/W2172088563","https://openalex.org/W2261858229","https://openalex.org/W2328824725","https://openalex.org/W2532500577","https://openalex.org/W2735946982","https://openalex.org/W2765659955","https://openalex.org/W3157585079","https://openalex.org/W4213009134","https://openalex.org/W4240781210","https://openalex.org/W4241108585","https://openalex.org/W4285719527","https://openalex.org/W4300790099"],"related_works":["https://openalex.org/W1511851241","https://openalex.org/W2130856794","https://openalex.org/W1523052313","https://openalex.org/W1975351486","https://openalex.org/W3106811412","https://openalex.org/W2079333248","https://openalex.org/W1978362621","https://openalex.org/W2058817145","https://openalex.org/W2066285288","https://openalex.org/W2137124862"],"abstract_inverted_index":{"Abstract.":[0],"We":[1],"consider":[2],"a":[3,28,81,92,98,107],"compressed":[4,20,47,87,100,121],"form":[5],"of":[6,18,22,27,43,62,83,105,119],"the":[7,15,25,39,74,117,120],"word":[8,88,133],"problem":[9,123],"for":[10,70,124,135],"finitely":[11,63],"presented":[12,64],"monoids,":[13,136],"where":[14],"input":[16],"consists":[17],"two":[19,36],"representations":[21],"words":[23,37],"over":[24],"generators":[26],"monoid":[29,41],"M,":[30],"and":[31],"we":[32,66,90,114],"ask":[33],"whether":[34],"these":[35],"represent":[38],"same":[40],"element":[42],"M.":[44],"Words":[45],"are":[46],"using":[48],"straight-line":[49],"programs,":[50],"i.e.,":[51],"context-free":[52,95,137],"grammars":[53],"that":[54],"generate":[55],"exactly":[56],"one":[57],"word.":[58],"For":[59],"several":[60],"classes":[61,72],"monoids":[65],"obtain":[67,91],"completeness":[68],"results":[69,85],"complexity":[71,118,127,139],"in":[73],"range":[75],"from":[76],"P":[77],"to":[78],"EXPSPACE.":[79],"As":[80],"by-product":[82],"our":[84],"on":[86],"problems":[89,134],"fixed":[93],"deterministic":[94],"language":[96,108],"with":[97],"PSPACE-complete":[99],"membership":[101,122],"problem.":[102],"The":[103],"existence":[104],"such":[106],"was":[109],"open":[110],"so":[111],"far.":[112],"Finally,":[113],"will":[115],"investigate":[116],"various":[125],"circuit":[126],"classes.":[128],"Key":[129],"words.":[130],"grammar-based":[131],"compression,":[132],"languages,":[138],"AMS":[140],"subject":[141],"classifications.":[142],"20F10,":[143],"68Q17,":[144],"68Q42":[145]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}