{"id":"https://openalex.org/W2807924989","doi":"https://doi.org/10.1137/17m113304x","title":"The Complexity of Boolean Holant Problems with Nonnegative Weights","display_name":"The Complexity of Boolean Holant Problems with Nonnegative Weights","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2807924989","doi":"https://doi.org/10.1137/17m113304x","mag":"2807924989"},"language":"en","primary_location":{"id":"doi:10.1137/17m113304x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m113304x","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/A5033357253","display_name":"Jiabao Lin","orcid":"https://orcid.org/0000-0002-5493-8497"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiabao Lin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5079106687","display_name":"Hanpin Wang","orcid":"https://orcid.org/0000-0002-2439-1670"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hanpin Wang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4724,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.90462749,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"47","issue":"3","first_page":"798","last_page":"828"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7742716670036316},{"id":"https://openalex.org/keywords/arity","display_name":"Arity","score":0.7576647996902466},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6648856997489929},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.541970431804657},{"id":"https://openalex.org/keywords/counting-problem","display_name":"Counting problem","score":0.5310314893722534},{"id":"https://openalex.org/keywords/boolean-domain","display_name":"Boolean domain","score":0.500330924987793},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.4955536127090454},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4897899627685547},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4846244752407074},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.45739516615867615},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.45527711510658264},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.41916772723197937},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.20708692073822021},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.12124213576316833},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12073296308517456}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7742716670036316},{"id":"https://openalex.org/C110546421","wikidata":"https://www.wikidata.org/wiki/Q1315869","display_name":"Arity","level":2,"score":0.7576647996902466},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6648856997489929},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.541970431804657},{"id":"https://openalex.org/C16592021","wikidata":"https://www.wikidata.org/wiki/Q5177154","display_name":"Counting problem","level":2,"score":0.5310314893722534},{"id":"https://openalex.org/C4926405","wikidata":"https://www.wikidata.org/wiki/Q3269980","display_name":"Boolean domain","level":5,"score":0.500330924987793},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.4955536127090454},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4897899627685547},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4846244752407074},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.45739516615867615},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.45527711510658264},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.41916772723197937},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.20708692073822021},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.12124213576316833},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12073296308517456},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/17m113304x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m113304x","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":[{"id":"https://openalex.org/G223583203","display_name":"\u57fa\u4e8e\u5206\u79bb\u903b\u8f91\u7684\u7a0b\u5e8f\u9a8c\u8bc1\u65b9\u6cd5\u7814\u7a76","funder_award_id":"61170299","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5181736916","display_name":null,"funder_award_id":"61370053","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8177734834","display_name":null,"funder_award_id":"61572003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1991486497","https://openalex.org/W1997590411","https://openalex.org/W2000217912","https://openalex.org/W2003722559","https://openalex.org/W2033026830","https://openalex.org/W2040145343","https://openalex.org/W2052936500","https://openalex.org/W2078752178","https://openalex.org/W2091345559","https://openalex.org/W2092436554","https://openalex.org/W2097738137","https://openalex.org/W2112167630","https://openalex.org/W2118223706","https://openalex.org/W2131358503","https://openalex.org/W2134600856","https://openalex.org/W2141382791","https://openalex.org/W2145707075","https://openalex.org/W2244287056","https://openalex.org/W2567588342","https://openalex.org/W2570207426","https://openalex.org/W2626596188","https://openalex.org/W2913798276","https://openalex.org/W2963623916","https://openalex.org/W3124201190","https://openalex.org/W4213390282"],"related_works":["https://openalex.org/W1820097894","https://openalex.org/W1716185740","https://openalex.org/W4310635490","https://openalex.org/W1671100188","https://openalex.org/W4226227610","https://openalex.org/W2003722559","https://openalex.org/W4389488889","https://openalex.org/W4320481209","https://openalex.org/W2952746417","https://openalex.org/W2807924989"],"abstract_inverted_index":{"Holant":[0,22,33],"problem":[1,68,124],"is":[2,29,46,70,90,106,110,125],"a":[3,16,54,91,114],"general":[4],"framework":[5],"to":[6,48,113],"study":[7],"the":[8,30,61,67,76,123],"computational":[9],"complexity":[10,17],"of":[11,56,82,94,96],"counting":[12],"problems.":[13],"We":[14,64],"prove":[15],"dichotomy":[18,34],"theorem":[19],"for":[20],"Boolean":[21,62],"problems":[23],"with":[24],"nonnegative":[25,57],"algebraic":[26],"weights.":[27],"It":[28],"first":[31],"complete":[32],"where":[35],"constraint":[36],"functions":[37,58,95],"are":[38],"not":[39],"necessarily":[40],"symmetric":[41],"and":[42],"no":[43],"auxiliary":[44],"function":[45,77,87,103],"assumed":[47],"be":[49,53],"available.":[50],"Let":[51],"$\\mathcal{F}$":[52,79,89,105,109],"set":[55,78],"defined":[59],"on":[60],"domain.":[63],"show":[65],"that":[66],"Holant$(\\mathcal{F})$":[69],"computable":[71],"in":[72,88,104],"polynomial":[73],"time":[74],"if":[75],"satisfies":[80],"one":[81],"three":[83],"conditions:":[84],"(1)":[85],"every":[86,102],"tensor":[92],"product":[93,115],"arity":[97],"at":[98],"most":[99],"2;":[100],"(2)":[101],"affine;":[107],"(3)":[108],"holographically":[111],"transformable":[112],"type":[116],"by":[117],"some":[118],"real":[119],"orthogonal":[120],"matrix.":[121],"Otherwise":[122],"#P-hard.":[126]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}