Pub Date : 2022-10-22DOI: 10.1007/s00037-022-00229-2
Dean Doron, A. Ta-Shma, R. Tell
{"title":"On Hitting-Set Generators for Polynomials that Vanish Rarely","authors":"Dean Doron, A. Ta-Shma, R. Tell","doi":"10.1007/s00037-022-00229-2","DOIUrl":"https://doi.org/10.1007/s00037-022-00229-2","url":null,"abstract":"","PeriodicalId":51005,"journal":{"name":"Computational Complexity","volume":"31 1","pages":"1-62"},"PeriodicalIF":1.4,"publicationDate":"2022-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43642740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-10-12DOI: 10.1007/s00037-022-00230-9
Vishwas Bhargava, Sumanta K Ghosh
{"title":"Improved Hitting Set for Orbit of ROABPs","authors":"Vishwas Bhargava, Sumanta K Ghosh","doi":"10.1007/s00037-022-00230-9","DOIUrl":"https://doi.org/10.1007/s00037-022-00230-9","url":null,"abstract":"","PeriodicalId":51005,"journal":{"name":"Computational Complexity","volume":"31 1","pages":"1-45"},"PeriodicalIF":1.4,"publicationDate":"2022-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46624748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-05DOI: 10.4230/LIPIcs.ICALP.2019.96
Thomas Watson
We provide a complete picture of the extent to which amplification of success probability is possible for randomized algorithms having access to one NP oracle query, in the settings of two-sided, onesided, and zero-sided error. We generalize this picture to amplifying one-query algorithms with q-query algorithms, and we show our inclusions are tight for relativizing techniques.
{"title":"Amplification with One NP Oracle Query","authors":"Thomas Watson","doi":"10.4230/LIPIcs.ICALP.2019.96","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICALP.2019.96","url":null,"abstract":"We provide a complete picture of the extent to which amplification of success probability is possible for randomized algorithms having access to one NP oracle query, in the settings of two-sided, onesided, and zero-sided error. We generalize this picture to amplifying one-query algorithms with q-query algorithms, and we show our inclusions are tight for relativizing techniques.","PeriodicalId":51005,"journal":{"name":"Computational Complexity","volume":"31 1","pages":"1-47"},"PeriodicalIF":1.4,"publicationDate":"2022-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44501730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-05DOI: 10.1007/s00037-021-00219-w
Thomas Watson
{"title":"Amplification with One NP Oracle Query","authors":"Thomas Watson","doi":"10.1007/s00037-021-00219-w","DOIUrl":"https://doi.org/10.1007/s00037-021-00219-w","url":null,"abstract":"","PeriodicalId":51005,"journal":{"name":"Computational Complexity","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43346849","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-03DOI: 10.1007/s00037-021-00218-x
Andreas Galanis, L. A. Goldberg, Andrés Herrera-Poyatos
{"title":"The complexity of approximating the complex-valued Potts model","authors":"Andreas Galanis, L. A. Goldberg, Andrés Herrera-Poyatos","doi":"10.1007/s00037-021-00218-x","DOIUrl":"https://doi.org/10.1007/s00037-021-00218-x","url":null,"abstract":"","PeriodicalId":51005,"journal":{"name":"Computational Complexity","volume":"31 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2022-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43027109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-11-17DOI: 10.1007/s00037-021-00216-z
D. Itsykson, Artur Riazanov, Danil Sagunov, Petr Smirnov
{"title":"Correction to: Near-Optimal Lower Bounds on Regular Resolution Refutations of Tseitin Formulas for All Constant-Degree Graphs","authors":"D. Itsykson, Artur Riazanov, Danil Sagunov, Petr Smirnov","doi":"10.1007/s00037-021-00216-z","DOIUrl":"https://doi.org/10.1007/s00037-021-00216-z","url":null,"abstract":"","PeriodicalId":51005,"journal":{"name":"Computational Complexity","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48946839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-10-09DOI: 10.1007/s00037-022-00234-5
M. Kaminski, I. Shparlinski, M. Waldschmidt
{"title":"On sets of linear forms of maximal complexity","authors":"M. Kaminski, I. Shparlinski, M. Waldschmidt","doi":"10.1007/s00037-022-00234-5","DOIUrl":"https://doi.org/10.1007/s00037-022-00234-5","url":null,"abstract":"","PeriodicalId":51005,"journal":{"name":"Computational Complexity","volume":"32 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46604563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-27DOI: 10.1007/s00037-021-00213-2
D. Itsykson, Artur Riazanov, Danil Sagunov, Petr Smirnov
{"title":"Near-Optimal Lower Bounds on Regular Resolution Refutations of Tseitin Formulas for All Constant-Degree Graphs","authors":"D. Itsykson, Artur Riazanov, Danil Sagunov, Petr Smirnov","doi":"10.1007/s00037-021-00213-2","DOIUrl":"https://doi.org/10.1007/s00037-021-00213-2","url":null,"abstract":"","PeriodicalId":51005,"journal":{"name":"Computational Complexity","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00037-021-00213-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43382025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-07-02DOI: 10.1007/s00037-021-00210-5
T. Pitassi, Morgan Shirley, Thomas Watson
{"title":"Nondeterministic and Randomized Boolean Hierarchies in Communication Complexity","authors":"T. Pitassi, Morgan Shirley, Thomas Watson","doi":"10.1007/s00037-021-00210-5","DOIUrl":"https://doi.org/10.1007/s00037-021-00210-5","url":null,"abstract":"","PeriodicalId":51005,"journal":{"name":"Computational Complexity","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2021-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00037-021-00210-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47006503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-05-01DOI: 10.4230/LIPIcs.STACS.2020.60
J. Torán, Florian Wörz
We show a new connection between the clause space measure in tree-like resolution and the reversible pebble game on graphs. Using this connection, we provide several formula classes for which there is a logarithmic factor separation between the clause space complexity measure in tree-like and general resolution. We also provide upper bounds for tree-like resolution clause space in terms of general resolution clause and variable space. In particular, we show that for any formula F , its tree-like resolution clause space is upper bounded by space $$(pi)$$ ( π ) $$(log({rm time}(pi))$$ ( log ( time ( π ) ) , where $$pi$$ π is any general resolution refutation of F . This holds considering as space $$(pi)$$ ( π ) the clause space of the refutation as well as considering its variable space. For the concrete case of Tseitin formulas, we are able to improve this bound to the optimal bound space $$(pi)log n$$ ( π ) log n , where n is the number of vertices of the corresponding graph
{"title":"Reversible Pebble Games and the Relation Between Tree-Like and General Resolution Space","authors":"J. Torán, Florian Wörz","doi":"10.4230/LIPIcs.STACS.2020.60","DOIUrl":"https://doi.org/10.4230/LIPIcs.STACS.2020.60","url":null,"abstract":"We show a new connection between the clause space measure in tree-like resolution and the reversible pebble game on graphs. Using this connection, we provide several formula classes for which there is a logarithmic factor separation between the clause space complexity measure in tree-like and general resolution. We also provide upper bounds for tree-like resolution clause space in terms of general resolution clause and variable space. In particular, we show that for any formula F , its tree-like resolution clause space is upper bounded by space $$(pi)$$ ( π ) $$(log({rm time}(pi))$$ ( log ( time ( π ) ) , where $$pi$$ π is any general resolution refutation of F . This holds considering as space $$(pi)$$ ( π ) the clause space of the refutation as well as considering its variable space. For the concrete case of Tseitin formulas, we are able to improve this bound to the optimal bound space $$(pi)log n$$ ( π ) log n , where n is the number of vertices of the corresponding graph","PeriodicalId":51005,"journal":{"name":"Computational Complexity","volume":"30 1","pages":"1-37"},"PeriodicalIF":1.4,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44065246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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