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A New Fast Computation of a Permanent 一种新的永常数的快速计算方法
arXiv: Computational Complexity Pub Date : 2020-04-07 DOI: 10.1088/1757-899X/790/1/012057
Niu Xuewei, Su Sheng-hui, Z. Jianghua
{"title":"A New Fast Computation of a Permanent","authors":"Niu Xuewei, Su Sheng-hui, Z. Jianghua","doi":"10.1088/1757-899X/790/1/012057","DOIUrl":"https://doi.org/10.1088/1757-899X/790/1/012057","url":null,"abstract":"This paper proposes a general algorithm called Store-zechin for quickly computing the permanent of an arbitrary square matrix. Its key idea is storage, multiplexing, and recursion. That is, in a recursive process, some sub-terms which have already been calculated are no longer calculated, but are directly substituted with the previous calculation results. The new algorithm utilizes sufficiently computer memories and stored data to speed the computation of a permanent. The Analyses show that computating the permanent of an n * n matrix by Store-zechin requires (2^(n - 1)- 1)n multiplications and (2^(n-1))(n - 2)+ 1 additions while does (2^n - 1)n + 1 multiplications and (2^n - n)(n + 1)- 2 additions by the Ryser algorithm, and does (2^(n - 1))n + (n + 2) multiplications and (2^(n - 1))(n + 1)+ (n^2 - n -1) additions by the R-N-W algorithm. Therefore, Store-zechin is excellent more than the latter two algorithms, and has a better application prospect.","PeriodicalId":113162,"journal":{"name":"arXiv: Computational Complexity","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129701580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Complexity Theory, Game Theory, and Economics: The Barbados Lectures 复杂性理论、博弈论和经济学:巴巴多斯讲座
arXiv: Computational Complexity Pub Date : 2020-02-10 DOI: 10.1561/9781680836554
T. Roughgarden
{"title":"Complexity Theory, Game Theory, and Economics: The Barbados Lectures","authors":"T. Roughgarden","doi":"10.1561/9781680836554","DOIUrl":"https://doi.org/10.1561/9781680836554","url":null,"abstract":"This document collects the lecture notes from my mini-course \"Complexity Theory, Game Theory, and Economics,\" taught at the Bellairs Research Institute of McGill University, Holetown, Barbados, February 19--23, 2017, as the 29th McGill Invitational Workshop on Computational Complexity. The goal of this mini-course is twofold: (i) to explain how complexity theory has helped illuminate several barriers in economics and game theory; and (ii) to illustrate how game-theoretic questions have led to new and interesting complexity theory, including recent several breakthroughs. It consists of two five-lecture sequences: the Solar Lectures, focusing on the communication and computational complexity of computing equilibria; and the Lunar Lectures, focusing on applications of complexity theory in game theory and economics. No background in game theory is assumed.","PeriodicalId":113162,"journal":{"name":"arXiv: Computational Complexity","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134241814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
ARRIVAL: A Zero-Player Graph Game in NP ∩ coNP 到达:NP∩coNP中的零玩家图游戏
arXiv: Computational Complexity Pub Date : 2016-05-11 DOI: 10.1007/978-3-319-44479-6_14
Jérôme Dohrau, B. Gartner, Manuel Kohler, J. Matouvsek, E. Welzl
{"title":"ARRIVAL: A Zero-Player Graph Game in NP ∩ coNP","authors":"Jérôme Dohrau, B. Gartner, Manuel Kohler, J. Matouvsek, E. Welzl","doi":"10.1007/978-3-319-44479-6_14","DOIUrl":"https://doi.org/10.1007/978-3-319-44479-6_14","url":null,"abstract":"","PeriodicalId":113162,"journal":{"name":"arXiv: Computational Complexity","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132036923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 13
Fractal dimension versus process complexity 分形维数与过程复杂性
arXiv: Computational Complexity Pub Date : 2013-09-06 DOI: 10.1155/2016/5030593
J. Joosten, F. Soler-Toscano, H. Zenil
{"title":"Fractal dimension versus process complexity","authors":"J. Joosten, F. Soler-Toscano, H. Zenil","doi":"10.1155/2016/5030593","DOIUrl":"https://doi.org/10.1155/2016/5030593","url":null,"abstract":"Complexity measures are designed to capture complex behavior and quantify *how* complex, according to that measure, that particular behavior is. It can be expected that different complexity measures from possibly entirely different fields are related to each other in a non-trivial fashion. Here we study small Turing machines (TMs) with two symbols, and two and three states. For any particular such machine $tau$ and any particular input $x$ we consider what we call the 'space-time' diagram which is the collection of consecutive tape configurations of the computation $tau(x)$. In our setting, we define fractal dimension of a Turing machine as the limiting fractal dimension of the corresponding space-time diagram. It turns out that there is a very strong relation between the fractal dimension of a Turing machine of the above-specified type and its runtime complexity. In particular, a TM with three states and two colors runs in at most linear time iff its dimension is 2, and its dimension is 1 iff it runs in super-polynomial time and it uses polynomial space. If a TM runs in time $O(x^n)$ we have empirically verified that the corresponding dimension is $(n+1)/n$, a result that we can only partially prove. We find the results presented here remarkable because they relate two completely different complexity measures: the geometrical fractal dimension on the one side versus the time complexity of a computation on the other side.","PeriodicalId":113162,"journal":{"name":"arXiv: Computational Complexity","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127247444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
Geometric Complexity Theory V: Efficient algorithms for Noether Normalization 几何复杂性理论V: Noether归一化的有效算法
arXiv: Computational Complexity Pub Date : 2012-09-26 DOI: 10.1090/JAMS/864
K. Mulmuley
{"title":"Geometric Complexity Theory V: Efficient algorithms for Noether Normalization","authors":"K. Mulmuley","doi":"10.1090/JAMS/864","DOIUrl":"https://doi.org/10.1090/JAMS/864","url":null,"abstract":"We study a basic algorithmic problem in algebraic geometry, which we call NNL, of constructing a normalizing map as per Noether's Normalization Lemma. For general explicit varieties, as formally defined in this paper, we give a randomized polynomial-time Monte Carlo algorithm for this problem. For some interesting cases of explicit varieties, we give deterministic quasi-polynomial time algorithms. These may be contrasted with the standard EXPSPACE-algorithms for these problems in computational algebraic geometry. \u0000In particular, we show that: \u0000(1) The categorical quotient for any finite dimensional representation $V$ of $SL_m$, with constant $m$, is explicit in characteristic zero. \u0000(2) NNL for this categorical quotient can be solved deterministically in time quasi-polynomial in the dimension of $V$. \u0000(3) The categorical quotient of the space of $r$-tuples of $m times m$ matrices by the simultaneous conjugation action of $SL_m$ is explicit in any characteristic. \u0000(4) NNL for this categorical quotient can be solved deterministically in time quasi-polynomial in $m$ and $r$ in any characteristic $p$ not in $[2, m/2]$. \u0000(5) NNL for every explicit variety in zero or large enough characteristic can be solved deterministically in quasi-polynomial time, assuming the hardness hypothesis for the permanent in geometric complexity theory. \u0000The last result leads to a geometric complexity theory approach to put NNL for every explicit variety in P.","PeriodicalId":113162,"journal":{"name":"arXiv: Computational Complexity","volume":"146 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130467761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 44
Proceedings CSR 2010 Workshop on High Productivity Computations 会议记录CSR 2010高生产力计算研讨会
arXiv: Computational Complexity Pub Date : 2011-03-08 DOI: 10.4204/EPTCS.52
F. Ablayev, B. Coecke, Alexander Vasiliev
{"title":"Proceedings CSR 2010 Workshop on High Productivity Computations","authors":"F. Ablayev, B. Coecke, Alexander Vasiliev","doi":"10.4204/EPTCS.52","DOIUrl":"https://doi.org/10.4204/EPTCS.52","url":null,"abstract":"This volume contains the proceedings of the Workshop on High Productivity Computations (HPC 2010) which took place on June 21-22 in Kazan, Russia. This workshop was held as a satellite workshop of the 5th International Computer Science Symposium in Russia (CSR 2010). \u0000HPC 2010 was intended to organize the discussions about high productivity computing means and models, including but not limited to high performance and quantum information processing.","PeriodicalId":113162,"journal":{"name":"arXiv: Computational Complexity","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116747953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Proceedings International Workshop on The Complexity of Simple Programs 简单程序复杂性国际研讨会论文集
arXiv: Computational Complexity Pub Date : 2009-06-25 DOI: 10.4204/EPTCS.1
Turlough Neary, D. Woods, A. Seda, Niall Murphy
{"title":"Proceedings International Workshop on The Complexity of Simple Programs","authors":"Turlough Neary, D. Woods, A. Seda, Niall Murphy","doi":"10.4204/EPTCS.1","DOIUrl":"https://doi.org/10.4204/EPTCS.1","url":null,"abstract":"This is the first volume of Electronic Proceedings in Theoretical Computer Science (EPTCS), a free international refereed open access venue for the rapid electronic publication of the proceedings of workshops and conferences, and of festschriften, etc, in the general area of theoretical computer science, broadly construed. \u0000It contains the proceedings of the International Workshop on The Complexity of Simple Programs, which was hosted at University College Cork on the 6th and 7th of December, 2008. All speakers were invited and all of the papers went through a thorough peer-review process.","PeriodicalId":113162,"journal":{"name":"arXiv: Computational Complexity","volume":"185 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2009-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134552888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Asymptotic Intrinsic Universality and Natural Reprogrammability by Behavioural Emulation 基于行为仿真的渐近内在通用性和自然可编程性
arXiv: Computational Complexity Pub Date : 1900-01-01 DOI: 10.1007/978-3-319-33924-5_9
H. Zenil, Jürgen Riedel
{"title":"Asymptotic Intrinsic Universality and Natural Reprogrammability by Behavioural Emulation","authors":"H. Zenil, Jürgen Riedel","doi":"10.1007/978-3-319-33924-5_9","DOIUrl":"https://doi.org/10.1007/978-3-319-33924-5_9","url":null,"abstract":"","PeriodicalId":113162,"journal":{"name":"arXiv: Computational Complexity","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122336986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Hamming Approximation of NP Witnesses NP证人的汉明近似
arXiv: Computational Complexity Pub Date : 1900-01-01 DOI: 10.4086/TOC.2013.V009A022
Daniel Sheldon Neal
{"title":"Hamming Approximation of NP Witnesses","authors":"Daniel Sheldon Neal","doi":"10.4086/TOC.2013.V009A022","DOIUrl":"https://doi.org/10.4086/TOC.2013.V009A022","url":null,"abstract":"Given a satisfiable 3-SAT formula, how hard is it to find an assignment to the variables that has Hamming distance at most n=2 to a satisfying assignment? More generally, consider any polynomial-time verifier for any NP-complete language. A d(n)-Hamming- approximation algorithm for the verifier is one that, given any member x of the language, outputs in polynomial time a string a with Hamming distance at most d(n) to some witness w, where (x; w) is accepted by the verifier. Previous results have shown that, if P6NP, every NP-complete language has a verifier for which there is no (n=2 n 2=3+d )-Hamming- approximation algorithm, for various constants d 0. Our main result is that, if P6NP, then every paddable NP-complete language has a verifier that admits no (n=2+ O( p n log n))-Hamming-approximation algorithm. That is, one can't get even half the bits right. We also consider natural verifiers for various well-known NP-complete problems. They do have n=2-Hamming-approximation algorithms, but, if P6NP, have no (n=2 n e )-Hamming-approximation algorithms for any constant e > 0. We show similar results for randomized algorithms.","PeriodicalId":113162,"journal":{"name":"arXiv: Computational Complexity","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114994053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
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