{"id":"https://openalex.org/W2544773140","doi":null,"title":"Implicit hitting set algorithms for reasoning beyond NP","display_name":"Implicit hitting set algorithms for reasoning beyond NP","publication_year":2016,"publication_date":"2016-04-25","ids":{"openalex":"https://openalex.org/W2544773140","mag":"2544773140"},"language":"en","primary_location":{"id":"mag:2544773140","doi":null,"is_oa":false,"landing_page_url":"https://www.dbai.tuwien.ac.at/user/wallner/files/SaikkoWJ2016.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306420732","display_name":"Principles of Knowledge Representation and Reasoning","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"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,"raw_source_name":"Principles of Knowledge Representation and Reasoning","raw_type":null},"volume":null,"type":"article","is_traditional":true,"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/A5043103417","display_name":"Paul Saikko","orcid":"https://orcid.org/0000-0001-7935-5338","observed_orcids":["https://orcid.org/0000-0001-7935-5338"]},"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"]},{"id":"https://openalex.org/I32943570","display_name":"Helsinki Institute for Information Technology","ror":"https://ror.org/05kph4940","country_code":"FI","type":"facility","lineage":["https://openalex.org/I133731052","https://openalex.org/I32943570","https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Paul Saikko","raw_affiliation_strings":["HIIT, Department of Computer Science, University of Helsinki, , Finland"],"raw_orcid":"https://orcid.org/0000-0001-7935-5338","affiliations":[{"raw_affiliation_string":"HIIT, Department of Computer Science, University of Helsinki, , Finland","institution_ids":["https://openalex.org/I133731052","https://openalex.org/I32943570"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059688960","display_name":"Johannes Peter Wallner","orcid":"https://orcid.org/0000-0002-3051-1966","observed_orcids":["https://orcid.org/0000-0002-3051-1966"]},"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"]},{"id":"https://openalex.org/I32943570","display_name":"Helsinki Institute for Information Technology","ror":"https://ror.org/05kph4940","country_code":"FI","type":"facility","lineage":["https://openalex.org/I133731052","https://openalex.org/I32943570","https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Johannes Wallner","raw_affiliation_strings":["HIIT, Department of Computer Science, University of Helsinki, , Finland"],"raw_orcid":"https://orcid.org/0000-0002-3051-1966","affiliations":[{"raw_affiliation_string":"HIIT, Department of Computer Science, University of Helsinki, , Finland","institution_ids":["https://openalex.org/I133731052","https://openalex.org/I32943570"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081120128","display_name":"Matti J\u00e4rvisalo","orcid":"https://orcid.org/0000-0003-2572-063X","observed_orcids":["https://orcid.org/0000-0003-2572-063X"]},"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"]},{"id":"https://openalex.org/I32943570","display_name":"Helsinki Institute for Information Technology","ror":"https://ror.org/05kph4940","country_code":"FI","type":"facility","lineage":["https://openalex.org/I133731052","https://openalex.org/I32943570","https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":false,"raw_author_name":"Matti J\u0084\u00e4rvisalo","raw_affiliation_strings":["HIIT, Department of Computer Science, University of Helsinki, , Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"HIIT, Department of Computer Science, University of Helsinki, , Finland","institution_ids":["https://openalex.org/I133731052","https://openalex.org/I32943570"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.0921,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.92468398,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"104","last_page":"113"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.5234000086784363,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.5234000086784363,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.4456000030040741,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.014399999752640724,"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/maxsat","display_name":"MaxSAT","score":0.824999988079071},{"id":"https://openalex.org/keywords/polynomial-hierarchy","display_name":"polynomial hierarchy","score":0.7820000052452087},{"id":"https://openalex.org/keywords/integer-programming-solvers","display_name":"integer programming solvers","score":0.9670000076293945},{"id":"https://openalex.org/keywords/disjunctive-logic-programming","display_name":"disjunctive logic programming","score":0.8510000109672546},{"id":"https://openalex.org/keywords/answer-set-semantics","display_name":"answer set semantics","score":0.9710000157356262},{"id":"https://openalex.org/keywords/knowledge-representation-and-reasoning","display_name":"knowledge representation and reasoning","score":0.7369999885559082}],"concepts":[{"id":"https://openalex.org/C182620335","wikidata":"https://www.wikidata.org/wiki/Q2852531","display_name":"Answer set programming","level":3,"score":0.8235527276992798},{"id":"https://openalex.org/C111797529","wikidata":"https://www.wikidata.org/wiki/Q17080584","display_name":"Maximum satisfiability problem","level":3,"score":0.7666505575180054},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.6244337558746338},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.6039609909057617},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6020119786262512},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.548072874546051},{"id":"https://openalex.org/C69562738","wikidata":"https://www.wikidata.org/wiki/Q200694","display_name":"Propositional calculus","level":2,"score":0.5277731418609619},{"id":"https://openalex.org/C127001435","wikidata":"https://www.wikidata.org/wiki/Q7595770","display_name":"Stable model semantics","level":4,"score":0.5228381752967834},{"id":"https://openalex.org/C74640108","wikidata":"https://www.wikidata.org/wiki/Q1372900","display_name":"Propositional formula","level":5,"score":0.5095389485359192},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4811233580112457},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.47677353024482727},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.43924790620803833},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.43454283475875854},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.42264753580093384},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3607718348503113},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31083881855010986},{"id":"https://openalex.org/C14523651","wikidata":"https://www.wikidata.org/wiki/Q3492863","display_name":"Propositional variable","level":4,"score":0.23420920968055725},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.1889510452747345},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.16487330198287964},{"id":"https://openalex.org/C156325763","wikidata":"https://www.wikidata.org/wiki/Q1930895","display_name":"Operational semantics","level":3,"score":0.09617358446121216},{"id":"https://openalex.org/C33203268","wikidata":"https://www.wikidata.org/wiki/Q5361594","display_name":"Intermediate logic","level":3,"score":0.07634943723678589},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2544773140","doi":null,"is_oa":false,"landing_page_url":"https://www.dbai.tuwien.ac.at/user/wallner/files/SaikkoWJ2016.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306420732","display_name":"Principles of Knowledge Representation and Reasoning","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"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,"raw_source_name":"Principles of Knowledge Representation and Reasoning","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":71,"referenced_works":["https://openalex.org/W37002918","https://openalex.org/W56211936","https://openalex.org/W72953418","https://openalex.org/W78606972","https://openalex.org/W89830494","https://openalex.org/W116541839","https://openalex.org/W133702756","https://openalex.org/W134459671","https://openalex.org/W139194355","https://openalex.org/W139322340","https://openalex.org/W147950966","https://openalex.org/W165188274","https://openalex.org/W186167798","https://openalex.org/W193459320","https://openalex.org/W194026504","https://openalex.org/W195515244","https://openalex.org/W952867079","https://openalex.org/W1482532598","https://openalex.org/W1490156001","https://openalex.org/W1503377936","https://openalex.org/W1505051593","https://openalex.org/W1531103278","https://openalex.org/W1568333198","https://openalex.org/W1568917966","https://openalex.org/W1592751104","https://openalex.org/W1596863163","https://openalex.org/W1649706165","https://openalex.org/W1654880077","https://openalex.org/W1780039904","https://openalex.org/W1834186039","https://openalex.org/W1841530067","https://openalex.org/W1898652832","https://openalex.org/W1982345710","https://openalex.org/W1994952052","https://openalex.org/W1997714358","https://openalex.org/W2014832702","https://openalex.org/W2045794350","https://openalex.org/W2083568285","https://openalex.org/W2085380335","https://openalex.org/W2087418187","https://openalex.org/W2087432892","https://openalex.org/W2091138122","https://openalex.org/W2100657934","https://openalex.org/W2101013415","https://openalex.org/W2108309071","https://openalex.org/W2123298155","https://openalex.org/W2125626101","https://openalex.org/W2127574686","https://openalex.org/W2130919252","https://openalex.org/W2159521617","https://openalex.org/W2162181360","https://openalex.org/W2170489073","https://openalex.org/W2177097160","https://openalex.org/W2205491070","https://openalex.org/W2218364719","https://openalex.org/W2254118105","https://openalex.org/W2261194965","https://openalex.org/W2294892320","https://openalex.org/W2296202685","https://openalex.org/W2322754705","https://openalex.org/W2395675633","https://openalex.org/W2402431820","https://openalex.org/W2596756838","https://openalex.org/W2911462334","https://openalex.org/W2964181285","https://openalex.org/W2972978374","https://openalex.org/W2993883515","https://openalex.org/W3104044769","https://openalex.org/W3137139687","https://openalex.org/W4285719527","https://openalex.org/W7124142526"],"related_works":["https://openalex.org/W2478872016","https://openalex.org/W2991416512","https://openalex.org/W2810353660","https://openalex.org/W3189524441","https://openalex.org/W4414359636","https://openalex.org/W2568070906","https://openalex.org/W7100337798","https://openalex.org/W7099484115","https://openalex.org/W7099192396","https://openalex.org/W2254118105"],"abstract_inverted_index":{"Lifting":[0],"a":[1,10,38,95,101],"recent":[2],"proposal":[3],"by":[4,27,73],"Moreno-Centeno":[5],"and":[6,43,80,137],"Karp,":[7],"we":[8],"propose":[9],"general":[11,157],"framework":[12,24,56,88],"for":[13,19,60,66,89,105,125],"so-called":[14],"implicit":[15,62],"hitting":[16,63],"set":[17,64,148],"algorithms":[18,65],"reasoning":[20,69,76],"beyond":[21],"NP.":[22],"The":[23,55],"is":[25],"motivated":[26],"empirically":[28,118],"successful":[29],"specific":[30],"instantiations":[31,85],"of":[32,51,86,98,112,122,131,155],"the":[33,49,87,90,109,113,123,129,156],"approach\u2014based":[34],"on":[35,135],"interactions":[36],"between":[37],"Boolean":[39],"satisfiability":[40,53,92],"(SAT)":[41],"solver":[42],"an":[44,120,132],"integer":[45],"programming":[46,145],"(IP)":[47],"solver\u2014in":[48],"context":[50],"maximum":[52],"(MaxSAT).":[54],"opens":[57],"up":[58],"opportunities":[59],"developing":[61],"various":[67],"important":[68],"problems":[70],"in":[71],"KR":[72,103],"implementing":[74],"domain-specific":[75],"modules":[77],"with":[78],"SAT":[79],"IP":[81],"solvers.":[82],"We":[83,116,150],"detail":[84],"minimum":[91],"problem\u2014":[93],"as":[94,100,142],"natural":[96],"dual":[97],"MaxSAT\u2014and,":[99],"central":[102],"problem,":[104],"propositional":[106,126,139],"abduction,":[107],"covering":[108],"second":[110],"level":[111],"polynomial":[114],"hierarchy.":[115],"show":[117],"that":[119],"implementation":[121],"instantiation":[124],"abduction":[127,140],"surpasses":[128],"efficiency":[130],"approach":[133],"based":[134],"encoding":[136],"solving":[138],"instances":[141],"disjunctive":[143],"logic":[144],"under":[146],"answer":[147],"semantics.":[149],"also":[151],"study":[152],"key":[153],"properties":[154],"framework.":[158]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-11-04T00:00:00"}
