International Symposium on Mathematical Foundations of Computer Science最新文献_第10页

Counting of Teams in First-Order Team Logics 一阶团队逻辑中的团队计数

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2019-02-01 DOI: 10.4230/LIPICS.MFCS.2019.19

A. Haak, J. Kontinen, Fabian Müller, H. Vollmer, Fan Yang

引用次数: 6

Solving Systems of Equations in Supernilpotent Algebras 超幂零代数方程组的求解

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2019-01-23 DOI: 10.4230/LIPICS.MFCS.2019.72

E. Aichinger

引用次数: 8

Random Subgroups of Rationals 有理数的随机子群

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2019-01-15 DOI: 10.4230/LIPIcs.MFCS.2019.25

Ziyuan Gao, Sanjay Jain, B. Khoussainov, Wei Li, A. Melnikov, Karen Seidel, F. Stephan

{"title":"Random Subgroups of Rationals","authors":"Ziyuan Gao, Sanjay Jain, B. Khoussainov, Wei Li, A. Melnikov, Karen Seidel, F. Stephan","doi":"10.4230/LIPIcs.MFCS.2019.25","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2019.25","url":null,"abstract":"This paper introduces and studies a notion of emph{algorithmic randomness} for subgroups of rationals. Given a randomly generated additive subgroup $(G,+)$ of rationals, two main questions are addressed: first, what are the model-theoretic and recursion-theoretic properties of $(G,+)$; second, what learnability properties can one extract from $G$ and its subclass of finitely generated subgroups? \u0000For the first question, it is shown that the theory of $(G,+)$ coincides with that of the additive group of integers and is therefore decidable; furthermore, while the word problem for $G$ with respect to any generating sequence for $G$ is not even semi-decidable, one can build a generating sequence $beta$ such that the word problem for $G$ with respect to $beta$ is co-recursively enumerable (assuming that the set of generators of $G$ is limit-recursive). \u0000In regard to the second question, it is proven that there is a generating sequence $beta$ for $G$ such that every non-trivial finitely generated subgroup of $G$ is recursively enumerable and the class of all such subgroups of $G$ is behaviourally correctly learnable, that is, every non-trivial finitely generated subgroup can be semantically identified in the limit (again assuming that the set of generators of $G$ is limit-recursive). On the other hand, the class of non-trivial finitely generated subgroups of $G$ cannot be syntactically identified in the limit with respect to any generating sequence for $G$. The present work thus contributes to a recent line of research studying algorithmically random infinite structures and uncovers an interesting connection between the arithmetical complexity of the set of generators of a randomly generated subgroup of rationals and the learnability of its finitely generated subgroups.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128404166","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

Quantum-Inspired Sublinear Algorithm for Solving Low-Rank Semidefinite Programming 求解低秩半定规划的量子启发次线性算法

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2019-01-10 DOI: 10.4230/LIPIcs.MFCS.2020.23

Nai-Hui Chia, Tongyang Li, Han-Hsuan Lin, Chunhao Wang

{"title":"Quantum-Inspired Sublinear Algorithm for Solving Low-Rank Semidefinite Programming","authors":"Nai-Hui Chia, Tongyang Li, Han-Hsuan Lin, Chunhao Wang","doi":"10.4230/LIPIcs.MFCS.2020.23","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2020.23","url":null,"abstract":"Semidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank constraints; specifically, given an SDP with $m$ constraint matrices, each of dimension $n$ and rank $r$, our algorithm can compute any entry and efficient descriptions of the spectral decomposition of the solution matrix. The algorithm runs in time $O(mcdotmathrm{poly}(log n,r,1/varepsilon))$ given access to a sampling-based low-overhead data structure for the constraint matrices, where $varepsilon$ is the precision of the solution. In addition, we apply our algorithm to a quantum state learning task as an application. \u0000Technically, our approach aligns with 1) SDP solvers based on the matrix multiplicative weight (MMW) framework by Arora and Kale [TOC '12]; 2) sampling-based dequantizing framework pioneered by Tang [STOC '19]. In order to compute the matrix exponential required in the MMW framework, we introduce two new techniques that may be of independent interest: \u0000$bullet$ Weighted sampling: assuming sampling access to each individual constraint matrix $A_{1},ldots,A_{tau}$, we propose a procedure that gives a good approximation of $A=A_{1}+cdots+A_{tau}$. \u0000$bullet$ Symmetric approximation: we propose a sampling procedure that gives the emph{spectral decomposition} of a low-rank Hermitian matrix $A$. To the best of our knowledge, this is the first sampling-based algorithm for spectral decomposition, as previous works only give singular values and vectors.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126696693","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: 15

Classes of Languages Generated by the Kleene Star of a Word 由单词的Kleene星生成的语言类别

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2018-10-01 DOI: 10.1007/978-3-662-48057-1_13

Laure Daviaud, Charles Paperman

引用次数: 2

Collective Fast Delivery by Energy-Efficient Agents 高效节能代理商的集体快速配送

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2018-08-31 DOI: 10.4230/LIPIcs.MFCS.2018.56

Andreas Bärtschi, Daniel Graf, Matús Mihalák

{"title":"Collective Fast Delivery by Energy-Efficient Agents","authors":"Andreas Bärtschi, Daniel Graf, Matús Mihalák","doi":"10.4230/LIPIcs.MFCS.2018.56","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2018.56","url":null,"abstract":"We consider k mobile agents initially located at distinct nodes of an undirected graph (on n nodes, with edge lengths) that have to deliver a single item from a given source node s to a given target node t. The agents can move along the edges of the graph, starting at time 0 with respect to the following: Each agent i has a weight w_i that defines the rate of energy consumption while travelling a distance in the graph, and a velocity v_i with which it can move. We are interested in schedules (operating the k agents) that result in a small delivery time T (time when the package arrives at t), and small total energy consumption E. Concretely, we ask for a schedule that: either (i) Minimizes T, (ii) Minimizes lexicographically (T,E) (prioritizing fast delivery), or (iii) Minimizes epsilon*T + (1-epsilon)*E, for a given epsilon, 0<epsilon<1. We show that (i) is solvable in polynomial time, and show that (ii) is polynomial-time solvable for uniform velocities and solvable in time O(n + k log k) for arbitrary velocities on paths, but in general is NP-hard even on planar graphs. As a corollary of our hardness result, (iii) is NP-hard, too. We show that there is a 3-approximation algorithm for (iii) using a single agent.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117133911","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: 7

Faster Exploration of Degree-Bounded Temporal Graphs 度有界时间图的快速探索

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2018-08-27 DOI: 10.4230/LIPIcs.MFCS.2018.36

T. Erlebach, Jakob T. Spooner

{"title":"Faster Exploration of Degree-Bounded Temporal Graphs","authors":"T. Erlebach, Jakob T. Spooner","doi":"10.4230/LIPIcs.MFCS.2018.36","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2018.36","url":null,"abstract":"A temporal graph can be viewed as a sequence of static graphs indexed by discrete time steps. The vertex set of each graph in the sequence remains the same; however, the edge sets are allowed to differ. A natural problem on temporal graphs is the Temporal Exploration problem (TEXP): given, as input, a temporal graph G of order n, we are tasked with computing an exploration schedule (i.e., a temporal walk that visits all vertices in G), such that the time step at which the walk arrives at the last unvisited vertex is minimised (we refer to this time step as the arrival time). It can be easily shown that general temporal graphs admit exploration schedules with arrival time no greater than O(n2). Moreover, it has been shown previously that there exists an infinite family of temporal graphs for which any exploration schedule has arrival time Ω(n2), making these bounds tight for general TEXP instances. We consider restricted instances of TEXP, in which the temporal graph given as input is, in every time step, of maximum degree d; we show an O( n 2 logn ) bound on the arrival time when d is constant, and an O(d log d · n2 logn ) bound when d is given as some function of n. 2012 ACM Subject Classification Mathematics of computing → Graph algorithms","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122552465","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: 22

Consistency for Counting Quantifiers 计数量词的一致性

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2018-08-27 DOI: 10.4230/LIPIcs.MFCS.2018.11

Florent R. Madelaine, B. Martin

引用次数: 0

Rainbow Vertex Coloring Bipartite Graphs and Chordal Graphs 彩虹顶点着色二部图与弦图

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2018-08-20 DOI: 10.4230/LIPIcs.MFCS.2018.83

P. Heggernes, Davis Issac, Juho Lauri, Paloma T. Lima, E. J. V. Leeuwen

{"title":"Rainbow Vertex Coloring Bipartite Graphs and Chordal Graphs","authors":"P. Heggernes, Davis Issac, Juho Lauri, Paloma T. Lima, E. J. V. Leeuwen","doi":"10.4230/LIPIcs.MFCS.2018.83","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2018.83","url":null,"abstract":"Given a graph with colors on its vertices, a path is called a rainbow vertex path if all its internal vertices have distinct colors. We say that the graph is rainbow vertex-connected if there is a rainbow vertex path between every pair of its vertices. We study the problem of deciding whether the vertices of a given graph can be colored with at most k colors so that the graph becomes rainbow vertex-connected. Although edge-colorings have been studied extensively under similar constraints, there are significantly fewer results on the vertex variant that we consider. In particular, its complexity on structured graph classes was explicitly posed as an open question.\u0000We show that the problem remains NP-complete even on bipartite apex graphs and on split graphs. The former can be seen as a first step in the direction of studying the complexity of rainbow coloring on sparse graphs, an open problem which has attracted attention but limited progress. We also give hardness of approximation results for both bipartite and split graphs. To complement the negative results, we show that bipartite permutation graphs, interval graphs, and block graphs can be rainbow vertex-connected optimally in polynomial time.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128937440","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: 5

A Simple Augmentation Method for Matchings with Applications to Streaming Algorithms 流算法应用匹配的一种简单增强方法

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2018-08-01 DOI: 10.4230/LIPIcs.MFCS.2018.74

C. Konrad

{"title":"A Simple Augmentation Method for Matchings with Applications to Streaming Algorithms","authors":"C. Konrad","doi":"10.4230/LIPIcs.MFCS.2018.74","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2018.74","url":null,"abstract":"Given a graph G , it is well known that any maximal matching M in G is at least half the size of a maximum matching M ∗ . In this paper, we show that if G is bipartite, then running the Greedy matching algorithm on a sampled subgraph of G produces enough additional edges that can be used to augment M such that the resulting matching is of size at least (2 −√ 2) | M ∗ | ≈ 0 . 5857 | M ∗ | (ignoring lower order terms) with high probability. The main applications of our method lie in the area of data streaming algorithms, where an algorithm performs few passes over the edges of an n -vertex graph while maintaining a memory of size O ( n polylog n ). Our method immediately yields a very simple two-pass algorithm for Maximum Bipartite Matching ( MBM ) with approximation factor 0 . 5857, which only runs the Greedy matching algorithm in each pass. This slightly improves on the much more involved 0 . 583-approximation algorithm of Esfandiari et al. [ICDMW 2016]. To obtain our main result, we combine our method with a residual sparsity property of the random order Greedy algorithm and give a one-pass random order streaming algorithm for MBM with approximation factor 0 . 5395. This substantially improves upon the one-pass random order 0 . 505-approximation algorithm of Konrad et al. [APPROX 2012].","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127568730","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: 27