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ACM Transactions on Computation Theory最新文献

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Separation Between Read-once Oblivious Algebraic Branching Programs (ROABPs) and Multilinear Depth-three Circuits 读一次无关代数分支程序(ROABPs)与多线性深度三电路的分离
IF 0.7
ACM Transactions on Computation Theory Pub Date : 2020-02-11 DOI: 10.1145/3369928
KayalNeeraj, NairVineet, SahaChandan
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引用次数: 3
Groups with ALOGTIME-hard Word Problems and PSPACE-complete Compressed Word Problems 具有ALOGTIME硬词问题和PSPACE完全压缩词问题的组
IF 0.7
ACM Transactions on Computation Theory Pub Date : 2019-09-30 DOI: 10.1145/3569708
L. Bartholdi, Michael Figelius, Markus Lohrey, A. Weiss
{"title":"Groups with ALOGTIME-hard Word Problems and PSPACE-complete Compressed Word Problems","authors":"L. Bartholdi, Michael Figelius, Markus Lohrey, A. Weiss","doi":"10.1145/3569708","DOIUrl":"https://doi.org/10.1145/3569708","url":null,"abstract":"We give lower bounds on the complexity of the word problem for a large class of non-solvable infinite groups that we call strongly efficiently non-solvable groups. This class includes free groups, Grigorchuk’s group, and Thompson’s groups. We prove that these groups have an NC1-hard word problem and that for some of them (including Grigorchuk’s group and Thompson’s groups) the compressed word problem (which is equivalent to the circuit evaluation problem) is PSPACE-complete.","PeriodicalId":44045,"journal":{"name":"ACM Transactions on Computation Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2019-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49495762","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: 8
Monotone Properties of k-Uniform Hypergraphs Are Weakly Evasive k-一致超图的单调性是弱回避的
IF 0.7
ACM Transactions on Computation Theory Pub Date : 2019-04-26 DOI: 10.1145/3313908
BlackTimothy
{"title":"Monotone Properties of k-Uniform Hypergraphs Are Weakly Evasive","authors":"BlackTimothy","doi":"10.1145/3313908","DOIUrl":"https://doi.org/10.1145/3313908","url":null,"abstract":"A Boolean function in n variables is weakly evasive if its decision-tree complexity is (n). By k-graphs, we mean k-uniform hypergraphs. A k-graph property on v vertices is a Boolean function on n =...","PeriodicalId":44045,"journal":{"name":"ACM Transactions on Computation Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2019-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83065583","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
Lower bounds for Sum and Sum of Products of Read-once Formulas 读一次公式的和和和的下界
IF 0.7
ACM Transactions on Computation Theory Pub Date : 2019-04-02 DOI: 10.1145/3313232
RamyaC., R. Raghavendra
{"title":"Lower bounds for Sum and Sum of Products of Read-once Formulas","authors":"RamyaC., R. Raghavendra","doi":"10.1145/3313232","DOIUrl":"https://doi.org/10.1145/3313232","url":null,"abstract":"We study limitations of polynomials computed by depth-2 circuits built over read-once formulas (ROFs). In particular: We prove a 2(n) lower bound for the sum of ROFs computing the 2n-variate polyno...","PeriodicalId":44045,"journal":{"name":"ACM Transactions on Computation Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2019-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1145/3313232","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64017579","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
Constructing Faithful Homomorphisms over Fields of Finite Characteristic 有限特征域上忠实同态的构造
IF 0.7
ACM Transactions on Computation Theory Pub Date : 2018-12-26 DOI: 10.1145/3580351
Prerona Chatterjee, Ramprasad Saptharishi
{"title":"Constructing Faithful Homomorphisms over Fields of Finite Characteristic","authors":"Prerona Chatterjee, Ramprasad Saptharishi","doi":"10.1145/3580351","DOIUrl":"https://doi.org/10.1145/3580351","url":null,"abstract":"We study the question of algebraic rank or transcendence degree preserving homomorphisms over finite fields. This concept was first introduced by Beecken et al. [3] and exploited by them, and Agrawal et al. [2] to design algebraic independence–based identity tests using the Jacobian criterion over characteristic zero fields. An analogue of such constructions over finite characteristic fields was unknown due to the failure of the Jacobian criterion over finite characteristic fields. Building on a recent criterion of Pandey et al. [15], we construct explicit faithful maps for some natural classes of polynomials in the positive characteristic field setting, when a certain parameter called the inseparable degree of the underlying polynomials is bounded (this parameter is always 1 in fields of characteristic zero). This presents the first generalisation of some of the results of Beecken et al. [3] and Agrawal et al. [2] in the positive characteristic setting.","PeriodicalId":44045,"journal":{"name":"ACM Transactions on Computation Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2018-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44335778","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
The Complexity Landscape of Fixed-Parameter Directed Steiner Network Problems 定参数有向Steiner网络问题的复杂性格局
IF 0.7
ACM Transactions on Computation Theory Pub Date : 2017-07-21 DOI: 10.4230/LIPIcs.ICALP.2016.27
A. Feldmann, D. Marx
{"title":"The Complexity Landscape of Fixed-Parameter Directed Steiner Network Problems","authors":"A. Feldmann, D. Marx","doi":"10.4230/LIPIcs.ICALP.2016.27","DOIUrl":"https://doi.org/10.4230/LIPIcs.ICALP.2016.27","url":null,"abstract":"Given a directed graph G and a list (s1, t1), …, (sd, td) of terminal pairs, the Directed Steiner Network problem asks for a minimum-cost subgraph of G that contains a directed si → ti path for every 1 ≤ i ≤ d. The special case Directed Steiner Tree (when we ask for paths from a root r to terminals t1, …, td) is known to be fixed-parameter tractable parameterized by the number of terminals, while the special case Strongly Connected Steiner Subgraph (when we ask for a path from every ti to every other tj) is known to be W[1]-hard parameterized by the number of terminals. We systematically explore the complexity landscape of directed Steiner problems to fully understand which other special cases are FPT or W[1]-hard. Formally, if ({mathcal {H}} ) is a class of directed graphs, then we look at the special case of Directed Steiner Network where the list (s1, t1), …, (sd, td) of demands form a directed graph that is a member of ({mathcal {H}} ) . Our main result is a complete characterization of the classes ({mathcal {H}} ) resulting in fixed-parameter tractable special cases: we show that if every pattern in ({mathcal {H}} ) has the combinatorial property of being “transitively equivalent to a bounded-length caterpillar with a bounded number of extra edges,” then the problem is FPT, and it is W[1]-hard for every recursively enumerable ({mathcal {H}} ) not having this property. This complete dichotomy unifies and generalizes the known results showing that Directed Steiner Tree is FPT [Dreyfus and Wagner, Networks 1971], q-Root Steiner Tree is FPT for constant q [Suchý, WG 2016], Strongly Connected Steiner Subgraph is W[1]-hard [Guo et al., SIAM J. Discrete Math. 2011], and Directed Steiner Network is solvable in polynomial-time for constant number of terminals [Feldman and Ruhl, SIAM J. Comput. 2006], and moreover reveals a large continent of tractable cases that were not known before.","PeriodicalId":44045,"journal":{"name":"ACM Transactions on Computation Theory","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2017-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43112911","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: 18
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