{"id":"https://openalex.org/W2000261666","doi":"https://doi.org/10.1016/0304-3975(95)00095-x","title":"The complexity of PDL with interleaving","display_name":"The complexity of PDL with interleaving","publication_year":1996,"publication_date":"1996-07-01","ids":{"openalex":"https://openalex.org/W2000261666","doi":"https://doi.org/10.1016/0304-3975(95)00095-x","mag":"2000261666"},"language":"en","primary_location":{"id":"doi:10.1016/0304-3975(95)00095-x","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0304-3975(95)00095-x","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/0304-3975(95)00095-x","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005354721","display_name":"Alain Mayer","orcid":null},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alain J. Mayer","raw_affiliation_strings":["Department of Computer Science, Columbia University, New York, NY 10027, USA","Columbia University, New York, NY;"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Columbia University, New York, NY 10027, USA","institution_ids":["https://openalex.org/I78577930"]},{"raw_affiliation_string":"Columbia University, New York, NY;","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5105884653","display_name":"Larry J. Stockmeyer","orcid":null},"institutions":[{"id":"https://openalex.org/I4210085935","display_name":"IBM Research - Almaden","ror":"https://ror.org/005w8dd04","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210085935","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Larry J. Stockmeyer","raw_affiliation_strings":["IBM Almaden Research Center, 650 Harry Road, San Jose, CA 95120, USA","IBM Almaden Research Center San Jose , CA"],"affiliations":[{"raw_affiliation_string":"IBM Almaden Research Center, 650 Harry Road, San Jose, CA 95120, USA","institution_ids":["https://openalex.org/I4210085935"]},{"raw_affiliation_string":"IBM Almaden Research Center San Jose , CA","institution_ids":["https://openalex.org/I4210085935"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5105884653"],"corresponding_institution_ids":["https://openalex.org/I4210085935"],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":{"value":2690,"currency":"USD","value_usd":2690},"fwci":0.0,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.111018,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"161","issue":"1-2","first_page":"109","last_page":"122"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","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"}},"topics":[{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","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/T10126","display_name":"Logic, programming, and type systems","score":0.9993000030517578,"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/T10142","display_name":"Formal Methods in Verification","score":0.9980999827384949,"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/interleaving","display_name":"Interleaving","score":0.832275390625},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6320353150367737},{"id":"https://openalex.org/keywords/concatenation","display_name":"Concatenation (mathematics)","score":0.5893042087554932},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.5501813888549805},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5360795259475708},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5315384864807129},{"id":"https://openalex.org/keywords/regular-expression","display_name":"Regular expression","score":0.45636504888534546},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.451262503862381},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4476008415222168},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3824804127216339},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27847135066986084}],"concepts":[{"id":"https://openalex.org/C28034677","wikidata":"https://www.wikidata.org/wiki/Q17092530","display_name":"Interleaving","level":2,"score":0.832275390625},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6320353150367737},{"id":"https://openalex.org/C87619178","wikidata":"https://www.wikidata.org/wiki/Q126002","display_name":"Concatenation (mathematics)","level":2,"score":0.5893042087554932},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.5501813888549805},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5360795259475708},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5315384864807129},{"id":"https://openalex.org/C121329065","wikidata":"https://www.wikidata.org/wiki/Q185612","display_name":"Regular expression","level":2,"score":0.45636504888534546},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.451262503862381},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4476008415222168},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3824804127216339},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27847135066986084},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/0304-3975(95)00095-x","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0304-3975(95)00095-x","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:ADA281044","is_oa":false,"landing_page_url":"http://oai.dtic.mil/oai/oai?&verb=getRecord&metadataPrefix=html&identifier=ADA281044","pdf_url":null,"source":{"id":"https://openalex.org/S4406923043","display_name":"Defense Technical Information Center (DTIC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"DTIC AND NTIS","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1016/0304-3975(95)00095-x","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0304-3975(95)00095-x","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1483164577","https://openalex.org/W1505623810","https://openalex.org/W1525112938","https://openalex.org/W1553204753","https://openalex.org/W1574129634","https://openalex.org/W1774255828","https://openalex.org/W1974817955","https://openalex.org/W1997716585","https://openalex.org/W2001388124","https://openalex.org/W2002089154","https://openalex.org/W2007464118","https://openalex.org/W2036157680","https://openalex.org/W2059396299","https://openalex.org/W2061488881","https://openalex.org/W2066064214","https://openalex.org/W2069709605","https://openalex.org/W2097864282","https://openalex.org/W2119397055","https://openalex.org/W2132750992","https://openalex.org/W2402038485","https://openalex.org/W3023466934","https://openalex.org/W4241108585","https://openalex.org/W4302339081","https://openalex.org/W6630094632","https://openalex.org/W6631056622","https://openalex.org/W6631192654","https://openalex.org/W6632971258","https://openalex.org/W6638028391","https://openalex.org/W6651922783","https://openalex.org/W6674874210","https://openalex.org/W6677924511","https://openalex.org/W6792635071"],"related_works":["https://openalex.org/W3076532779","https://openalex.org/W2069997585","https://openalex.org/W2045502027","https://openalex.org/W4302076808","https://openalex.org/W2952654623","https://openalex.org/W2061488881","https://openalex.org/W2913798541","https://openalex.org/W2963726605","https://openalex.org/W2000261666","https://openalex.org/W811645096"],"abstract_inverted_index":{"To":[0],"provide":[1],"a":[2,170],"logic":[3,18],"for":[4,26,46,51,65,133,182,186],"reasoning":[5],"about":[6],"concurrently":[7],"executing":[8],"programs,":[9,28,106],"Abrahamson":[10],"has":[11,87],"defined":[12],"an":[13,24],"extension":[14],"of":[15,120,173,188],"propositional":[16],"dynamic":[17],"(PDL)":[19],"by":[20],"allowing":[21],"interleaving":[22,47,97,137],"as":[23],"operator":[25,98],"combining":[27],"in":[29,62,84],"addition":[30],"to":[31,78,124,149],"the":[32,43,85,88,96,115,121,130,174,177,183,189],"regular":[33,105,116,134,166],"PDL":[34,48],"operators":[35],"union,":[36],"concatenation,":[37],"and":[38,55,99,142],"star.":[39],"We":[40],"show":[41],"that":[42,56,129,143],"satisfiability":[44],"problem":[45,58,132,185],"is":[49,128],"complete":[50],"deterministic":[52],"double-exponential":[53,61],"time,":[54],"this":[57,71,126,144,168],"requires":[59,138],"time":[60],"cnlog":[63],"n":[64,141],"some":[66],"positive":[67],"constant":[68],"c.":[69],"Moreover,":[70,176],"lower":[72,145,179],"bound":[73,146,180],"holds":[74,147,181],"even":[75,148],"when":[76],"restricted":[77],"formulas":[79],"where":[80,93,100,159],"each":[81],"program":[82],"appearing":[83],"formula":[86],"form":[89,190],"a1\u00a6a2\u00a6":[90],"\u2026":[91,153,192],"\u00a6ak":[92],"\u00a6":[94],"denotes":[95],"a1,":[101],"\u2026,":[102,161],"ak":[103],"are":[104,164],"i.e.,":[107],"programs":[108,112],"built":[109],"from":[110],"atomic":[111],"using":[113],"only":[114],"operators.":[117],"Another":[118],"consequence":[119],"method":[122],"used":[123],"prove":[125],"result":[127,172],"equivalence":[131],"expressions":[135,187],"with":[136],"space":[139],"2cnlog":[140],"decide":[150],"whether":[151],"(E1\u00a6E2\u00a6":[152],"\u00a6Ek)":[154],"\u222a":[155],"F":[156,163],"\u2261":[157],"\u2211\u2217":[158],"E1,":[160],"Ek,":[162],"ordinary":[165],"expressions;":[167],"improves":[169],"previous":[171],"authors.":[175],"same":[178],"containment":[184],"E1\u00a6E2\u00a6":[191],"\u00a6Ek.":[193]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}