Electron. Colloquium Comput. Complex.最新文献_第9页

Efficient decoding up to a constant fraction of the code length for asymptotically good quantum codes 对于渐近良好的量子码，有效解码到码长的常数分数

Electron. Colloquium Comput. Complex. Pub Date : 2022-06-15 DOI: 10.48550/arXiv.2206.07571

Anthony Leverrier, Gilles Z'emor

引用次数: 22

QBF Merge Resolution is powerful but unnatural QBF合并分辨率功能强大，但不自然

Electron. Colloquium Comput. Complex. Pub Date : 2022-05-26 DOI: 10.48550/arXiv.2205.13428

M. Mahajan, Gaurav Sood

{"title":"QBF Merge Resolution is powerful but unnatural","authors":"M. Mahajan, Gaurav Sood","doi":"10.48550/arXiv.2205.13428","DOIUrl":"https://doi.org/10.48550/arXiv.2205.13428","url":null,"abstract":"The Merge Resolution proof system (M-Res) for QBFs, proposed by Beyersdorff et al. in 2019, explicitly builds partial strategies inside refutations. The original motivation for this approach was to overcome the limitations encountered in long-distance Q-Resolution proof system (LD-Q-Res), where the syntactic side-conditions, while prohibiting all unsound resolutions, also end up prohibiting some sound resolutions. However, while the advantage of M-Res over many other resolution-based QBF proof systems was already demonstrated, a comparison with LD-Q-Res itself had remained open. In this paper, we settle this question. We show that M-Res has an exponential advantage over not only LD-Q-Res, but even over LQU$^+$-Res and IRM, the most powerful among currently known resolution-based QBF proof systems. Combining this with results from Beyersdorff et al. 2020, we conclude that M-Res is incomparable with LQU-Res and LQU$^+$-Res. Our proof method reveals two additional and curious features about M-Res: (i) MRes is not closed under restrictions, and is hence not a natural proof system, and (ii) weakening axiom clauses with existential variables provably yields an exponential advantage over M-Res without weakening. We further show that in the context of regular derivations, weakening axiom clauses with universal variables provably yields an exponential advantage over M-Res without weakening. These results suggest that MRes is better used with weakening, though whether M-Res with weakening is closed under restrictions remains open. We note that even with weakening, M-Res continues to be simulated by eFrege $+$ $forall$red (the simulation of ordinary M-Res was shown recently by Chew and Slivovsky).","PeriodicalId":11639,"journal":{"name":"Electron. Colloquium Comput. Complex.","volume":"34 1","pages":"22:1-22:19"},"PeriodicalIF":0.0,"publicationDate":"2022-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82282195","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

Hardness of Maximum Likelihood Learning of DPPs dpp最大似然学习的硬度

Electron. Colloquium Comput. Complex. Pub Date : 2022-05-24 DOI: 10.48550/arXiv.2205.12377

Elena Grigorescu, Brendan Juba, K. Wimmer, Ning Xie

{"title":"Hardness of Maximum Likelihood Learning of DPPs","authors":"Elena Grigorescu, Brendan Juba, K. Wimmer, Ning Xie","doi":"10.48550/arXiv.2205.12377","DOIUrl":"https://doi.org/10.48550/arXiv.2205.12377","url":null,"abstract":"Determinantal Point Processes (DPPs) are a widely used probabilistic model for negatively corre-lated sets. DPPs have been successfully employed in Machine Learning applications to select a diverse, yet representative subset of data. In these applications, the parameters of the DPP need to be ﬁtted to match the data; typically, we seek a set of parameters that maximize the likelihood of the data. The algorithms used for this task to date either optimize over a limited family of DPPs, or use local improvement heuristics that do not provide theoretical guarantees of optimality. It is natural to ask if there exist efﬁcient algorithms for ﬁnding a maximum likelihood DPP model for a given data set. In seminal work on DPPs in Machine Learning, Kulesza conjectured in his PhD Thesis (2012) that the problem is NP-complete. The lack of a formal proof prompted Brunel, Moitra, Rigollet and Urschel (2017a) to conjecture that, in opposition to Kulesza’s conjecture, there exists a polynomial-time algorithm for computing a maximum-likelihood DPP. They also presented some preliminary evidence supporting their conjecture. In this work we prove Kulesza’s conjecture. In fact, we prove the following stronger hardness of approximation result: even computing a 1 − 1 polylog N -approximation to the maximum log-likelihood of a DPP on a ground set of N elements is NP-complete. At the same time, we also obtain the ﬁrst polynomial-time algorithm that achieves a nontrivial worst-case approximation to the optimal log-likelihood: the approximation factor is unconditionally (for data sets that consist of al., 2013b; et al., 2015; Affandi et al., 2013a), signal processing (Xu and Ou, Krause et al., Guestrin et al., 2005), clustering (Zou and 2012; Kang, 2013; and Ghahramani, 2013), recommendation systems (Zhou et al., 2010), revenue maximization (Dughmi et al., 2009), multi-agent reinforcement and al., 2020), modeling neural sketching for linear and low-rank","PeriodicalId":11639,"journal":{"name":"Electron. Colloquium Comput. Complex.","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80645881","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: 2

Average-Case Hardness of Proving Tautologies and Theorems 证明重言式和定理的平均情形硬度

Electron. Colloquium Comput. Complex. Pub Date : 2022-05-16 DOI: 10.48550/arXiv.2205.07803

Hunter Monroe

{"title":"Average-Case Hardness of Proving Tautologies and Theorems","authors":"Hunter Monroe","doi":"10.48550/arXiv.2205.07803","DOIUrl":"https://doi.org/10.48550/arXiv.2205.07803","url":null,"abstract":"We consolidate two widely believed conjectures about tautologies -- no optimal proof system exists, and most require superpolynomial size proofs in any system -- into a $p$-isomorphism-invariant condition satisfied by all paddable $textbf{coNP}$-complete languages or none. The condition is: for any Turing machine (TM) $M$ accepting the language, $textbf{P}$-uniform input families requiring superpolynomial time by $M$ exist (equivalent to the first conjecture) and appear with positive upper density in an enumeration of input families (implies the second). In that case, no such language is easy on average (in $textbf{AvgP}$) for a distribution applying non-negligible weight to the hard families. The hardness of proving tautologies and theorems is likely related. Motivated by the fact that arithmetic sentences encoding\"string $x$ is Kolmogorov random\"are true but unprovable with positive density in a finitely axiomatized theory $mathcal{T}$ (Calude and J{\"u}rgensen), we conjecture that any propositional proof system requires superpolynomial size proofs for a dense set of $textbf{P}$-uniform families of tautologies encoding\"there is no $mathcal{T}$ proof of size $leq t$ showing that string $x$ is Kolmogorov random\". This implies the above condition. The conjecture suggests that there is no optimal proof system because undecidable theories help prove tautologies and do so more efficiently as axioms are added, and that constructing hard tautologies seems difficult because it is impossible to construct Kolmogorov random strings. Similar conjectures that computational blind spots are manifestations of noncomputability would resolve other open problems.","PeriodicalId":11639,"journal":{"name":"Electron. Colloquium Comput. Complex.","volume":"135 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77529249","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

Sketching Approximability of (Weak) Monarchy Predicates (弱)君主制谓词的近似性概述

Electron. Colloquium Comput. Complex. Pub Date : 2022-05-04 DOI: 10.48550/arXiv.2205.02345

Chi-Ning Chou, Alexander Golovnev, Amirbehshad Shahrasbi, M. Sudan, Santhoshini Velusamy

{"title":"Sketching Approximability of (Weak) Monarchy Predicates","authors":"Chi-Ning Chou, Alexander Golovnev, Amirbehshad Shahrasbi, M. Sudan, Santhoshini Velusamy","doi":"10.48550/arXiv.2205.02345","DOIUrl":"https://doi.org/10.48550/arXiv.2205.02345","url":null,"abstract":"We analyze the sketching approximability of constraint satisfaction problems on Boolean domains, where the constraints are balanced linear threshold functions applied to literals. In~particular, we explore the approximability of monarchy-like functions where the value of the function is determined by a weighted combination of the vote of the first variable (the president) and the sum of the votes of all remaining variables. The pure version of this function is when the president can only be overruled by when all remaining variables agree. For every $k geq 5$, we show that CSPs where the underlying predicate is a pure monarchy function on $k$ variables have no non-trivial sketching approximation algorithm in $o(sqrt{n})$ space. We also show infinitely many weaker monarchy functions for which CSPs using such constraints are non-trivially approximable by $O(log(n))$ space sketching algorithms. Moreover, we give the first example of sketching approximable asymmetric Boolean CSPs. Our results work within the framework of Chou, Golovnev, Sudan, and Velusamy (FOCS 2021) that characterizes the sketching approximability of all CSPs. Their framework can be applied naturally to get a computer-aided analysis of the approximability of any specific constraint satisfaction problem. The novelty of our work is in using their work to get an analysis that applies to infinitely many problems simultaneously.","PeriodicalId":11639,"journal":{"name":"Electron. Colloquium Comput. Complex.","volume":"10 1","pages":"35:1-35:17"},"PeriodicalIF":0.0,"publicationDate":"2022-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85160630","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

Superredundancy: A tool for Boolean formula minimization complexity analysis 超级冗余:布尔公式最小化复杂性分析的工具

Electron. Colloquium Comput. Complex. Pub Date : 2022-05-02 DOI: 10.48550/arXiv.2205.00762

P. Liberatore

引用次数: 1

Low Degree Testing over the Reals 实数的低度测试

Electron. Colloquium Comput. Complex. Pub Date : 2022-04-18 DOI: 10.48550/arXiv.2204.08404

Vipul Arora, Arnab Bhattacharyya, Noah Fleming, E. Kelman, Yuichi Yoshida

引用次数: 2

An Optimal Algorithm for Certifying Monotone Functions 单调函数的最优证明算法

Electron. Colloquium Comput. Complex. Pub Date : 2022-04-04 DOI: 10.48550/arXiv.2204.01224

Meghal Gupta, N. Manoj

引用次数: 1

Polynomial Bounds On Parallel Repetition For All 3-Player Games With Binary Inputs 具有二进制输入的所有3人博弈并行重复的多项式界

Electron. Colloquium Comput. Complex. Pub Date : 2022-04-02 DOI: 10.48550/arXiv.2204.00858

Uma Girish, Kunal Mittal, R. Raz, Wei Zhan

引用次数: 4

Matrix Polynomial Factorization via Higman Linearization 基于Higman线性化的矩阵多项式分解

Electron. Colloquium Comput. Complex. Pub Date : 2022-03-31 DOI: 10.48550/arXiv.2203.16978

V. Arvind, Pushkar S. Joglekar

引用次数: 0