{"id":"https://openalex.org/W2059200976","doi":"https://doi.org/10.1137/0214044","title":"On the Equivalence and Containment Problems for Unambiguous Regular Expressions, Regular Grammars and Finite Automata","display_name":"On the Equivalence and Containment Problems for Unambiguous Regular Expressions, Regular Grammars and Finite Automata","publication_year":1985,"publication_date":"1985-08-01","ids":{"openalex":"https://openalex.org/W2059200976","doi":"https://doi.org/10.1137/0214044","mag":"2059200976"},"language":"en","primary_location":{"id":"doi:10.1137/0214044","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0214044","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/A5052202085","display_name":"Richard E. Stearns","orcid":"https://orcid.org/0000-0001-5058-1999"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"R. E. Stearns","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5086835651","display_name":"Harry B. Hunt","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"H. B. Hunt III","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5052202085"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5034,"has_fulltext":false,"cited_by_count":123,"citation_normalized_percentile":{"value":0.89892597,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"14","issue":"3","first_page":"598","last_page":"611"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":1.0,"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":1.0,"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/T12029","display_name":"DNA and Biological Computing","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T10911","display_name":"Chemical Synthesis and Analysis","score":0.9962000250816345,"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/nondeterministic-finite-automaton","display_name":"Nondeterministic finite automaton","score":0.7655574083328247},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6594749689102173},{"id":"https://openalex.org/keywords/quantum-finite-automata","display_name":"Quantum finite automata","score":0.6079623103141785},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5665864944458008},{"id":"https://openalex.org/keywords/regular-language","display_name":"Regular language","score":0.5450265407562256},{"id":"https://openalex.org/keywords/deterministic-finite-automaton","display_name":"Deterministic finite automaton","score":0.5310801863670349},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5069787502288818},{"id":"https://openalex.org/keywords/regular-expression","display_name":"Regular expression","score":0.5043619871139526},{"id":"https://openalex.org/keywords/automata-theory","display_name":"Automata theory","score":0.4953121244907379},{"id":"https://openalex.org/keywords/nondeterministic-algorithm","display_name":"Nondeterministic algorithm","score":0.48784399032592773},{"id":"https://openalex.org/keywords/unary-operation","display_name":"Unary operation","score":0.45841169357299805},{"id":"https://openalex.org/keywords/deterministic-context-free-grammar","display_name":"Deterministic context-free grammar","score":0.4571104645729065},{"id":"https://openalex.org/keywords/rule-based-machine-translation","display_name":"Rule-based machine translation","score":0.436227023601532},{"id":"https://openalex.org/keywords/automaton","display_name":"Automaton","score":0.43250972032546997},{"id":"https://openalex.org/keywords/pspace","display_name":"PSPACE","score":0.4254877269268036},{"id":"https://openalex.org/keywords/containment","display_name":"Containment (computer programming)","score":0.4235166907310486},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3739354610443115},{"id":"https://openalex.org/keywords/finite-state-machine","display_name":"Finite-state machine","score":0.3211482763290405},{"id":"https://openalex.org/keywords/context-free-grammar","display_name":"Context-free grammar","score":0.2897266149520874},{"id":"https://openalex.org/keywords/tree-adjoining-grammar","display_name":"Tree-adjoining grammar","score":0.21988555788993835},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.20454898476600647},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18477025628089905},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.18250316381454468},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.13167789578437805}],"concepts":[{"id":"https://openalex.org/C158008952","wikidata":"https://www.wikidata.org/wiki/Q617295","display_name":"Nondeterministic finite automaton","level":4,"score":0.7655574083328247},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6594749689102173},{"id":"https://openalex.org/C174327141","wikidata":"https://www.wikidata.org/wiki/Q176837","display_name":"Quantum finite automata","level":4,"score":0.6079623103141785},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5665864944458008},{"id":"https://openalex.org/C52370388","wikidata":"https://www.wikidata.org/wiki/Q752532","display_name":"Regular language","level":3,"score":0.5450265407562256},{"id":"https://openalex.org/C104091681","wikidata":"https://www.wikidata.org/wiki/Q837528","display_name":"Deterministic finite automaton","level":3,"score":0.5310801863670349},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5069787502288818},{"id":"https://openalex.org/C121329065","wikidata":"https://www.wikidata.org/wiki/Q185612","display_name":"Regular expression","level":2,"score":0.5043619871139526},{"id":"https://openalex.org/C116248031","wikidata":"https://www.wikidata.org/wiki/Q214526","display_name":"Automata theory","level":3,"score":0.4953121244907379},{"id":"https://openalex.org/C176181172","wikidata":"https://www.wikidata.org/wiki/Q3490301","display_name":"Nondeterministic algorithm","level":2,"score":0.48784399032592773},{"id":"https://openalex.org/C78023250","wikidata":"https://www.wikidata.org/wiki/Q657596","display_name":"Unary operation","level":2,"score":0.45841169357299805},{"id":"https://openalex.org/C177638518","wikidata":"https://www.wikidata.org/wiki/Q3435975","display_name":"Deterministic context-free grammar","level":5,"score":0.4571104645729065},{"id":"https://openalex.org/C53893814","wikidata":"https://www.wikidata.org/wiki/Q7378909","display_name":"Rule-based machine translation","level":2,"score":0.436227023601532},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.43250972032546997},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.4254877269268036},{"id":"https://openalex.org/C2777019822","wikidata":"https://www.wikidata.org/wiki/Q390066","display_name":"Containment (computer programming)","level":2,"score":0.4235166907310486},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3739354610443115},{"id":"https://openalex.org/C167822520","wikidata":"https://www.wikidata.org/wiki/Q176452","display_name":"Finite-state machine","level":2,"score":0.3211482763290405},{"id":"https://openalex.org/C97212296","wikidata":"https://www.wikidata.org/wiki/Q338047","display_name":"Context-free grammar","level":3,"score":0.2897266149520874},{"id":"https://openalex.org/C134083981","wikidata":"https://www.wikidata.org/wiki/Q1754022","display_name":"Tree-adjoining grammar","level":4,"score":0.21988555788993835},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.20454898476600647},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18477025628089905},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18250316381454468},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.13167789578437805},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0214044","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0214044","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W611290337","https://openalex.org/W1655990431","https://openalex.org/W1966072464","https://openalex.org/W1982206794","https://openalex.org/W1983423379","https://openalex.org/W1998090528","https://openalex.org/W2011523226","https://openalex.org/W2025256949","https://openalex.org/W2462139357","https://openalex.org/W2592184324"],"related_works":["https://openalex.org/W3143588635","https://openalex.org/W2160879187","https://openalex.org/W2125008689","https://openalex.org/W2057386223","https://openalex.org/W2561116436","https://openalex.org/W1530258609","https://openalex.org/W1485256158","https://openalex.org/W4291131296","https://openalex.org/W2394954760","https://openalex.org/W2047588061"],"abstract_inverted_index":{"The":[0,61],"known":[1],"proofs":[2],"that":[3,34],"the":[4,45,81,97],"equivalence":[5,46],"and":[6,14,29,47,57,93],"containment":[7,48],"problems":[8,49],"for":[9,44,50],"regular":[10,12,52,55,110],"expressions,":[11,27,53],"grammars":[13,28,56],"nondeterministic":[15],"finite":[16,59],"automata":[17],"are":[18,42,63],"PSPACE-complete":[19],"[SM]":[20],"depend":[21,75],"upon":[22,76],"consideration":[23],"of":[24,83,85,99,101,103],"highly":[25],"unambiguous":[26,51,54,58],"automata.":[30,60],"Here,":[31],"we":[32],"prove":[33],"such":[35],"dependence":[36],"is":[37],"inherent.":[38],"Deterministic":[39],"polynomial-time":[40],"algorithms":[41,62,74],"presented":[43],"then":[64],"extended":[65],"to":[66],"ambiguity":[67],"bounded":[68],"by":[69,108],"a":[70,104,109],"fixed":[71],"k.":[72],"Our":[73],"several":[77],"elementary":[78],"observations":[79],"on":[80],"solutions":[82],"systems":[84],"homogeneous":[86],"linear":[87],"difference":[88],"equations":[89],"with":[90,96],"constant":[91],"coefficients":[92],"their":[94],"relationship":[95],"number":[98],"derivations":[100],"strings":[102],"given":[105],"length":[106],"n":[107],"grammar.":[111]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
