Theoretical Computer Science最新文献_第10页

Greedy algorithm for maximization of semi-monotone non-submodular functions with applications 半单调非次模函数最大化的贪婪算法及其应用

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-07-29 DOI: 10.1016/j.tcs.2024.114755

引用次数: 0

Cascade products and Wheeler automata 级联产品和惠勒自动机

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-07-26 DOI: 10.1016/j.tcs.2024.114754

{"title":"Cascade products and Wheeler automata","authors":"","doi":"10.1016/j.tcs.2024.114754","DOIUrl":"10.1016/j.tcs.2024.114754","url":null,"abstract":"<div>The Krohn-Rhodes Decomposition Theorem (KRDT) holds a central position in automata and semigroup theories. It asserts that any finite-state automaton can be broken down into a collection, a cascade, of automata of two simple types (reset and permutation) that, combined, simulate the original automaton.In this paper we show how the cascade product operation and the related decomposition are particularly well-suited for the class of Wheeler automata. In these automata, recently introduced in the context of data compression, states are ordered and transitions map state-intervals to state-intervals. First, we prove that Wheeler DFAs are closed under cascade products in an efficient way: the cascade product of two Wheeler automata is still a Wheeler automaton and has always a number of states which is at most the sum (after removing unreachable states) of the number of states of the two input automata, a result that cannot be achieved for general (even counter-free) automata. Second, we prove that each Wheeler automaton can be decomposed into a cascade of a linear number of reset blocks. Crucially, our line of reasoning avoids the necessity of using full KRDT and proves our results directly by an inductive argument.</div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933773","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

Dynamic Euclidean bottleneck matching 动态欧氏瓶颈匹配

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-07-25 DOI: 10.1016/j.tcs.2024.114727

{"title":"Dynamic Euclidean bottleneck matching","authors":"","doi":"10.1016/j.tcs.2024.114727","DOIUrl":"10.1016/j.tcs.2024.114727","url":null,"abstract":"<div>A fundamental question in computational geometry is for a set of input points in the Euclidean space, that is subject to discrete changes (insertion/deletion of points at each time step), whether it is possible to maintain an exact/approximate minimum weight perfect matching and/or bottleneck matching (a perfect matching that minimizes the length of the longest matched edge), in sublinear update time. In this work, we answer this question in the affirmative for points on a real line and for points in the plane with a bounded geometric spread.For a set P of n points on a line, we show that there exists a dynamic algorithm that maintains an exact bottleneck matching of P and supports insertion and deletion in <math><mi>O</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math> time. Moreover, we show that a modified version of this algorithm maintains an exact minimum-weight perfect matching with <math><mi>O</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math> update (insertion and deletion) time. Next, for a set P of n points in the plane, we show that a (<math><mn>6</mn><msqrt><mrow><mn>2</mn></mrow></msqrt></math>)-factor approximate bottleneck matching of <math><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub></math>, at each time step k, can be maintained in <math><mi>O</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>Δ</mi><mo>)</mo></math> amortized time per insertion and <math><mi>O</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>Δ</mi><mo>+</mo><mo>|</mo><msub><mrow><mi>P</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>|</mo><mo>)</mo></math> amortized time per deletion, where Δ is the geometric spread of P (the ratio between the diameter of P and the distance between the closest pair of points in P).</div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141933713","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

Kolmogorov complexity and nondeterminism versus determinism for polynomial time computations 多项式时间计算的柯尔莫哥洛夫复杂性和非确定性与确定性比较

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-07-25 DOI: 10.1016/j.tcs.2024.114747

{"title":"Kolmogorov complexity and nondeterminism versus determinism for polynomial time computations","authors":"","doi":"10.1016/j.tcs.2024.114747","DOIUrl":"10.1016/j.tcs.2024.114747","url":null,"abstract":"<div>We call any consistent and sufficiently powerful formal theory that enables to algorithmically verify whether a text is a proof algorithmically verifiable mathematics (av-mathematics). We study the fundamental question whether nondeterminism is more powerful than determinism for polynomial time computations in the framework of av-mathematics.Our goal is to show strong indications that nondeterminism is more powerful than determinism for polynomial time computations. To do that, we do not consider decision problems only, but also compression algorithms. We show that at least one of the following three claims must be true:<ul><li>(i)<figure><img></figure></li><li>(ii)non-determinism is more powerful than determinism for polynomial-time compression</li><li>(iii)for each polynomial-time compression algorithm there exists another one of the same asymptotic time complexity that compresses infinitely many strings logarithmically stronger</li></ul>Another surprising consequence of P = NP would be that time-bounded Kolmogorov complexity for any polynomial bound can be computed by deterministic algorithms in polynomial time.</div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304397524003645/pdfft?md5=cc80c7c87843aa9d2e4febe406dc48b5&pid=1-s2.0-S0304397524003645-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141853997","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

On one-sided testing affine subspaces 关于单边测试仿射子空间

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-07-25 DOI: 10.1016/j.tcs.2024.114745

引用次数: 0

Resource efficient stabilization for local tasks despite unknown capacity links 在未知容量链路的情况下，为本地任务提供资源效率高的稳定性

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-07-25 DOI: 10.1016/j.tcs.2024.114744

{"title":"Resource efficient stabilization for local tasks despite unknown capacity links","authors":"","doi":"10.1016/j.tcs.2024.114744","DOIUrl":"10.1016/j.tcs.2024.114744","url":null,"abstract":"<div>Self-stabilizing protocols enable distributed systems to recover correct behavior starting from any arbitrary configuration. In particular, when processors communicate by message passing and the communication links are unbounded, fake messages may be placed in communication links by an adversary. When the number of such fake messages is unknown, self-stabilization may require huge resources:<ul><li>•generic solutions (a.k.a. data link protocols) require unbounded resources, which makes them unrealistic to deploy,</li><li>•specific solutions (e.g., census or tree construction) require <math><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math> or <math><mi>O</mi><mo>(</mo><mi>Δ</mi><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math> bits of memory per node, where n denotes the network size and Δ its maximum degree, which may prevent scalability.</li></ul>We investigate the possibility of resource-efficient self-stabilizing protocols in this context.Specifically, we present self-stabilizing protocols for <math><mo>(</mo><mi>Δ</mi><mo>+</mo><mn>1</mn><mo>)</mo></math>-coloring and maximal independent set construction in any n-node graph, under the asynchronous message-passing model. The problems of <math><mo>(</mo><mi>Δ</mi><mo>+</mo><mn>1</mn><mo>)</mo></math>-coloring and maximal independent set construction are widely regarded as benchmark problems for evaluating local algorithms. Our protocols offer many desirable features. They are deterministic, converge in <math><mi>O</mi><mo>(</mo><mi>k</mi><mi>Δ</mi><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math> message exchanges, where k is the (unknown) initial number of (possibly corrupted) messages in a communication link. They use messages of <math><mi>O</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>+</mo><mi>log</mi><mo>⁡</mo><mi>Δ</mi><mo>)</mo></math> bits with a memory of <math><mi>O</mi><mo>(</mo><mi>Δ</mi><mi>log</mi><mo>⁡</mo><mi>Δ</mi><mo>+</mo><mi>log</mi><mo>⁡</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math> bits at each node. The resource consumption of our protocols is thus almost oblivious to the number of nodes, enabling scalability. Moreover, a striking property of our protocols is that the nodes do not need to know the number, or any bound on the number of messages initially present in each communication link of the initial (potentially corrupted) network configuration. This permits our protocols to handle any future network with unknown message capacity communication links.A key building block of our coloring and maximal independent set schemes is an algorithm to obtain an acyclic orientation of graph edges, that is of independent interest, and","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141842367","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

Chess is hard even for a single player 单人下棋也很难

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-07-23 DOI: 10.1016/j.tcs.2024.114726

{"title":"Chess is hard even for a single player","authors":"","doi":"10.1016/j.tcs.2024.114726","DOIUrl":"10.1016/j.tcs.2024.114726","url":null,"abstract":"<div>We introduce a generalization of “Solo Chess”, a single-player variant of the game that can be played on chess.com. The standard version of the game is played on a regular 8 × 8 chessboard by a single player, with only white pieces, using the following rules: every move must capture a piece, no piece may capture more than 2 times, and if there is a King on the board, it must be the final piece. The goal is to clear the board, i.e., make a sequence of captures after which only one piece is left.We generalize this game to unbounded boards with n pieces, each of which have a given number of captures that they are permitted to make. We show that Generalized Solo Chess is NP-complete, even when it is played by only rooks that have at most two captures remaining. It also turns out to be NP-complete even when every piece is a queen with exactly two captures remaining in the initial configuration. In contrast, we show that solvable instances of Generalized Solo Chess can be completely characterized when the game is: a) played by rooks on a one-dimensional board, and b) played by pawns with two captures left on a 2D board.Inspired by Generalized Solo Chess, we also introduce the Graph Capture Game, which involves clearing a graph of tokens via captures along edges. This game subsumes Generalized Solo Chess played by knights. We show that the Graph Capture Game is NP-complete for undirected graphs and DAGs.</div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141984656","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

Quantum Büchi automata 量子布奇自动机

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-07-22 DOI: 10.1016/j.tcs.2024.114740

引用次数: 0

Approximating power node-deletion problems 近似电源节点删除问题

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-07-17 DOI: 10.1016/j.tcs.2024.114733

{"title":"Approximating power node-deletion problems","authors":"","doi":"10.1016/j.tcs.2024.114733","DOIUrl":"10.1016/j.tcs.2024.114733","url":null,"abstract":"<div>In the Power Vertex Cover (PVC) problem introduced in [1] as a generalization of the well-known Vertex Cover, we are allowed to specify costs for covering edges in a graph individually. Namely, two (nonnegative) weights, <math><mi>w</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo><mtext> and </mtext><mi>w</mi><mo>(</mo><mi>v</mi><mo>,</mo><mi>u</mi><mo>)</mo></math>, are associated with each edge <math><mo>{</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>}</mo><mo>∈</mo><mi>E</mi></math> of an input graph <math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math>, and to cover an edge <math><mo>{</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>}</mo></math>, it is required to assign “power” <math><mi>p</mi><mo>∈</mo><msubsup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow><mrow><mi>V</mi></mrow></msubsup></math> on vertices of G such that either <math><mi>p</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>≥</mo><mi>w</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></math> or <math><mi>p</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>≥</mo><mi>w</mi><mo>(</mo><mi>v</mi><mo>,</mo><mi>u</mi><mo>)</mo></math>. The objective is to minimize the total power assigned on V, <math><msub><mrow><mo>∑</mo></mrow><mrow><mi>v</mi><mo>∈</mo><mi>V</mi></mrow></msub><mi>p</mi><mo>(</mo><mi>v</mi><mo>)</mo></math>, while covering all the edges of G by p.The node-deletion problem for a graph property π is the problem of computing a minimum vertex subset <math><mi>C</mi><mo>⊆</mo><mi>V</mi></math> in a given graph <math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math>, such that the graph satisfies π when all the vertices in C are removed from G. In this paper we consider node-deletion problems extended with the “covering-by-power” condition as in PVC, and present a unified approach for effectively approximating them. The node-deletion problems considered are Partial Vertex Cover (PartVC), Bounded Degree Deletion (BDD), and Feedback Vertex Set (FVS), each corresponding to graph properties π= “the graph has at most <math><mo>|</mo><mi>E</mi><mo>|</mo><mo>−</mo><mi>k</mi></math> edges”, π= “vertex degree of v is no larger than <math><mi>b</mi><mo>(</mo><mi>v</mi><mo>)</mo></math>”, and π= “the graph is acyclic”, respectively. After reducing these problems to the Submodular Set Cover (SSC) problem, we conduct an extended analysis of the approximability of these problems in the new setting of power covering by applying some of the existing techniques for approximating SSC. It will be shown that 1) PPartVC can be approximated within a factor of 2, 2) PBD","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141841678","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

Decision algorithms for reversibility of 1D cellular automata under reflective boundary conditions 反射边界条件下一维蜂窝自动机可逆性的决策算法

IF 0.9 4区计算机科学

Theoretical Computer Science Pub Date : 2024-07-15 DOI: 10.1016/j.tcs.2024.114732

引用次数: 0