{"id":"https://openalex.org/W7161243267","doi":"https://doi.org/10.48550/arxiv.2605.14093","title":"New Algorithms for Parity-SAT and Its Bounded-Occurrence Versions","display_name":"New Algorithms for Parity-SAT and Its Bounded-Occurrence Versions","publication_year":2026,"publication_date":"2026-05-13","ids":{"openalex":"https://openalex.org/W7161243267","doi":"https://doi.org/10.48550/arxiv.2605.14093"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.14093","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.14093","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.14093","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021519204","display_name":"Sanjay Jain","orcid":"https://orcid.org/0000-0002-6606-3077"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jain, Sanjay","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136242278","display_name":"Junqiang Peng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peng, Junqiang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136222925","display_name":"Frank Stephan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stephan, Frank","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136198097","display_name":"Haoyun Tang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tang, Haoyun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5136262442","display_name":"Mingyu Xiao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiao, Mingyu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.5527999997138977,"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/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.5527999997138977,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.18019999563694,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.03310000151395798,"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/exponential-time-hypothesis","display_name":"Exponential time hypothesis","score":0.6417999863624573},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.632099986076355},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.604200005531311},{"id":"https://openalex.org/keywords/parity","display_name":"Parity (physics)","score":0.5042999982833862},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.47519999742507935},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.47380000352859497},{"id":"https://openalex.org/keywords/efficient-algorithm","display_name":"Efficient algorithm","score":0.42809998989105225},{"id":"https://openalex.org/keywords/exponential-growth","display_name":"Exponential growth","score":0.42579999566078186},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.399399995803833}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6535000205039978},{"id":"https://openalex.org/C71017364","wikidata":"https://www.wikidata.org/wiki/Q5421532","display_name":"Exponential time hypothesis","level":3,"score":0.6417999863624573},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.632099986076355},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.604200005531311},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.544700026512146},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.5042999982833862},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.47519999742507935},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.47380000352859497},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4526999890804291},{"id":"https://openalex.org/C3018263672","wikidata":"https://www.wikidata.org/wiki/Q1296251","display_name":"Efficient algorithm","level":2,"score":0.42809998989105225},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.42579999566078186},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.399399995803833},{"id":"https://openalex.org/C206175624","wikidata":"https://www.wikidata.org/wiki/Q595731","display_name":"Branching (polymer chemistry)","level":2,"score":0.37310001254081726},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.3562000095844269},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.34929999709129333},{"id":"https://openalex.org/C2988809283","wikidata":"https://www.wikidata.org/wiki/Q1514868","display_name":"Combinatorial algorithms","level":2,"score":0.34779998660087585},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3391000032424927},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3375999927520752},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.33709999918937683},{"id":"https://openalex.org/C200415742","wikidata":"https://www.wikidata.org/wiki/Q1350285","display_name":"True quantified Boolean formula","level":2,"score":0.3239000141620636},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.3107999861240387},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.2973000109195709},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2944999933242798},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C64731005","wikidata":"https://www.wikidata.org/wiki/Q333464","display_name":"Analysis of algorithms","level":2,"score":0.26089999079704285}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.14093","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.14093","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.14093","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.14093","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Parity-SAT":[0,42],"is":[1],"the":[2,29,36,58,67,119,128,148,152,166,182,187],"problem":[3,33],"of":[4,15,28,60,91,197],"determining":[5],"whether":[6],"a":[7,19,25,88,113,134,193],"given":[8],"CNF":[9],"formula":[10,167],"has":[11],"an":[12,157],"odd":[13],"number":[14],"satisfying":[16],"assignments.":[17],"As":[18],"canonical":[20],"$\\oplus$P-complete":[21],"problem,":[22],"it":[23],"represents":[24],"fundamental":[26],"variant":[27],"exact":[30,189,216],"model":[31,217],"counting":[32,190],"(#SAT).":[34],"Under":[35],"Strong":[37],"Exponential":[38],"Time":[39],"Hypothesis":[40],"(SETH),":[41],"admits":[43,207],"no":[44],"$O^*((2-\\varepsilon)^n)$-time":[45],"or":[46,69,143],"$O^*((2-\\varepsilon)^m)$-time":[47],"algorithm":[48,138,159],"for":[49,122,127,160,186],"any":[50],"constant":[51],"$\\varepsilon>0$,":[52],"where":[53,96,163],"$n$":[54],"and":[55,62,87,105,211,219],"$m$":[56],"denote":[57],"numbers":[59],"variables":[61],"clauses,":[63,104],"respectively.":[64],"Thus,":[65],"breaking":[66,118],"$2^n$":[68],"$2^m$":[70,120],"barrier":[71,83,121],"appears":[72,99],"impossible":[73],"in":[74,100,140],"full":[75],"generality.":[76],"In":[77],"this":[78,82],"work,":[79],"we":[80,111,132,155],"revisit":[81],"through":[84],"structural":[85,149,209],"restrictions":[86],"refined":[89],"exploitation":[90],"parity.":[92],"We":[93],"study":[94],"Parity-$d$-occ-SAT,":[95],"each":[97],"variable":[98],"at":[101],"most":[102],"$d$":[103],"obtain":[106,156],"three":[107],"main":[108],"results.":[109],"First,":[110],"design":[112],"randomized":[114],"$O^*(2^{m(1-1/O(d))})$-time":[115],"algorithm,":[116],"thereby":[117],"every":[123],"fixed":[124],"$d$.":[125],"Second,":[126],"special":[129],"case":[130],"$d=2$,":[131],"develop":[133],"significantly":[135],"sharper":[136],"branching":[137,214],"running":[139],"$O^*(1.1193^n)$":[141],"time":[142],"$O^*(1.3248^m)$":[144],"time.":[145],"Third,":[146],"leveraging":[147],"insights":[150],"underlying":[151],"$d=2$":[153],"case,":[154],"$O^*(1.1052^L)$-time":[158],"general":[161],"Parity-SAT,":[162],"$L$":[164],"denotes":[165],"length.":[168],"All":[169],"algorithms":[170],"use":[171],"only":[172],"polynomial":[173],"space.":[174],"Notably,":[175],"our":[176,202],"running-time":[177],"bounds":[178,185],"are":[179],"better":[180],"than":[181,215],"best":[183],"known":[184],"corresponding":[188],"counterparts,":[191],"highlighting":[192],"genuine":[194],"algorithmic":[195],"advantage":[196],"parity":[198,206],"over":[199],"counting.":[200],"Conceptually,":[201],"results":[203],"demonstrate":[204],"that":[205,220],"finer":[208],"reductions":[210],"more":[212],"efficient":[213],"counting,":[218],"bounded":[221],"occurrence":[222],"can":[223],"be":[224],"systematically":[225],"leveraged":[226],"to":[227],"circumvent":[228],"classical":[229],"exponential":[230],"barriers.":[231]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-16T00:00:00"}