arXiv - CS - Computational Complexity最新文献_第6页

Probabilistic and Causal Satisfiability: the Impact of Marginalization 概率可满足性和因果可满足性：边缘化的影响

arXiv - CS - Computational Complexity Pub Date : 2024-05-12 DOI: arxiv-2405.07373

Julian Dörfler, Benito van der Zander, Markus Bläser, Maciej Liskiewicz

{"title":"Probabilistic and Causal Satisfiability: the Impact of Marginalization","authors":"Julian Dörfler, Benito van der Zander, Markus Bläser, Maciej Liskiewicz","doi":"arxiv-2405.07373","DOIUrl":"https://doi.org/arxiv-2405.07373","url":null,"abstract":"The framework of Pearl's Causal Hierarchy (PCH) formalizes three types of\u0000reasoning: observational, interventional, and counterfactual, that reflect the\u0000progressive sophistication of human thought regarding causation. We investigate\u0000the computational complexity aspects of reasoning in this framework focusing\u0000mainly on satisfiability problems expressed in probabilistic and causal\u0000languages across the PCH. That is, given a system of formulas in the standard\u0000probabilistic and causal languages, does there exist a model satisfying the\u0000formulas? The resulting complexity changes depending on the level of the\u0000hierarchy as well as the operators allowed in the formulas (addition,\u0000multiplication, or marginalization). We focus on formulas involving marginalization that are widely used in\u0000probabilistic and causal inference, but whose complexity issues are still\u0000little explored. Our main contribution are the exact computational complexity\u0000results showing that linear languages (allowing addition and marginalization)\u0000yield NP^PP-, PSPACE-, and NEXP-complete satisfiability problems, depending on\u0000the level of the PCH. Moreover, we prove that the problem for the full language\u0000(allowing additionally multiplication) is complete for the class succ$exists$R\u0000for languages on the highest, counterfactual level. Previous work has shown\u0000that the satisfiability problem is complete for succ$exists$R on the lower\u0000levels leaving the counterfactual case open. Finally, we consider constrained\u0000models that are restricted to a small polynomial size. The constraint on the\u0000size reduces the complexity of the interventional and counterfactual languages\u0000to NEXP-complete.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140935005","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

Newman's theorem via Carathéodory 通过 Carathéodory 的纽曼定理

arXiv - CS - Computational Complexity Pub Date : 2024-05-09 DOI: arxiv-2406.08500

Ali Mohammad Lavasani, Yaqiao Li, Mehran Shakerinava

引用次数: 0

Decision algorithms for reversibility of one-dimensional non-linear cellular automata under null boundary conditions 空边界条件下一维非线性蜂窝自动机可逆性的决策算法

arXiv - CS - Computational Complexity Pub Date : 2024-05-06 DOI: arxiv-2405.03609

Ma Junchi, Chen Weilin, Wang Chen, Lin Defu, Wang Chao

{"title":"Decision algorithms for reversibility of one-dimensional non-linear cellular automata under null boundary conditions","authors":"Ma Junchi, Chen Weilin, Wang Chen, Lin Defu, Wang Chao","doi":"arxiv-2405.03609","DOIUrl":"https://doi.org/arxiv-2405.03609","url":null,"abstract":"The property of reversibility is quite meaningful for the classic theoretical\u0000computer science model, cellular automata. For the reversibility problem for a\u0000CA under null boundary conditions, while linear rules have been studied a lot,\u0000the non-linear rules remain unexplored at present. The paper investigates the\u0000reversibility problem of general one-dimensional CA on a finite field\u0000$mathbb{Z}_p$, and proposes an approach to optimize the Amoroso's infinite CA\u0000surjectivity detection algorithm. This paper proposes algorithms for deciding\u0000the reversibility of one-dimensional CA under null boundary conditions. We\u0000propose a method to decide the strict reversibility of one-dimensional CA under\u0000null boundary conditions. We also provide a bucket chain based algorithm for\u0000calculating the reversibility function of one-dimensional CA under null\u0000boundary conditions. These decision algorithms work for not only linear rules\u0000but also non-linear rules. In addition, it has been confirmed that the\u0000reversibility function always has a period, and its periodicity is related to\u0000the periodicity of the corresponding bucket chain. Some of our experiment\u0000results of reversible CA are presented in the paper, complementing and\u0000validating the theoretical aspects, and thereby further supporting the research\u0000conclusions of this paper.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140883817","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

Maximizing Network Phylogenetic Diversity 最大化网络系统发育多样性

arXiv - CS - Computational Complexity Pub Date : 2024-05-02 DOI: arxiv-2405.01091

Leo van Iersel, Mark Jones, Jannik Schestag, Celine Scornavacca, Mathias Weller

引用次数: 0

A Smoothed Analysis of the Space Complexity of Computing a Chaotic Sequence 计算混沌序列空间复杂性的平滑分析

arXiv - CS - Computational Complexity Pub Date : 2024-05-01 DOI: arxiv-2405.00327

Naoaki Okada, Shuji Kijima

引用次数: 0

An Oracle with no $mathrm{UP}$-Complete Sets, but $mathrm{NP}=mathrm{PSPACE}$ 没有 $mathrm{UP}$ 完整集合，但有 $mathrm{NP}=mathrm{PSPACE}$ 的 Oracle

arXiv - CS - Computational Complexity Pub Date : 2024-04-29 DOI: arxiv-2404.19104

David Dingel, Fabian Egidy, Christian Glaßer

引用次数: 0

Limits of Sequential Local Algorithms on the Random $k$-XORSAT Problem 随机 $k$-XORSAT 问题上序列局部算法的极限

arXiv - CS - Computational Complexity Pub Date : 2024-04-27 DOI: arxiv-2404.17775

Kingsley Yung

{"title":"Limits of Sequential Local Algorithms on the Random $k$-XORSAT Problem","authors":"Kingsley Yung","doi":"arxiv-2404.17775","DOIUrl":"https://doi.org/arxiv-2404.17775","url":null,"abstract":"The random $k$-XORSAT problem is a random constraint satisfaction problem of\u0000$n$ Boolean variables and $m=rn$ clauses, which a random instance can be\u0000expressed as a $Gmathbb{F}(2)$ linear system of the form $Ax=b$, where $A$ is\u0000a random $m times n$ matrix with $k$ ones per row, and $b$ is a random vector.\u0000It is known that there exist two distinct thresholds $r_{core}(k) < r_{sat}(k)$\u0000such that as $n rightarrow infty$ for $r < r_{sat}(k)$ the random instance\u0000has solutions with high probability, while for $r_{core} < r < r_{sat}(k)$ the\u0000solution space shatters into an exponential number of clusters. Sequential\u0000local algorithms are a natural class of algorithms which assign values to\u0000variables one by one iteratively. In each iteration, the algorithm runs some\u0000heuristics, called local rules, to decide the value assigned, based on the\u0000local neighborhood of the selected variables under the factor graph\u0000representation of the instance. We prove that for any $r > r_{core}(k)$ the sequential local algorithms with\u0000certain local rules fail to solve the random $k$-XORSAT with high probability.\u0000They include (1) the algorithm using the Unit Clause Propagation as local rule\u0000for $k ge 9$, and (2) the algorithms using any local rule that can calculate\u0000the exact marginal probabilities of variables in instances with factor graphs\u0000that are trees, for $kge 13$. The well-known Belief Propagation and Survey\u0000Propagation are included in (2). Meanwhile, the best known linear-time\u0000algorithm succeeds with high probability for $r < r_{core}(k)$. Our results\u0000support the intuition that $r_{core}(k)$ is the sharp threshold for the\u0000existence of a linear-time algorithm for random $k$-XORSAT.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140826977","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

Maximizing Minimum Cycle Bases Intersection 最大化最小循环基数交叉点

arXiv - CS - Computational Complexity Pub Date : 2024-04-26 DOI: arxiv-2404.17223

Dimitri WatelSAMOVAR, ENSIIE, Marc-Antoine WeisserGALaC, Dominique BarthUVSQ, DAVID, Ylène AboulfathUVSQ, DAVID, Thierry MautorUVSQ, DAVID

引用次数: 0

A Multivariate to Bivariate Reduction for Noncommutative Rank and Related Results 非交换秩的多变量到双变量还原及相关结果

arXiv - CS - Computational Complexity Pub Date : 2024-04-25 DOI: arxiv-2404.16382

Vikraman Arvind, Pushkar S Joglekar

引用次数: 0

A Brief Note on a Recent Claim About NP-Hard Problems and BQP 关于 NP 难问题和 BQP 的最新说法的简要说明

arXiv - CS - Computational Complexity Pub Date : 2024-04-25 DOI: arxiv-2406.08495

Michael C. Chavrimootoo

引用次数: 0