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Improving $$3N$$ Circuit Complexity Lower Bounds 改进 $3N$$ 电路复杂度下限
IF 1.4 3区 计算机科学
Computational Complexity Pub Date : 2023-12-01 DOI: 10.1007/s00037-023-00246-9
Magnus Gausdal Find, Alexander Golovnev, Edward A. Hirsch, Alexander S. Kulikov
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引用次数: 0
On vanishing sums of roots of unity in polynomial calculus and sum-of-squares 多项式微积分与平方和中单位根的消失和
3区 计算机科学
Computational Complexity Pub Date : 2023-11-12 DOI: 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}
引用次数: 0
A Lower Bound on the Complexity of Testing Grained Distributions 测试粒度分布复杂度的下界
3区 计算机科学
Computational Complexity Pub Date : 2023-10-26 DOI: 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}
引用次数: 3
Parallel algorithms for power circuits and the word problem of the Baumslag group 电力电路的并行算法与Baumslag群的词问题
3区 计算机科学
Computational Complexity Pub Date : 2023-09-13 DOI: 10.1007/s00037-023-00244-x
Caroline Mattes, Armin Weiß
{"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}
引用次数: 2
On Time-Space Tradeoffs for Bounded-Length Collisions in Merkle-Damgård Hashing 关于merkle - damg<s:1> rd哈希中有界长度碰撞的时空权衡
3区 计算机科学
Computational Complexity Pub Date : 2023-09-13 DOI: 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}
引用次数: 5
Absolute reconstruction for sums of powers of linear forms: degree 3 and beyond 线性形式幂和的绝对重构：3次及以上
IF 1.4 3区 计算机科学
Computational Complexity Pub Date : 2023-08-03 DOI: 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}
引用次数: 1
A Characterization of Functions over the Integers Computable in Polynomial Time Using Discrete Ordinary Differential Equations 用离散常微分方程表征多项式时间可计算整数上的函数
IF 1.4 3区 计算机科学
Computational Complexity Pub Date : 2023-07-12 DOI: 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}
引用次数: 2
Is it possible to improve Yao’s XOR lemma using reductions that exploit the efficiency of their oracle? 是否有可能通过利用oracle的效率来改进Yao的异或引理?
IF 1.4 3区 计算机科学
Computational Complexity Pub Date : 2023-05-23 DOI: 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}
引用次数: 3
A Complexity Trichotomy for k-Regular Asymmetric Spin Systems Using Number Theory 用数论研究k规则非对称自旋系统的复杂度三分法
IF 1.4 3区 计算机科学
Computational Complexity Pub Date : 2023-05-17 DOI: 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}
引用次数: 0
Explicit construction of q+1 regular local Ramanujan graphs, for all prime-powers q q+1正则局部Ramanujan图的显式构造，对于所有素数幂q
IF 1.4 3区 计算机科学
Computational Complexity Pub Date : 2023-04-06 DOI: 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}
引用次数: 0
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