International Symposium on Mathematical Foundations of Computer Science最新文献_第9页

Ambiguity Hierarchy of Regular Infinite Tree Languages 正则无限树语言的歧义层次

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2020-09-07 DOI: 10.46298/lmcs-17(3:18)2021

A. Rabinovich, Doron Tiferet

{"title":"Ambiguity Hierarchy of Regular Infinite Tree Languages","authors":"A. Rabinovich, Doron Tiferet","doi":"10.46298/lmcs-17(3:18)2021","DOIUrl":"https://doi.org/10.46298/lmcs-17(3:18)2021","url":null,"abstract":"An automaton is unambiguous if for every input it has at most one accepting\u0000computation. An automaton is k-ambiguous (for k > 0) if for every input it has\u0000at most k accepting computations. An automaton is boundedly ambiguous if it is\u0000k-ambiguous for some $k in mathbb{N}$. An automaton is finitely\u0000(respectively, countably) ambiguous if for every input it has at most finitely\u0000(respectively, countably) many accepting computations.\u0000 The degree of ambiguity of a regular language is defined in a natural way. A\u0000language is k-ambiguous (respectively, boundedly, finitely, countably\u0000ambiguous) if it is accepted by a k-ambiguous (respectively, boundedly,\u0000finitely, countably ambiguous) automaton. Over finite words every regular\u0000language is accepted by a deterministic automaton. Over finite trees every\u0000regular language is accepted by an unambiguous automaton. Over $omega$-words\u0000every regular language is accepted by an unambiguous B\"uchi automaton and by a\u0000deterministic parity automaton. Over infinite trees Carayol et al. showed that\u0000there are ambiguous languages.\u0000 We show that over infinite trees there is a hierarchy of degrees of\u0000ambiguity: For every k > 1 there are k-ambiguous languages that are not k - 1\u0000ambiguous; and there are finitely (respectively countably, uncountably)\u0000ambiguous languages that are not boundedly (respectively finitely, countably)\u0000ambiguous.\u0000","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123131374","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

Linear High-Order Deterministic Tree Transducers with Regular Look-Ahead 具有规则正向的线性高阶确定性树形换能器

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2020-08-28 DOI: 10.4230/LIPIcs.MFCS.2020.38

Paul Gallot, Aurélien Lemay, Sylvain Salvati

{"title":"Linear High-Order Deterministic Tree Transducers with Regular Look-Ahead","authors":"Paul Gallot, Aurélien Lemay, Sylvain Salvati","doi":"10.4230/LIPIcs.MFCS.2020.38","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2020.38","url":null,"abstract":"We introduce the notion of high-order deterministic top-down tree transducers (HODT) whose outputs correspond to single-typed lambda-calculus formulas. These transducers are natural generalizations of known models of top-tree transducers such as: Deterministic Top-Down Tree Transducers, Macro Tree Transducers, Streaming Tree Transducers... We focus on the linear restriction of high order tree transducers with look-ahead (HODTR lin), and prove this corresponds to tree to tree functional transformations defined by Monadic Second Order (MSO) logic. We give a specialized procedure for the composition of those transducers that uses a flow analysis based on coherence spaces and allows us to preserve the linearity of transducers. This procedure has a better complexity than classical algorithms for composition of other equivalent tree transducers, but raises the order of transducers. However, we also indicate that the order of a HODTR lin can always be bounded by 3, and give a procedure that reduces the order of a HODTR lin to 3. As those resulting HODTR lin can then be transformed into other equivalent models, this gives an important insight on composition algorithm for other classes of transducers. Finally, we prove that those results partially translate to the case of almost linear HODTR: the class corresponds to the class of tree transformations performed by MSO with unfolding (not closed by composition), and provide a mechanism to reduce the order to 3 in this case.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"205 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123261789","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: 3

An Improved Approximation Algorithm for Scheduling Under Arborescence Precedence Constraints 树形优先约束下调度的改进逼近算法

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2020-08-25 DOI: 10.4230/LIPIcs.MFCS.2020.84

K. Nguyen

引用次数: 0

A Complexity Dichotomy for Permutation Pattern Matching on Grid Classes 网格类上排列模式匹配的复杂度二分法

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2020-08-11 DOI: 10.4230/LIPIcs.MFCS.2020.52

V'it Jel'inek, Michal Opler, J. Pek'arek

{"title":"A Complexity Dichotomy for Permutation Pattern Matching on Grid Classes","authors":"V'it Jel'inek, Michal Opler, J. Pek'arek","doi":"10.4230/LIPIcs.MFCS.2020.52","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2020.52","url":null,"abstract":"Permutation Pattern Matching (PPM) is the problem of deciding for a given pair of permutations P and T whether the pattern P is contained in the text T. Bose, Buss and Lubiw showed that PPM is NP-complete. In view of this result, it is natural to ask how the situation changes when we restrict the pattern P to a fixed permutation class C; this is known as the C-Pattern PPM problem. \u0000Grid classes are special kind of permutation classes, consisting of permutations admitting a grid-like decomposition into simpler building blocks. Of particular interest are the so-called monotone grid classes, in which each building block is a monotone sequence. Recently, it has been discovered that grid classes, especially the monotone ones, play a fundamental role in the understanding of the structure of general permutation classes. This motivates us to study the hardness of C-Pattern PPM for a (monotone) grid class C. \u0000We provide a complexity dichotomy for C-Pattern PPM when C is taken to be a monotone grid class. Specifically, we show that the problem is polynomial-time solvable if a certain graph associated with C, called the cell graph, is a forest, and it is NP-complete otherwise. We further generalize our results to grid classes whose blocks belong to classes of bounded grid-width. We show that the C-Pattern PPM for such a grid class C is polynomial-time solvable if the cell graph of C avoids a cycle or a certain special type of path, and it is NP-complete otherwise.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132202230","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

Hierarchical Clusterings of Unweighted Graphs 无加权图的层次聚类

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2020-08-07 DOI: 10.4230/LIPIcs.MFCS.2020.47

Svein Høgemo, C. Paul, J. A. Telle

引用次数: 2

Dynamic Time Warping-Based Proximity Problems 基于动态时间翘曲的邻近问题

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2020-08-01 DOI: 10.4230/LIPIcs.MFCS.2020.9

B. Aronov, M. J. Katz, Elad Sulami

{"title":"Dynamic Time Warping-Based Proximity Problems","authors":"B. Aronov, M. J. Katz, Elad Sulami","doi":"10.4230/LIPIcs.MFCS.2020.9","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2020.9","url":null,"abstract":"Dynamic Time Warping (DTW) is a well-known similarity measure for curves, i.e., sequences of points, and especially for time series. We study several proximity problems for curves, where dynamic time warping is the underlying similarity measure. More precisely, we focus on the variants of these problems, in which, whenever we refer to the dynamic time warping distance between two curves, one of them is a line segment (i.e., a sequence of length two). These variants already reveal some of the difficulties that occur when dealing with the more general ones. Specifically, we study the following three problems: (i) distance oracle: given a curve C in R, preprocess it to accommodate distance computations between query segments and C, (ii) segment center : given a set C of curves in R, find a segment s that minimizes the maximum distance between s and a curve in C, and (iii) segment nearest neighbor : given C, construct a data structure for segment nearest neighbor queries, i.e., return the curve in C which is closest to a query segment s. We present solutions to these problems in any constant dimension d ≥ 1, using L∞ for inter-point distances. We also consider the approximation version of the first problem, using L1 for inter-point distances. That is, given a length-m curve C in R, we construct a data structure of size O(m log m) that allows one to compute a 2-approximation of the distance between a query segment s and C in O(log3 m) time. Finally, we describe an interesting experimental study that we performed, which is related to the first problem above. 2012 ACM Subject Classification Theory of computation → Computational geometry; Theory of computation → Design and analysis of algorithms","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"12 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132692985","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 Positivity and Minimality for Second-Order Holonomic Sequences 二阶完整序列的正极小性

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2020-07-23 DOI: 10.4230/LIPIcs.MFCS.2021.67

George Kenison, O. Klurman, Engel Lefaucheux, F. Luca, P. Moree, J. Ouaknine, Markus A. Whiteland, J. Worrell

{"title":"On Positivity and Minimality for Second-Order Holonomic Sequences","authors":"George Kenison, O. Klurman, Engel Lefaucheux, F. Luca, P. Moree, J. Ouaknine, Markus A. Whiteland, J. Worrell","doi":"10.4230/LIPIcs.MFCS.2021.67","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.67","url":null,"abstract":"An infinite sequence $langle{u_n}rangle_{ninmathbb{N}}$ of real numbers is holonomic (also known as P-recursive or P-finite) if it satisfies a linear recurrence relation with polynomial coefficients. Such a sequence is said to be positive if each $u_n geq 0$, and minimal if, given any other linearly independent sequence $langle{v_n}rangle_{n inmathbb{N}}$ satisfying the same recurrence relation, the ratio $u_n/v_n$ converges to $0$. In this paper, we focus on holonomic sequences satisfying a second-order recurrence $g_3(n)u_n = g_2(n)u_{n-1} + g_1(n)u_{n-2}$, where each coefficient $g_3, g_2,g_1 in mathbb{Q}[n]$ is a polynomial of degree at most $1$. We establish two main results. First, we show that deciding positivity for such sequences reduces to deciding minimality. And second, we prove that deciding minimality is equivalent to determining whether certain numerical expressions (known as periods, exponential periods, and period-like integrals) are equal to zero. Periods and related expressions are classical objects of study in algebraic geometry and number theory, and several established conjectures (notably those of Kontsevich and Zagier) imply that they have a decidable equality problem, which in turn would entail decidability of Positivity and Minimality for a large class of second-order holonomic sequences.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"288 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115217487","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: 6

The mergegram of a dendrogram and its stability 树状图的合并图及其稳定性

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2020-07-22 DOI: 10.4230/LIPIcs.MFCS.2020.32

Yu.G. Elkin, V. Kurlin

引用次数: 12

On LTL Model Checking for Low-Dimensional Discrete Linear Dynamical Systems 低维离散线性动力系统的LTL模型检验

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2020-07-06 DOI: 10.4230/LIPIcs.MFCS.2020.54

T. Karimov, J. Ouaknine, J. Worrell

引用次数: 8

Solving Packing Problems with Few Small Items Using Rainbow Matchings 解决包装问题，使用彩虹匹配很少的小项目

International Symposium on Mathematical Foundations of Computer Science Pub Date : 2020-07-06 DOI: 10.4230/LIPIcs.MFCS.2020.11

Max Bannach, Sebastian Berndt, M. Maack, Matthias Mnich, Alexandra Lassota, M. Rau, Malte Skambath

{"title":"Solving Packing Problems with Few Small Items Using Rainbow Matchings","authors":"Max Bannach, Sebastian Berndt, M. Maack, Matthias Mnich, Alexandra Lassota, M. Rau, Malte Skambath","doi":"10.4230/LIPIcs.MFCS.2020.11","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2020.11","url":null,"abstract":"An important area of combinatorial optimization is the study of packing and covering problems, such as Bin Packing, Multiple Knapsack, and Bin Covering. Those problems have been studied extensively from the viewpoint of approximation algorithms, but their parameterized complexity has only been investigated barely. For problem instances containing no \"small\" items, classical matching algorithms yield optimal solutions in polynomial time. In this paper we approach them by their distance from triviality, measuring the problem complexity by the number $k$ of small items. \u0000Our main results are fixed-parameter algorithms for vector versions of Bin Packing, Multiple Knapsack, and Bin Covering parameterized by $k$. The algorithms are randomized with one-sided error and run in time $4^{k} cdot k! cdot n^{O(1)}$. To achieve this, we introduce a colored matching problem to which we reduce all these packing problems. The colored matching problem is natural in itself and we expect it to be useful for other applications. We also present a deterministic fixed-parameter for Bin Packing with run time $(k!)^{2}cdot k cdot 2^{k}cdot ncdot log(n)$.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122403647","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: 3