{"id":"https://openalex.org/W4415267733","doi":"https://doi.org/10.1137/22m153851x","title":"On Bounded Depth Proofs for Tseitin Formulas on the Grid; Revisited","display_name":"On Bounded Depth Proofs for Tseitin Formulas on the Grid; Revisited","publication_year":2025,"publication_date":"2025-10-16","ids":{"openalex":"https://openalex.org/W4415267733","doi":"https://doi.org/10.1137/22m153851x"},"language":"en","primary_location":{"id":"doi:10.1137/22m153851x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m153851x","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/A5013166918","display_name":"Johan H\u00e5stad","orcid":"https://orcid.org/0000-0002-5379-345X"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Johan H\u00e5stad","raw_affiliation_strings":["KTH Royal Institute of Technology, Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086575008","display_name":"Kilian Risse","orcid":"https://orcid.org/0000-0002-6913-3341"},"institutions":[{"id":"https://openalex.org/I187531555","display_name":"Lund University","ror":"https://ror.org/012a77v79","country_code":"SE","type":"education","lineage":["https://openalex.org/I187531555"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Kilian Risse","raw_affiliation_strings":["Lund University, LTH, Lund, Sweden"],"raw_orcid":"https://orcid.org/0000-0002-6913-3341","affiliations":[{"raw_affiliation_string":"Lund University, LTH, Lund, Sweden","institution_ids":["https://openalex.org/I187531555"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5013166918"],"corresponding_institution_ids":["https://openalex.org/I86987016"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.27255626,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"54","issue":"5","first_page":"FOCS22","last_page":"288"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12923","display_name":"Digital Image Processing Techniques","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T11567","display_name":"semigroups and automata theory","score":0.9980000257492065,"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/lemma","display_name":"Lemma (botany)","score":0.8873999714851379},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7976999878883362},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7865999937057495},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5440000295639038},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4401000142097473},{"id":"https://openalex.org/keywords/contradiction","display_name":"Contradiction","score":0.3837999999523163},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.3610999882221222}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.8873999714851379},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7976999878883362},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7865999937057495},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6407999992370605},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5906999707221985},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5440000295639038},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4401000142097473},{"id":"https://openalex.org/C2776728590","wikidata":"https://www.wikidata.org/wiki/Q363948","display_name":"Contradiction","level":2,"score":0.3837999999523163},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.3610999882221222},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34610000252723694},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.29089999198913574},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.289900004863739},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2879999876022339},{"id":"https://openalex.org/C105605280","wikidata":"https://www.wikidata.org/wiki/Q7249999","display_name":"Proof complexity","level":3,"score":0.27959999442100525},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.262800008058548},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/22m153851x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m153851x","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"},{"id":"pmh:oai:lup.lub.lu.se:05e83ea2-b7f4-414f-b67b-8a85d57eed9a","is_oa":false,"landing_page_url":"https://lup.lub.lu.se/record/05e83ea2-b7f4-414f-b67b-8a85d57eed9a","pdf_url":null,"source":{"id":"https://openalex.org/S4306400536","display_name":"Lund University Publications (Lund University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I187531555","host_organization_name":"Lund University","host_organization_lineage":["https://openalex.org/I187531555"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0097-5397","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3052677248","display_name":null,"funder_award_id":"200021-184656","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320322327","display_name":"Knut och Alice Wallenbergs Stiftelse","ror":"https://ror.org/004hzzk67"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1563012911","https://openalex.org/W1988083342","https://openalex.org/W2029390834","https://openalex.org/W2045924252","https://openalex.org/W2060270693","https://openalex.org/W2069767473","https://openalex.org/W2075146634","https://openalex.org/W2075906306","https://openalex.org/W2089534194","https://openalex.org/W2091937735","https://openalex.org/W2169713712","https://openalex.org/W3105030258"],"related_works":[],"abstract_inverted_index":{"We":[0,17],"study":[1],"Frege":[2,110],"proofs":[3],"using":[4],"depth-d":[5],"Boolean":[6],"formulas":[7],"for":[8,82,103],"the":[9,24,31,72,89,100,124,128],"Tseitin":[10,90],"contradiction":[11],"on":[12,55,144],"n":[13,15],"\\times":[14],"grids.":[16],"prove":[18],"that":[19],"if":[20],"each":[21],"line":[22],"in":[23,37,114,119,127],"proof":[25,105],"is":[26,35,67],"of":[27,33,45,57,75,85,107,131,146],"size":[28,106],"M,":[29],"then":[30],"number":[32],"lines":[34],"exponential":[36,113,118],"n/(log":[38],"M)O(d).":[39],"This":[40,122],"strengthens":[41,123],"a":[42,68,83],"recent":[43],"result":[44],"Pitassi,":[46],"Ramakrishman,":[47],"and":[48,136],"Tan":[49],"[2022":[50],"IEEE":[51,140],"62nd":[52],"Annual":[53,142],"Symposium":[54,143],"Foundations":[56,145],"Computer":[58,147],"Science,":[59,148],"2022,":[60,149],"pp.":[61,150],"445-456].":[62],"The":[63,92],"key":[64],"technical":[65],"step":[66],"multiswitching":[69],"lemma":[70,74,94],"extending":[71],"switching":[73],"H\\rastad":[76,135],"[J.":[77,134],"ACM,":[78],"68":[79],"(2021),":[80],"1]":[81],"space":[84],"restrictions":[86],"related":[87],"to":[88,98,117],"contradiction.":[91],"strengthened":[93],"also":[95],"allows":[96],"us":[97],"improve":[99],"lower":[101],"bound":[102],"standard":[104],"bounded":[108],"depth":[109],"refutations":[111],"from":[112],"\\Omega(\\~":[115,120],"n1/59d)":[116],"n1/d).":[121],"bounds":[125],"given":[126],"preliminary":[129],"version":[130],"this":[132],"paper":[133],"K.":[137],"Risse,":[138],"2022":[139],"63rd":[141],"1138-1149].":[151]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-17T00:00:00"}