arXiv - CS - Computational Complexity最新文献_第5页

Extensively Not P-Bi-Immune promiseBQP-Complete Languages 广泛的非 Pi-Immune promiseBQP-Complete 语言

arXiv - CS - Computational Complexity Pub Date : 2024-06-24 DOI: arxiv-2406.16764

Andrew Jackson

引用次数: 0

Assembly Theory and its Relationship with Computational Complexity 组装理论及其与计算复杂性的关系

arXiv - CS - Computational Complexity Pub Date : 2024-06-18 DOI: arxiv-2406.12176

Christopher Kempes, Sara I. Walker, Michael Lachmann, Leroy Cronin

{"title":"Assembly Theory and its Relationship with Computational Complexity","authors":"Christopher Kempes, Sara I. Walker, Michael Lachmann, Leroy Cronin","doi":"arxiv-2406.12176","DOIUrl":"https://doi.org/arxiv-2406.12176","url":null,"abstract":"Assembly theory (AT) quantifies selection using the assembly equation and\u0000identifies complex objects that occur in abundance based on two measurements,\u0000assembly index and copy number. The assembly index is determined by the minimal\u0000number of recursive joining operations necessary to construct an object from\u0000basic parts, and the copy number is how many of the given object(s) are\u0000observed. Together these allow defining a quantity, called Assembly, which\u0000captures the amount of causation required to produce the observed objects in\u0000the sample. AT's focus on how selection generates complexity offers a distinct\u0000approach to that of computational complexity theory which focuses on minimum\u0000descriptions via compressibility. To explore formal differences between the two\u0000approaches, we show several simple and explicit mathematical examples\u0000demonstrating that the assembly index, itself only one piece of the theoretical\u0000framework of AT, is formally not equivalent to other commonly used complexity\u0000measures from computer science and information theory including Huffman\u0000encoding and Lempel-Ziv-Welch compression.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141507162","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

On $NP$ versus ${rm co}NP$ 关于 $NP$ 与 ${rm co}NP$

arXiv - CS - Computational Complexity Pub Date : 2024-06-15 DOI: arxiv-2406.10476

Tianrong Lin

引用次数: 0

A Refinement of the McCreight-Meyer Union Theorem 麦克雷特-迈耶联合定理的完善

arXiv - CS - Computational Complexity Pub Date : 2024-06-12 DOI: arxiv-2406.08600

Matthew Fox, Chaitanya Karamchedu

引用次数: 0

PSMC: Provable and Scalable Algorithms for Motif Conductance Based Graph Clustering PSMC：基于动机传导的图形聚类的可证明和可扩展算法

arXiv - CS - Computational Complexity Pub Date : 2024-06-11 DOI: arxiv-2406.07357

Longlong Lin, Tao Jia, Zeli Wang, Jin Zhao, Rong-Hua Li

{"title":"PSMC: Provable and Scalable Algorithms for Motif Conductance Based Graph Clustering","authors":"Longlong Lin, Tao Jia, Zeli Wang, Jin Zhao, Rong-Hua Li","doi":"arxiv-2406.07357","DOIUrl":"https://doi.org/arxiv-2406.07357","url":null,"abstract":"Higher-order graph clustering aims to partition the graph using frequently\u0000occurring subgraphs. Motif conductance is one of the most promising\u0000higher-order graph clustering models due to its strong interpretability.\u0000However, existing motif conductance based graph clustering algorithms are\u0000mainly limited by a seminal two-stage reweighting computing framework, needing\u0000to enumerate all motif instances to obtain an edge-weighted graph for\u0000partitioning. However, such a framework has two-fold vital defects: (1) It can\u0000only provide a quadratic bound for the motif with three vertices, and whether\u0000there is provable clustering quality for other motifs is still an open\u0000question. (2) The enumeration procedure of motif instances incurs prohibitively\u0000high costs against large motifs or large dense graphs due to combinatorial\u0000explosions. Besides, expensive spectral clustering or local graph diffusion on\u0000the edge-weighted graph also makes existing methods unable to handle massive\u0000graphs with millions of nodes. To overcome these dilemmas, we propose a\u0000Provable and Scalable Motif Conductance algorithm PSMC, which has a fixed and\u0000motif-independent approximation ratio for any motif. Specifically, PSMC first\u0000defines a new vertex metric Motif Resident based on the given motif, which can\u0000be computed locally. Then, it iteratively deletes the vertex with the smallest\u0000motif resident value very efficiently using novel dynamic update technologies.\u0000Finally, it outputs the locally optimal result during the above iterative\u0000process. To further boost efficiency, we propose several effective bounds to\u0000estimate the motif resident value of each vertex, which can greatly reduce\u0000computational costs. Empirical results show that our proposed algorithms\u0000achieve 3.2-32 times speedup and improve the quality by at least 12 times than\u0000the baselines.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141507164","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

Completeness classes in algebraic complexity theory 代数复杂性理论中的完备性类

arXiv - CS - Computational Complexity Pub Date : 2024-06-10 DOI: arxiv-2406.06217

Peter Bürgisser

引用次数: 0

On Kolmogorov Structure Functions 关于柯尔莫哥洛夫结构函数

arXiv - CS - Computational Complexity Pub Date : 2024-06-09 DOI: arxiv-2406.05903

Samuel Epstein

引用次数: 0

ActionReasoningBench: Reasoning about Actions with and without Ramification Constraints 行动推理平台（ActionReasoningBench）：推理有拉姆约束和无拉姆约束的行动

arXiv - CS - Computational Complexity Pub Date : 2024-06-06 DOI: arxiv-2406.04046

Divij Handa, Pavel Dolin, Shrinidhi Kumbhar, Chitta Baral, Tran Cao Son

{"title":"ActionReasoningBench: Reasoning about Actions with and without Ramification Constraints","authors":"Divij Handa, Pavel Dolin, Shrinidhi Kumbhar, Chitta Baral, Tran Cao Son","doi":"arxiv-2406.04046","DOIUrl":"https://doi.org/arxiv-2406.04046","url":null,"abstract":"Reasoning about actions and change (RAC) has historically driven the\u0000development of many early AI challenges, such as the frame problem, and many AI\u0000disciplines, including non-monotonic and commonsense reasoning. The role of RAC\u0000remains important even now, particularly for tasks involving dynamic\u0000environments, interactive scenarios, and commonsense reasoning. Despite the\u0000progress of Large Language Models (LLMs) in various AI domains, their\u0000performance on RAC is underexplored. To address this gap, we introduce a new\u0000benchmark, ActionReasoningBench, encompassing 13 domains and rigorously\u0000evaluating LLMs across eight different areas of RAC. These include - Object\u0000Tracking, Fluent Tracking, State Tracking, Action Executability, Effects of\u0000Actions, Numerical RAC, Hallucination Detection, and Composite Questions.\u0000Furthermore, we also investigate the indirect effect of actions due to\u0000ramification constraints for every domain. Finally, we evaluate our benchmark\u0000using open-sourced and commercial state-of-the-art LLMs, including GPT-4o,\u0000Gemini-1.0-Pro, Llama2-7b-chat, Llama2-13b-chat, Llama3-8b-instruct,\u0000Gemma-2b-instruct, and Gemma-7b-instruct. Our findings indicate that these\u0000models face significant challenges across all categories included in our\u0000benchmark.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141546382","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

Proportionally dense subgraphs of maximum size in degree-constrained graphs 度受限图中最大尺寸的比例致密子图

arXiv - CS - Computational Complexity Pub Date : 2024-05-31 DOI: arxiv-2405.20847

Narmina Baghirova, Antoine Castillon

{"title":"Proportionally dense subgraphs of maximum size in degree-constrained graphs","authors":"Narmina Baghirova, Antoine Castillon","doi":"arxiv-2405.20847","DOIUrl":"https://doi.org/arxiv-2405.20847","url":null,"abstract":"A proportionally dense subgraph (PDS) of a graph is an induced subgraph of\u0000size at least two such that every vertex in the subgraph has proportionally as\u0000many neighbors inside as outside of the subgraph. Then, maxPDS is the problem\u0000of determining a PDS of maximum size in a given graph. If we further require\u0000that a PDS induces a connected subgraph, we refer to such problem as connected\u0000maxPDS. In this paper, we study the complexity of maxPDS with respect to\u0000parameters representing the density of a graph and its complement. We consider\u0000$Delta$, representing the maximum degree, $h$, representing the $h$-index, and\u0000degen, representing the degeneracy of a graph. We show that maxPDS is NP-hard\u0000parameterized by $Delta,h$ and degen. More specifically, we show that maxPDS\u0000is NP-hard on graphs with $Delta=4$, $h=4$ and degen=2. Then, we show that\u0000maxPDS is NP-hard when restricted to dense graphs, more specifically graphs $G$\u0000such that $Delta(overline{G})leq 6$, and graphs $G$ such that\u0000$degen(overline{G}) leq 2$ and $overline{G}$ is bipartite, where\u0000$overline{G}$ represents the complement of $G$. On the other hand, we show\u0000that maxPDS is polynomial-time solvable on graphs with $hle2$. Finally, we\u0000consider graphs $G$ such that $h(overline{G})le 2$ and show that there exists\u0000a polynomial-time algorithm for finding a PDS of maximum size in such graphs.\u0000This result implies polynomial-time complexity on graphs with $n$ vertices of\u0000minimum degree $n-3$, i.e. graphs $G$ such that $Delta(overline{G})le 2$.\u0000For each result presented in this paper, we consider connected maxPDS and\u0000explain how to extend it when we require connectivity.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141257054","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

A linear bound for the size of the finite terminal assembly of a directed non-cooperative tile assembly system 有向非合作瓦片组装系统有限终端组装规模的线性约束

arXiv - CS - Computational Complexity Pub Date : 2024-05-28 DOI: arxiv-2405.18630

Sergiu Ivanov, Damien Regnault

{"title":"A linear bound for the size of the finite terminal assembly of a directed non-cooperative tile assembly system","authors":"Sergiu Ivanov, Damien Regnault","doi":"arxiv-2405.18630","DOIUrl":"https://doi.org/arxiv-2405.18630","url":null,"abstract":"The abstract tile assembly model (aTam) is a model of DNA self-assembly. Most\u0000of the studies focus on cooperative aTam where a form of synchronization\u0000between the tiles is possible. Simulating Turing machines is achievable in this\u0000context. Few results and constructions are known for the non-cooperative case\u0000(a variant of Wang tilings where assemblies do not need to cover the whole\u0000plane and some mismatches may occur). Introduced by P.E. Meunier and D. Regnault, efficient paths are a non-trivial\u0000construction for non-cooperative aTam. These paths of width nlog(n) are\u0000designed with n different tile types. Assembling them relies heavily on a form\u0000of ``non-determinism''. Indeed, the set of tiles may produced different finite\u0000terminal assemblies but they all contain the same efficient path. Directed\u0000non-cooperative aTam does not allow this non-determinism as only one assembly\u0000may be produced by a tile assembly system. This variant of aTam is the only one\u0000who was shown to be decidable. In this paper, we show that if the terminal assembly of a directed\u0000non-cooperative tile assembly system is finite then its width and length are of\u0000linear size according to the size of the tile assembly system. This result\u0000implies that the construction of efficient paths cannot be generalized to the\u0000directed case and that some computation must rely on a competition between\u0000different paths. It also implies that the construction of a square of width n\u0000using 2n-1 tiles types is asymptotically optimal. Moreover, we hope that the\u0000techniques introduced here will lead to a better comprehension of the\u0000non-directed case.","PeriodicalId":501024,"journal":{"name":"arXiv - CS - Computational Complexity","volume":"53 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141196664","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