Pub Date : 2023-12-01DOI: 10.1007/s00037-023-00246-9
Magnus Gausdal Find, Alexander Golovnev, Edward A. Hirsch, Alexander S. Kulikov
{"title":"Improving $$3N$$ Circuit Complexity Lower Bounds","authors":"Magnus Gausdal Find, Alexander Golovnev, Edward A. Hirsch, Alexander S. Kulikov","doi":"10.1007/s00037-023-00246-9","DOIUrl":"https://doi.org/10.1007/s00037-023-00246-9","url":null,"abstract":"","PeriodicalId":51005,"journal":{"name":"Computational Complexity","volume":"62 ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139021866","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 : 2023-11-12DOI: 10.1007/s00037-023-00242-z
Ilario Bonacina, Nicola Galesi, Massimo Lauria
{"title":"On vanishing sums of roots of unity in polynomial calculus and sum-of-squares","authors":"Ilario Bonacina, Nicola Galesi, Massimo Lauria","doi":"10.1007/s00037-023-00242-z","DOIUrl":"https://doi.org/10.1007/s00037-023-00242-z","url":null,"abstract":"","PeriodicalId":51005,"journal":{"name":"Computational Complexity","volume":"82 18","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135037342","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 : 2023-10-26DOI: 10.1007/s00037-023-00245-w
Oded Goldreich, Dana Ron
{"title":"A Lower Bound on the Complexity of Testing Grained Distributions","authors":"Oded Goldreich, Dana Ron","doi":"10.1007/s00037-023-00245-w","DOIUrl":"https://doi.org/10.1007/s00037-023-00245-w","url":null,"abstract":"","PeriodicalId":51005,"journal":{"name":"Computational Complexity","volume":"104 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136377194","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 : 2023-09-13DOI: 10.1007/s00037-023-00244-x
Caroline Mattes, Armin Weiß
Abstract Power circuits have been introduced in 2012 by Myasnikov, Ushakov and Won as a data structure for non-elementarily compressed integers supporting the arithmetic operations addition and $$(x,y) mapsto xcdot 2^y$$ (x,y)↦x·2y . The same authors applied power circuits to give a polynomial time solution to the word problem of the Baumslag group, which has a non-elementary Dehn function. In this work, we examine power circuits and the word problem of the Baumslag group under parallel complexity aspects. In particular, we establish that the word problem of the Baumslag group can be solved in NC $$textemdash$$ — even though one of the essential steps is to compare two integers given by power circuits and this, in general, is shown to be P -complete. The key observation is that the depth of the occurring power circuits is logarithmic and such power circuits can be compared in NC .
{"title":"Parallel algorithms for power circuits and the word problem of the Baumslag group","authors":"Caroline Mattes, Armin Weiß","doi":"10.1007/s00037-023-00244-x","DOIUrl":"https://doi.org/10.1007/s00037-023-00244-x","url":null,"abstract":"Abstract Power circuits have been introduced in 2012 by Myasnikov, Ushakov and Won as a data structure for non-elementarily compressed integers supporting the arithmetic operations addition and $$(x,y) mapsto xcdot 2^y$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>,</mml:mo> <mml:mi>y</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>↦</mml:mo> <mml:mi>x</mml:mi> <mml:mo>·</mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mi>y</mml:mi> </mml:msup> </mml:mrow> </mml:math> . The same authors applied power circuits to give a polynomial time solution to the word problem of the Baumslag group, which has a non-elementary Dehn function. In this work, we examine power circuits and the word problem of the Baumslag group under parallel complexity aspects. In particular, we establish that the word problem of the Baumslag group can be solved in NC $$textemdash$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mo>—</mml:mo> </mml:math> even though one of the essential steps is to compare two integers given by power circuits and this, in general, is shown to be P -complete. The key observation is that the depth of the occurring power circuits is logarithmic and such power circuits can be compared in NC .","PeriodicalId":51005,"journal":{"name":"Computational Complexity","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134989638","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 : 2023-09-13DOI: 10.1007/s00037-023-00243-y
Ashrujit Ghoshal, Ilan Komargodski
{"title":"On Time-Space Tradeoffs for Bounded-Length Collisions in Merkle-Damgård Hashing","authors":"Ashrujit Ghoshal, Ilan Komargodski","doi":"10.1007/s00037-023-00243-y","DOIUrl":"https://doi.org/10.1007/s00037-023-00243-y","url":null,"abstract":"","PeriodicalId":51005,"journal":{"name":"Computational Complexity","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135733834","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 : 2023-08-03DOI: 10.1007/s00037-023-00239-8
Pascal Koiran, Subhayan Saha
{"title":"Absolute reconstruction for sums of powers of linear forms: degree 3 and beyond","authors":"Pascal Koiran, Subhayan Saha","doi":"10.1007/s00037-023-00239-8","DOIUrl":"https://doi.org/10.1007/s00037-023-00239-8","url":null,"abstract":"","PeriodicalId":51005,"journal":{"name":"Computational Complexity","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49359490","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 : 2023-07-12DOI: 10.1007/s00037-023-00240-1
Olivier Bournez, Arnaud Durand
{"title":"A Characterization of Functions over the Integers Computable in Polynomial Time Using Discrete Ordinary Differential Equations","authors":"Olivier Bournez, Arnaud Durand","doi":"10.1007/s00037-023-00240-1","DOIUrl":"https://doi.org/10.1007/s00037-023-00240-1","url":null,"abstract":"","PeriodicalId":51005,"journal":{"name":"Computational Complexity","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46410767","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 : 2023-05-23DOI: 10.1007/s00037-023-00238-9
Ronen Shaltiel
{"title":"Is it possible to improve Yao’s XOR lemma using reductions that exploit the efficiency of their oracle?","authors":"Ronen Shaltiel","doi":"10.1007/s00037-023-00238-9","DOIUrl":"https://doi.org/10.1007/s00037-023-00238-9","url":null,"abstract":"","PeriodicalId":51005,"journal":{"name":"Computational Complexity","volume":"32 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42037960","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 : 2023-05-17DOI: 10.1007/s00037-023-00237-w
Jin-Yi Cai, Zhiguo Fu, K. Girstmair, M. Kowalczyk
{"title":"A Complexity Trichotomy for k-Regular Asymmetric Spin Systems Using Number Theory","authors":"Jin-Yi Cai, Zhiguo Fu, K. Girstmair, M. Kowalczyk","doi":"10.1007/s00037-023-00237-w","DOIUrl":"https://doi.org/10.1007/s00037-023-00237-w","url":null,"abstract":"","PeriodicalId":51005,"journal":{"name":"Computational Complexity","volume":" ","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44214086","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 : 2023-04-06DOI: 10.1007/s00037-023-00235-y
Rishabh Batra, Nitin Saxena, Devansh Shringi
{"title":"Explicit construction of q+1 regular local Ramanujan graphs, for all prime-powers q","authors":"Rishabh Batra, Nitin Saxena, Devansh Shringi","doi":"10.1007/s00037-023-00235-y","DOIUrl":"https://doi.org/10.1007/s00037-023-00235-y","url":null,"abstract":"","PeriodicalId":51005,"journal":{"name":"Computational Complexity","volume":"32 1","pages":"1-34"},"PeriodicalIF":1.4,"publicationDate":"2023-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46512619","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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