{"id":"https://openalex.org/W3127916250","doi":"https://doi.org/10.4230/lipics.csl.2021.27","title":"On the Complexity of Horn and Krom Fragments of Second-Order Boolean Logic.","display_name":"On the Complexity of Horn and Krom Fragments of Second-Order Boolean Logic.","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3127916250","doi":"https://doi.org/10.4230/lipics.csl.2021.27","mag":"3127916250"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.4230/LIPIcs.CSL.2021.27","pdf_url":null,"source":{"id":"https://openalex.org/S4306417978","display_name":"Computer Science Logic","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":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"proceedings-article","indexed_in":[],"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/A5031183978","display_name":"Miika Hannula","orcid":"https://orcid.org/0000-0002-9637-6664"},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Miika Hannula","raw_affiliation_strings":["University of Helsinki, Helsinki, Finland"],"affiliations":[{"raw_affiliation_string":"University of Helsinki, Helsinki, Finland","institution_ids":["https://openalex.org/I133731052"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069777444","display_name":"Juha Kontinen","orcid":"https://orcid.org/0000-0003-0115-5154"},"institutions":[{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Juha Kontinen","raw_affiliation_strings":["University of Helsinki, Helsinki, Finland"],"affiliations":[{"raw_affiliation_string":"University of Helsinki, Helsinki, Finland","institution_ids":["https://openalex.org/I133731052"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062261702","display_name":"Martin L\u00fcck","orcid":null},"institutions":[{"id":"https://openalex.org/I114112103","display_name":"Leibniz University Hannover","ror":"https://ror.org/0304hq317","country_code":"DE","type":"education","lineage":["https://openalex.org/I114112103"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin L\u00fcck","raw_affiliation_strings":["Leibniz University Hannover, Hanover, Germany"],"affiliations":[{"raw_affiliation_string":"Leibniz University Hannover, Hanover, Germany","institution_ids":["https://openalex.org/I114112103"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073358565","display_name":"Jonni Virtema","orcid":"https://orcid.org/0000-0002-1582-3718"},"institutions":[{"id":"https://openalex.org/I114112103","display_name":"Leibniz University Hannover","ror":"https://ror.org/0304hq317","country_code":"DE","type":"education","lineage":["https://openalex.org/I114112103"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jonni Virtema","raw_affiliation_strings":["Leibniz University Hannover, Hanover, Germany"],"affiliations":[{"raw_affiliation_string":"Leibniz University Hannover, Hanover, Germany","institution_ids":["https://openalex.org/I114112103"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":0,"max":57},"biblio":{"volume":null,"issue":null,"first_page":"22","last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9925,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9925,"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/T10142","display_name":"Formal Methods in Verification","score":0.9884,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9608,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/alternation","display_name":"Alternation (linguistics)","score":0.53020966},{"id":"https://openalex.org/keywords/fragment","display_name":"Fragment (logic)","score":0.43984908}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6791338},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.61398655},{"id":"https://openalex.org/C26826806","wikidata":"https://www.wikidata.org/wiki/Q438358","display_name":"Alternation (linguistics)","level":2,"score":0.53020966},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.521726},{"id":"https://openalex.org/C88548561","wikidata":"https://www.wikidata.org/wiki/Q347599","display_name":"sort","level":2,"score":0.50766623},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.45678836},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.44787556},{"id":"https://openalex.org/C2776235265","wikidata":"https://www.wikidata.org/wiki/Q18392052","display_name":"Fragment (logic)","level":2,"score":0.43984908},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.42450938},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3506598},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3075481},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.23488125},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.4230/LIPIcs.CSL.2021.27","pdf_url":null,"source":{"id":"https://openalex.org/S4306417978","display_name":"Computer Science Logic","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":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W63340727","https://openalex.org/W3040774944","https://openalex.org/W3033601567","https://openalex.org/W2951261477","https://openalex.org/W2950290821","https://openalex.org/W2904498177","https://openalex.org/W2559012721","https://openalex.org/W2549023517","https://openalex.org/W2252339295","https://openalex.org/W2240048967","https://openalex.org/W2178865018","https://openalex.org/W2149816638","https://openalex.org/W21201483","https://openalex.org/W2114710125","https://openalex.org/W2079842345","https://openalex.org/W2045554431","https://openalex.org/W1962883301","https://openalex.org/W1507251275","https://openalex.org/W1499126844","https://openalex.org/W133313031"],"abstract_inverted_index":{"Second-order":[0],"Boolean":[1,46,94],"logic":[2],"is":[3],"a":[4,76],"generalization":[5],"of":[6,20,29,31,44,56,62,79,92,100,108,121,132,154],"QBF,":[7],"whose":[8],"constant":[9],"alternation":[10],"fragments":[11,91],"are":[12,124,158],"known":[13],"to":[14,36,41],"be":[15],"complete":[16,125],"for":[17,126,141],"the":[18,21,42,45,49,82,93,98,127,133,142,155],"levels":[19],"exponential":[22,134],"time":[23,135],"hierarchy.":[24,136],"We":[25,96,110],"consider":[26,53,86],"two":[27,54,106],"types":[28,107],"restriction":[30],"this":[32],"logic:":[33],"1)":[34],"restrictions":[35,40,153],"term":[37],"constructions,":[38],"2)":[39],"form":[43],"matrix.":[47,95],"Of":[48,81],"first":[50,156],"sort,":[51,84],"we":[52,85,138],"kinds":[55],"restrictions:":[57],"firstly,":[58],"disallowing":[59],"nested":[60],"use":[61],"proper":[63],"function":[64,71,122],"variables,":[65],"and":[66,89,144,151],"secondly":[67],"stipulating":[68],"that":[69],"each":[70],"variable":[72],"must":[73],"appear":[74],"with":[75,117],"fixed":[77],"sequence":[78],"arguments.":[80],"second":[83],"Horn,":[87],"Krom,":[88],"core":[90,145],"classify":[97],"complexity":[99],"logics":[101,116],"obtained":[102],"by":[103],"combining":[104],"these":[105],"restrictions.":[109],"show":[111],"that,":[112],"in":[113,159],"most":[114],"cases,":[115],"k":[118,148],"alternating":[119],"blocks":[120],"quantifiers":[123],"kth":[128],"or":[129],"(k-1)th":[130],"level":[131],"Furthermore,":[137],"establish":[139],"NL-completeness":[140],"Krom":[143],"fragments,":[146],"when":[147],"=":[149],"1":[150],"both":[152],"sort":[157],"effect.":[160]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W3127916250","counts_by_year":[],"updated_date":"2024-12-08T13:55:52.935841","created_date":"2021-02-15"}