Information Processing Letters最新文献_第10页

Skolem and positivity completeness of ergodic Markov chains 遍历马尔可夫链的斯科莱姆和实在性完备性

IF 0.5 4区计算机科学

Information Processing Letters Pub Date : 2024-08-01 Epub Date: 2024-02-07 DOI: 10.1016/j.ipl.2024.106481

Mihir Vahanwala

{"title":"Skolem and positivity completeness of ergodic Markov chains","authors":"Mihir Vahanwala","doi":"10.1016/j.ipl.2024.106481","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106481","url":null,"abstract":"<div>We consider the following Markov Reachability decision problems that view Markov Chains as Linear Dynamical Systems: given a finite, rational Markov Chain, source and target states, and a rational threshold, does the probability of reaching the target from the source at the <math><msup><mrow><mi>n</mi></mrow><mrow><mi>t</mi><mi>h</mi></mrow></msup></math> step: (i) equal the threshold for some n? (ii) cross the threshold for some n? (iii) cross the threshold for infinitely many n? These problems are respectively known to be equivalent to the Skolem, Positivity, and Ultimate Positivity problems for Linear Recurrence Sequences (LRS), number-theoretic problems whose decidability has been open for decades. We present an elementary reduction from LRS Problems to Markov Reachability Problems that improves the state of the art as follows. (a) We map LRS to ergodic (irreducible and aperiodic) Markov Chains that are ubiquitous, not least by virtue of their spectral structure, and (b) our reduction maps LRS of order k to Markov Chains of order <math><mi>k</mi><mo>+</mo><mn>1</mn></math>: a substantial improvement over the previous reduction that mapped LRS of order k to reducible and periodic Markov chains of order <math><mn>4</mn><mi>k</mi><mo>+</mo><mn>5</mn></math>. This contribution is significant in view of the fact that the number-theoretic hardness of verifying Linear Dynamical Systems can often be mitigated by spectral assumptions and restrictions on order.</div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106481"},"PeriodicalIF":0.5,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0020019024000115/pdfft?md5=da39be99a4cd399e31f45e5c0e089132&pid=1-s2.0-S0020019024000115-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139738314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Sparsifying Count Sketch 稀疏化计数草图

IF 0.5 4区计算机科学

Information Processing Letters Pub Date : 2024-08-01 Epub Date: 2024-02-29 DOI: 10.1016/j.ipl.2024.106490

Bhisham Dev Verma , Rameshwar Pratap , Punit Pankaj Dubey

{"title":"Sparsifying Count Sketch","authors":"Bhisham Dev Verma , Rameshwar Pratap , Punit Pankaj Dubey","doi":"10.1016/j.ipl.2024.106490","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106490","url":null,"abstract":"<div>The seminal work of Charikar et al. [1] called Count-Sketch suggests a sketching algorithm for real-valued vectors that has been used in frequency estimation for data streams and pairwise inner product estimation for real-valued vectors etc. One of the major advantages of Count-Sketch over other similar sketching algorithms, such as random projection, is that its running time, as well as the sparsity of sketch, depends on the sparsity of the input. Therefore, sparse datasets enjoy space-efficient (sparse sketches) and faster running time. However, on dense datasets, these advantages of Count-Sketch might be negligible over other baselines. In this work, we address this challenge by suggesting a simple and effective approach that outputs (asymptotically) a sparser sketch than that obtained via Count-Sketch, and as a by-product, we also achieve a faster running time. Simultaneously, the quality of our estimate is closely approximate to that of Count-Sketch. For frequency estimation and pairwise inner product estimation problems, our proposal Sparse-Count-Sketch provides unbiased estimates. These estimations, however, have slightly higher variances than their respective estimates obtained via Count-Sketch. To address this issue, we present improved estimators for these problems based on maximum likelihood estimation (MLE) that offer smaller variances even w.r.t. Count-Sketch. We suggest a rigorous theoretical analysis of our proposal for frequency estimation for data streams and pairwise inner product estimation for real-valued vectors.</div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106490"},"PeriodicalIF":0.5,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140042110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The autocorrelation of a class of quaternary sequences of length pq with high complexity 一类长度为 pq 的高复杂度四元序列的自相关性

IF 0.5 4区计算机科学

Information Processing Letters Pub Date : 2024-08-01 Epub Date: 2024-03-24 DOI: 10.1016/j.ipl.2024.106494

Feifei Yan , Pinhui Ke , Zuling Chang

引用次数: 0

Expressive completeness by separation for discrete time interval temporal logic with expanding modalities 通过分离实现具有扩展模态的离散时间间隔时态逻辑的表达完备性

IF 0.5 4区计算机科学

Information Processing Letters Pub Date : 2024-08-01 Epub Date: 2024-02-05 DOI: 10.1016/j.ipl.2024.106480

Dimitar P. Guelev , Ben Moszkowski

引用次数: 0

Long directed detours: Reduction to 2-Disjoint Paths 长定向迂回：还原为二叉路径

IF 0.5 4区计算机科学

Information Processing Letters Pub Date : 2024-08-01 Epub Date: 2024-03-13 DOI: 10.1016/j.ipl.2024.106491

Ashwin Jacob, Michał Włodarczyk, Meirav Zehavi

{"title":"Long directed detours: Reduction to 2-Disjoint Paths","authors":"Ashwin Jacob, Michał Włodarczyk, Meirav Zehavi","doi":"10.1016/j.ipl.2024.106491","DOIUrl":"10.1016/j.ipl.2024.106491","url":null,"abstract":"<div>In the Longest <math><mo>(</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>)</mo></math>-Detour problem, we look for an <math><mo>(</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>)</mo></math>-path that is at least k vertices longer than a shortest one. We study the parameterized complexity of Longest <math><mo>(</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>)</mo></math>-Detour when parameterized by k: this falls into the research paradigm of ‘parameterization above guarantee’. Whereas the problem is known to be fixed-parameter tractable (FPT) on undirected graphs, the status of Longest <math><mo>(</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>)</mo></math>-Detour on directed graphs remains highly unclear: it is not even known to be solvable in polynomial time for <math><mi>k</mi><mo>=</mo><mn>1</mn></math>. Recently, Fomin et al. made progress in this direction by showing that the problem is FPT on every class of directed graphs where the 3-Disjoint Paths problem is solvable in polynomial time. We improve upon their result by weakening this assumption: we show that only a polynomial-time algorithm for 2-Disjoint Paths is required.</div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106491"},"PeriodicalIF":0.5,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140153962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Tight inapproximability of Nash equilibria in public goods games 公共物品博弈中纳什均衡的严密不可逼近性

IF 0.5 4区计算机科学

Information Processing Letters Pub Date : 2024-08-01 Epub Date: 2024-02-27 DOI: 10.1016/j.ipl.2024.106486

Jérémi Do Dinh , Alexandros Hollender

引用次数: 0

Regular resolution effectively simulates resolution 常规分辨率有效模拟分辨率

IF 0.5 4区计算机科学

Information Processing Letters Pub Date : 2024-08-01 Epub Date: 2024-02-28 DOI: 10.1016/j.ipl.2024.106489

Sam Buss , Emre Yolcu

引用次数: 0

Learning-augmented maximum flow 学习增强最大流量

IF 0.5 4区计算机科学

Information Processing Letters Pub Date : 2024-08-01 Epub Date: 2024-02-28 DOI: 10.1016/j.ipl.2024.106487

Adam Polak , Maksym Zub

{"title":"Learning-augmented maximum flow","authors":"Adam Polak , Maksym Zub","doi":"10.1016/j.ipl.2024.106487","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106487","url":null,"abstract":"<div>We propose a framework for speeding up maximum flow computation by using predictions. A prediction is a flow, i.e., an assignment of non-negative flow values to edges, which satisfies the flow conservation property, but does not necessarily respect the edge capacities of the actual instance (since these were unknown at the time of learning). We present an algorithm that, given an m-edge flow network and a predicted flow, computes a maximum flow in <math><mi>O</mi><mo>(</mo><mi>m</mi><mi>η</mi><mo>)</mo></math> time, where η is the <math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub></math> error of the prediction, i.e., the sum over the edges of the absolute difference between the predicted and optimal flow values. Moreover, we prove that, given an oracle access to a distribution over flow networks, it is possible to efficiently PAC-learn a prediction minimizing the expected <math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub></math> error over that distribution. Our results fit into the recent line of research on learning-augmented algorithms, which aims to improve over worst-case bounds of classical algorithms by using predictions, e.g., machine-learned from previous similar instances. So far, the main focus in this area was on improving competitive ratios for online problems. Following Dinitz et al. (2021) [6], our results are among the firsts to improve the running time of an offline problem.</div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106487"},"PeriodicalIF":0.5,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140030945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Prenex universal first-order safety properties Prenex 通用一阶安全特性

IF 0.5 4区计算机科学

Information Processing Letters Pub Date : 2024-08-01 Epub Date: 2024-02-28 DOI: 10.1016/j.ipl.2024.106488

Besik Dundua , Ioane Kapanadze , Helmut Seidl

引用次数: 0

Red Blue Set Cover problem on axis-parallel hyperplanes and other objects 轴平行超平面和其他物体上的红蓝套覆盖问题

IF 0.5 4区计算机科学

Information Processing Letters Pub Date : 2024-08-01 Epub Date: 2024-02-29 DOI: 10.1016/j.ipl.2024.106485

V.P. Abidha , Pradeesha Ashok

{"title":"Red Blue Set Cover problem on axis-parallel hyperplanes and other objects","authors":"V.P. Abidha , Pradeesha Ashok","doi":"10.1016/j.ipl.2024.106485","DOIUrl":"https://doi.org/10.1016/j.ipl.2024.106485","url":null,"abstract":"<div>Given a universe <math><mi>U</mi><mo>=</mo><mi>R</mi><mo>∪</mo><mi>B</mi></math> of a finite set of red elements R, and a finite set of blue elements B and a family <math><mi>F</mi></math> of subsets of <math><mi>U</mi></math>, the Red Blue Set Cover problem is to find a subset <math><msup><mrow><mi>F</mi></mrow><mrow><mo>′</mo></mrow></msup></math> of <math><mi>F</mi></math> that covers all blue elements of B and minimum number of red elements from R.We prove that the Red Blue Set Cover problem is NP-hard even when R and B respectively are sets of red and blue points in <math><msup><mrow><mi>IR</mi></mrow><mrow><mn>2</mn></mrow></msup></math> and the sets in <math><mi>F</mi></math> are defined by axis−parallel lines i.e., every set is a maximal set of points with the same x or y coordinate.We then study the parameterized complexity of a generalization of this problem, where <math><mi>U</mi></math> is a set of points in <math><msup><mrow><mi>IR</mi></mrow><mrow><mi>d</mi></mrow></msup></math> and <math><mi>F</mi></math> is a collection of set of axis−parallel hyperplanes in <math><msup><mrow><mi>IR</mi></mrow><mrow><mi>d</mi></mrow></msup></math> under different parameterizations, where d is a constant. For every parameter, we show that the problem is fixed-parameter tractable and also show the existence of a polynomial kernel. We further consider the Red Blue Set Cover problem for some special types of rectangles in <math><msup><mrow><mi>IR</mi></mrow><mrow><mn>2</mn></mrow></msup></math>.</div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"186 ","pages":"Article 106485"},"PeriodicalIF":0.5,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140042109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0