{"id":"https://openalex.org/W4414179977","doi":"https://doi.org/10.1142/s0129054125410084","title":"The Pumping Lemma for Regular Languages is Hard","display_name":"The Pumping Lemma for Regular Languages is Hard","publication_year":2025,"publication_date":"2025-09-15","ids":{"openalex":"https://openalex.org/W4414179977","doi":"https://doi.org/10.1142/s0129054125410084"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054125410084","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054125410084","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"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 Foundations of Computer Science","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/A5040523230","display_name":"Hermann Gruber","orcid":"https://orcid.org/0000-0002-1953-3697"},"institutions":[{"id":"https://openalex.org/I1283382300","display_name":"BMW (Germany)","ror":"https://ror.org/05vs9tj88","country_code":"DE","type":"company","lineage":["https://openalex.org/I1283382300","https://openalex.org/I4210156768"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Hermann Gruber","raw_affiliation_strings":["Planerio GmbH, Theresienh\u00f6he\u00a011A, 80538 M\u00fcnchen, Germany"],"raw_orcid":"https://orcid.org/0000-0002-1953-3697","affiliations":[{"raw_affiliation_string":"Planerio GmbH, Theresienh\u00f6he\u00a011A, 80538 M\u00fcnchen, Germany","institution_ids":["https://openalex.org/I1283382300"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016664760","display_name":"Markus Holzer","orcid":"https://orcid.org/0000-0003-4224-4014"},"institutions":[{"id":"https://openalex.org/I200763008","display_name":"Justus-Liebig-Universit\u00e4t Gie\u00dfen","ror":"https://ror.org/033eqas34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200763008"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Markus Holzer","raw_affiliation_strings":["Institut f\u00fcr Informatik, Universit\u00e4t Giessen, Arndtstr.\u00a02, 35392 Giessen, Germany"],"raw_orcid":"https://orcid.org/0000-0003-4224-4014","affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, Universit\u00e4t Giessen, Arndtstr.\u00a02, 35392 Giessen, Germany","institution_ids":["https://openalex.org/I200763008"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038490194","display_name":"Christian Rauch","orcid":null},"institutions":[{"id":"https://openalex.org/I106157433","display_name":"University of Kassel","ror":"https://ror.org/04zc7p361","country_code":"DE","type":"education","lineage":["https://openalex.org/I106157433"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Rauch","raw_affiliation_strings":["School of Electrical Engineering and Computer Science, University of Kassel, 34121 Kassel, Germany"],"raw_orcid":"https://orcid.org/0000-0003-1008-4642","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering and Computer Science, University of Kassel, 34121 Kassel, Germany","institution_ids":["https://openalex.org/I106157433"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5040523230"],"corresponding_institution_ids":["https://openalex.org/I1283382300"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.24899936,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"37","issue":"01","first_page":"193","last_page":"213"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.998199999332428,"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":0.998199999332428,"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/T11130","display_name":"Coding theory and cryptography","score":0.9908000230789185,"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/T12029","display_name":"DNA and Biological Computing","score":0.9718999862670898,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/pumping-lemma-for-regular-languages","display_name":"Pumping lemma for regular languages","score":0.7627000212669373},{"id":"https://openalex.org/keywords/regular-language","display_name":"Regular language","score":0.7045999765396118},{"id":"https://openalex.org/keywords/nondeterministic-algorithm","display_name":"Nondeterministic algorithm","score":0.6970000267028809},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.6230000257492065},{"id":"https://openalex.org/keywords/nondeterministic-finite-automaton","display_name":"Nondeterministic finite automaton","score":0.5889000296592712},{"id":"https://openalex.org/keywords/finite-state-machine","display_name":"Finite-state machine","score":0.5755000114440918},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5647000074386597},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4991999864578247},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.4848000109195709}],"concepts":[{"id":"https://openalex.org/C157968401","wikidata":"https://www.wikidata.org/wiki/Q2292874","display_name":"Pumping lemma for regular languages","level":5,"score":0.7627000212669373},{"id":"https://openalex.org/C52370388","wikidata":"https://www.wikidata.org/wiki/Q752532","display_name":"Regular language","level":3,"score":0.7045999765396118},{"id":"https://openalex.org/C176181172","wikidata":"https://www.wikidata.org/wiki/Q3490301","display_name":"Nondeterministic algorithm","level":2,"score":0.6970000267028809},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6861000061035156},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6230000257492065},{"id":"https://openalex.org/C158008952","wikidata":"https://www.wikidata.org/wiki/Q617295","display_name":"Nondeterministic finite automaton","level":4,"score":0.5889000296592712},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.5755000114440918},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5647000074386597},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5561000108718872},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4991999864578247},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.4848000109195709},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4392000138759613},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.429500013589859},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4138000011444092},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.4032000005245209},{"id":"https://openalex.org/C104091681","wikidata":"https://www.wikidata.org/wiki/Q837528","display_name":"Deterministic finite automaton","level":3,"score":0.3968999981880188},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.38760000467300415},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3741999864578247},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.3734000027179718},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36970001459121704},{"id":"https://openalex.org/C2983497884","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite state","level":3,"score":0.3440000116825104},{"id":"https://openalex.org/C194525867","wikidata":"https://www.wikidata.org/wiki/Q5265707","display_name":"Deterministic automaton","level":3,"score":0.33309999108314514},{"id":"https://openalex.org/C146072743","wikidata":"https://www.wikidata.org/wiki/Q192161","display_name":"Formal language","level":2,"score":0.32829999923706055},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.32280001044273376},{"id":"https://openalex.org/C165753454","wikidata":"https://www.wikidata.org/wiki/Q1020380","display_name":"B\u00fcchi automaton","level":4,"score":0.3100000023841858},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.30790001153945923},{"id":"https://openalex.org/C115988155","wikidata":"https://www.wikidata.org/wiki/Q3262192","display_name":"Decision problem","level":2,"score":0.2809000015258789},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.251800000667572}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129054125410084","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054125410084","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"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 Foundations of Computer Science","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":13,"referenced_works":["https://openalex.org/W1491169489","https://openalex.org/W1567676570","https://openalex.org/W1982129592","https://openalex.org/W1995725694","https://openalex.org/W2008342226","https://openalex.org/W2066306723","https://openalex.org/W2080108335","https://openalex.org/W2092386826","https://openalex.org/W2094342580","https://openalex.org/W2914414140","https://openalex.org/W4285891680","https://openalex.org/W4299138792","https://openalex.org/W4381855730"],"related_works":[],"abstract_inverted_index":{"We":[0],"investigate":[1],"the":[2,6,23,35,47,85,94,99,123],"computational":[3],"complexity":[4],"of":[5,84,109],"Pumping-Problem,":[7],"that":[8,52,93],"is,":[9],"for":[10,64,74,80,98,117],"a":[11,17,29,107,118],"given":[12,119],"finite":[13,66,76],"automaton":[14],"A":[15],"and":[16,69],"value":[18,36],"p,":[19],"to":[20],"decide":[21],"whether":[22],"language":[24],"[Formula:":[25,110,114],"see":[26,111,115],"text]":[27,112],"satisfies":[28],"previously":[30],"fixed":[31],"pumping":[32,44,87,96,101],"lemma":[33],"w.r.t.":[34],"p.":[37],"Here":[38],"we":[39,91],"concentrate":[40],"on":[41],"two":[42],"different":[43],"lemmata":[45,102],"from":[46],"literature.":[48],"It":[49],"turns":[50],"out":[51],"this":[53],"problem":[54],"is":[55,59],"intractable,":[56],"namely,":[57],"it":[58,70],"already":[60],"coNP":[61],"-complete,":[62],"even":[63],"deterministic":[65],"automata":[67],"(DFAs),":[68],"becomes":[71],"PSPACE":[72],"-complete":[73],"nondeterministic":[75],"state":[77],"devices":[78],"(NFAs),":[79],"at":[81],"least":[82],"one":[83],"considered":[86,100],"lemmata.":[88],"In":[89],"addition,":[90],"show":[92],"minimal":[95],"constant":[97],"cannot":[103],"be":[104],"approximated":[105],"within":[106],"factor":[108],"with":[113],"text],":[116],"n-state":[120],"NFA,":[121],"unless":[122],"Exponential":[124],"Time":[125],"Hypothesis":[126],"(ETH)":[127],"fails.":[128]},"counts_by_year":[],"updated_date":"2026-02-14T06:23:00.392402","created_date":"2025-10-10T00:00:00"}