Theoretical Computer Science最新文献

{"title":"Complexity of the game connected domination problem","authors":"Vesna Iršič Chenoweth","doi":"10.1016/j.tcs.2025.115559","DOIUrl":"10.1016/j.tcs.2025.115559","url":null,"abstract":"<div><div>The connected domination game is a variant of the domination game where the played vertices must form a connected subgraph at all stages of the game. In this paper we prove that deciding whether the game connected domination number is smaller than a given integer is PSPACE-complete using log-space reductions for both Dominator- and Staller-start connected domination game.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1057 ","pages":"Article 115559"},"PeriodicalIF":1.0,"publicationDate":"2025-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222574","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}

{"title":"A convergence technique for the game i-MARK","authors":"Gabriel Nivasch,&nbsp;Oz Rubinstein","doi":"10.1016/j.tcs.2025.115557","DOIUrl":"10.1016/j.tcs.2025.115557","url":null,"abstract":"<div><div>The game of <span><math><mrow><mi>i</mi><mi>-MARK</mi></mrow></math></span> is an impartial combinatorial game introduced by Sopena (2016). The game is parametrized by two sets of positive integers <span><math><mi>S</mi></math></span>, <span><math><mi>D</mi></math></span>, where <span><math><mrow><mi>min</mi><mi>D</mi><mo>≥</mo><mn>2</mn></mrow></math></span>. From position <span><math><mrow><mi>n</mi><mo>≥</mo><mn>0</mn></mrow></math></span> one can move to any position <span><math><mrow><mi>n</mi><mo>−</mo><mi>s</mi></mrow></math></span>, <span><math><mrow><mi>s</mi><mo>∈</mo><mi>S</mi></mrow></math></span>, as long as <span><math><mrow><mi>n</mi><mo>−</mo><mi>s</mi><mo>≥</mo><mn>0</mn></mrow></math></span>, as well as to any position <span><math><mrow><mi>n</mi><mo>/</mo><mi>d</mi></mrow></math></span>, <span><math><mrow><mi>d</mi><mo>∈</mo><mi>D</mi></mrow></math></span>, as long as <span><math><mrow><mi>n</mi><mo>&gt;</mo><mn>0</mn></mrow></math></span> and <span><math><mi>d</mi></math></span> divides <span><math><mi>n</mi></math></span>. The game ends when no more moves are possible, and the last player to move is the winner. Sopena, and subsequently Friman and Nivasch (2021), characterized the Sprague–Grundy sequences of many cases of <span><math><mrow><mi>i</mi><mi>-MARK</mi><mo>(</mo><mi>S</mi><mo>,</mo><mi>D</mi><mo>)</mo></mrow></math></span> with <span><math><mrow><mo>|</mo><mi>D</mi><mo>|</mo><mo>=</mo><mn>1</mn></mrow></math></span>. Friman and Nivasch also obtained some partial results for the case <span><math><mrow><mi>i</mi><mi>-MARK</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>}</mo><mo>,</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></mrow></math></span>. In this paper we present a convergence technique that gives polynomial-time algorithms for the Sprague–Grundy sequence of many instances of <span><math><mrow><mi>i</mi><mi>-MARK</mi></mrow></math></span> with <span><math><mrow><mo>|</mo><mi>D</mi><mo>|</mo><mo>&gt;</mo><mn>1</mn></mrow></math></span>. In particular, we prove our technique works for all games <span><math><mrow><mi>i</mi><mi>-MARK</mi><mo>(</mo><mrow><mo>{</mo><mn>1</mn><mo>}</mo></mrow><mo>,</mo><mrow><mo>{</mo><msub><mi>d</mi><mn>1</mn></msub><mo>,</mo><msub><mi>d</mi><mn>2</mn></msub><mo>}</mo></mrow><mo>)</mo></mrow></math></span>.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1057 ","pages":"Article 115557"},"PeriodicalIF":1.0,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160026","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}

{"title":"The diagnosability of multiprocessor systems under the enhanced comparison model","authors":"Shiying Wang,&nbsp;Wei Feng","doi":"10.1016/j.tcs.2025.115534","DOIUrl":"10.1016/j.tcs.2025.115534","url":null,"abstract":"<div><div>Diagnosability of a multiprocessor system <span><math><mi>G</mi></math></span> is a fundamental topic. The <span><math><mi>g</mi></math></span>-extra diagnosability of <span><math><mi>G</mi></math></span> requires that every fault-free component in <span><math><mrow><mi>G</mi><mo>−</mo><mi>F</mi></mrow></math></span> has at least <span><math><mrow><mi>g</mi><mo>+</mo><mn>1</mn></mrow></math></span> vertices, while the <span><math><mi>g</mi></math></span>-good-neighbor diagnosability requires that every fault-free vertex has at least <span><math><mi>g</mi></math></span> fault-free neighbors. In this paper, we first propose a new model, the <em>enhanced comparison</em> (EC) model on <span><math><mi>G</mi></math></span>, and establish the relationship between the <span><math><mi>g</mi></math></span>-extra diagnosability and the <span><math><mi>g</mi></math></span>-good-neighbor diagnosability of <span><math><mi>G</mi></math></span>. Second, we present and prove necessary and sufficient conditions for the <span><math><mi>g</mi></math></span>-extra diagnosability of <span><math><mi>G</mi></math></span>, and determine the <span><math><mi>g</mi></math></span>-extra diagnosability of the hyper Petersen network. Finally, we present and prove necessary and sufficient conditions for the <span><math><mi>g</mi></math></span>-good-neighbor diagnosability of <span><math><mi>G</mi></math></span>, and determine the <span><math><mi>g</mi></math></span>-good-neighbor diagnosability of the star graph.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1057 ","pages":"Article 115534"},"PeriodicalIF":1.0,"publicationDate":"2025-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160025","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}

{"title":"Domains, information frames, and their logic","authors":"Dieter Spreen","doi":"10.1016/j.tcs.2025.115558","DOIUrl":"10.1016/j.tcs.2025.115558","url":null,"abstract":"<div><div>In [10], continuous information frames were introduced that capture exactly all continuous domains. They are obtained from the information frames considered in [9] by omitting the conservativity requirement. Information frames generalise Scott’s information systems [8]: Instead of the global consistency predicate, there is now a local consistency predicate for each token. Strong information frames are obtained by strengthening the conditions for these predicates. Let <span><math><mi>CIF</mi></math></span> and <span><math><mi>SIF</mi></math></span> be the corresponding categories.</div><div>In [11] another generalisation of Scott’s information systems was introduced which also exactly captures all continuous domains. As shown in [6], the definition can be simplified while maintaining the representation result. Let <span><math><mi>CIS</mi></math></span> and <span><math><mi>SCIS</mi></math></span> be the corresponding categories. It is shown that all these categories are equivalent. Moreover, the equivalence extends to the subcategories of (strong) continuous information frames with truth elements. Such information frames capture exactly all pointed continuous domains.</div><div>Continuous information frames are families of rudimentary logics, associated with each token is a local consistency predicate and an entailment relation. However, they lack the expressive power of propositional logic. In an attempt to make each of this logics more expressible, continuous stratified conjunctive logics are introduced. These are families of conjunctive logics. The category <span><math><mi>CSL</mi></math></span> of such logics is shown to be isomorphic to <span><math><msub><mi>SIF</mi><mi>t</mi></msub></math></span>, the category of strong continuous information frames with a truth element.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1057 ","pages":"Article 115558"},"PeriodicalIF":1.0,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145270192","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}

{"title":"The 1-good-neighbour diagnosability of modified bubblesort graphs under the PMC and MM* models","authors":"Asghar A. Asgharian Sardroud ,&nbsp;Mohsen Ghasemi ,&nbsp;Shuming Zhou","doi":"10.1016/j.tcs.2025.115556","DOIUrl":"10.1016/j.tcs.2025.115556","url":null,"abstract":"<div><div>The modified bubblesort graph, denoted as <span><math><mrow><mi>M</mi><msub><mi>B</mi><mi>n</mi></msub></mrow></math></span> <span><math><mrow><mo>(</mo><mi>n</mi><mo>≥</mo><mn>2</mn><mo>)</mo></mrow></math></span>, is a noteworthy topological structure in the choice of interconnection networks. In this paper, we determine the <span><math><mi>h</mi></math></span>-extra connectivity of <span><math><mrow><mi>M</mi><msub><mi>B</mi><mi>n</mi></msub></mrow></math></span>. Additionally, we evaluate the 1-good-neighbor diagnosability of modified bubblesort graphs under the PMC and <span><math><msup><mtext>MM</mtext><mo>*</mo></msup></math></span> models. Finally, we investigate the 1-good-neighbor non-inclusive diagnosability of <span><math><mrow><mi>M</mi><msub><mi>B</mi><mi>n</mi></msub></mrow></math></span>.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1057 ","pages":"Article 115556"},"PeriodicalIF":1.0,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160024","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}

{"title":"Efficient shape formation by 3D hybrid programmable matter: An algorithm for low diameter intermediate structures","authors":"Kristian Hinnenthal,&nbsp;David Liedtke,&nbsp;Christian Scheideler","doi":"10.1016/j.tcs.2025.115552","DOIUrl":"10.1016/j.tcs.2025.115552","url":null,"abstract":"<div><div>This paper considers the shape formation problem within the 3D hybrid model, where a single agent with a strictly limited viewing range and the computational capacity of a deterministic finite automaton manipulates passive tiles through pickup, movement, and placement actions. The goal is to reconfigure a set of tiles into a specific shape termed an <em>icicle</em>. The icicle, identified as a dense, hole-free structure, is strategically chosen to function as an intermediate shape for more intricate shape formation tasks. It is designed for easy exploration by a finite-state agent, enabling the identification of tiles that can be lifted without breaking connectivity. Compared to the line shape, the icicle presents distinct advantages, including a reduced diameter and the presence of multiple removable tiles. We propose an algorithm that transforms an arbitrary initially connected tile structure into an icicle in <span><math><mrow><mi>O</mi><mo>(</mo><msup><mi>n</mi><mn>3</mn></msup><mo>)</mo></mrow></math></span> steps, matching the runtime of the line formation algorithm from prior work. Our theoretical contribution is accompanied by an extensive experimental analysis, indicating that our algorithm decreases the diameter of tile structures on average.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1057 ","pages":"Article 115552"},"PeriodicalIF":1.0,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145099422","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}

{"title":"Hop domination on subclasses of perfect graphs","authors":"D. Karthika ,&nbsp;R. Muthucumaraswamy ,&nbsp;Sriram Bhyravarapu ,&nbsp;Pritesh Kumar","doi":"10.1016/j.tcs.2025.115547","DOIUrl":"10.1016/j.tcs.2025.115547","url":null,"abstract":"<div><div>A set <span><math><mrow><mi>S</mi><mo>⊆</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></math></span> is said to be a <em>hop dominating set</em> if every vertex <span><math><mrow><mi>u</mi><mo>∈</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>∖</mo><mi>S</mi></mrow></math></span>, there exists a vertex <span><math><mrow><mi>v</mi><mo>∈</mo><mi>S</mi></mrow></math></span> such that <span><math><mrow><mi>d</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo><mo>=</mo><mn>2</mn></mrow></math></span> where <span><math><mrow><mi>d</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></math></span> represents the distance between <span><math><mi>u</mi></math></span> and <span><math><mi>v</mi></math></span> in <span><math><mi>G</mi></math></span>. Given a graph <span><math><mi>G</mi></math></span>, <span>Hop Domination</span> asks to find the minimum size of a hop dominating set of <span><math><mi>G</mi></math></span>, also called the <em>hop domination number</em>. Henning et al. (Graphs Combin. 2017) showed that <span>Hop Domination</span> is <span>NP</span>-hard for bipartite graphs and chordal graphs. Since the class of chordal graphs is contained in the class of perfect graphs, the problem is <span>NP</span>-hard on perfect graphs. We would like to study the complexity of the problem on subclasses of perfect graphs and understand where the complexity of the problem shifts from tractable to intractable.</div><div>The following are the results of this paper. We present polynomial algorithms for <span>Hop Domination</span> on permutation graphs, interval graphs and biconvex bipartite graphs. This generalizes the polynomial time algorithm for <span>Hop Domination</span> on bipartite permutation graphs. We also initiate a study on this problem from the parameterized complexity perspective. We show that the decision version of <span>Hop Domination</span> is <span><math><mrow><mi>W</mi><mo>[</mo><mn>2</mn><mo>]</mo></mrow></math></span>-hard when parameterized by solution size.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1057 ","pages":"Article 115547"},"PeriodicalIF":1.0,"publicationDate":"2025-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160023","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}

{"title":"Strategy templates for almost-sure and positive winning of stochastic parity games towards permissive and resilient control","authors":"Kittiphon Phalakarn ,&nbsp;Sasinee Pruekprasert ,&nbsp;Ichiro Hasuo","doi":"10.1016/j.tcs.2025.115535","DOIUrl":"10.1016/j.tcs.2025.115535","url":null,"abstract":"<div><div><em>Stochastic games</em> are fundamental in various applications, including the control of cyber-physical systems (CPS), where both controller and environment are modeled as players. Traditional algorithms typically aim to determine a single <em>winning strategy</em> to develop a controller. However, in CPS control and other domains, permissive controllers are essential, as they enable the system to adapt when additional constraints arise and remain resilient to runtime changes. This work generalizes the concept of <em>(permissive winning) strategy templates</em>, originally introduced by Anand et al. at TACAS and CAV 2023 for deterministic games, to incorporate stochastic games. These templates capture an infinite number of winning strategies, allowing for efficient strategy adaptation to system changes. We focus on two winning criteria (almost-sure and positive winning) and five winning objectives (safety, reachability, Büchi, co-Büchi, and parity). Our contributions include algorithms for constructing templates for each winning criterion and objective and a novel approach for extracting a winning strategy from a given template. Discussions on comparisons between templates and between strategy extraction methods are provided.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1057 ","pages":"Article 115535"},"PeriodicalIF":1.0,"publicationDate":"2025-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110011","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}

{"title":"Bi-criteria sublinear time algorithms for clustering with outliers in high dimensions","authors":"Jiawei Huang ,&nbsp;Wenjie Liu ,&nbsp;Hu Ding","doi":"10.1016/j.tcs.2025.115538","DOIUrl":"10.1016/j.tcs.2025.115538","url":null,"abstract":"<div><div>Real-world datasets often contain outliers, and the presence of outliers can make clustering problems be much more challenging. Existing algorithms for clustering with outliers often have high computational complexities. In this paper, we propose a simple yet effective sublinear framework for solving the representative center-based clustering with outliers problems: <span><math><mi>k</mi></math></span>-median/means clustering with outliers. Our analysis is fundamentally different from the previous (uniform and non-uniform) sampling based ideas. In particular, our sample complexity is independent of the input size and dimensionality, and thus it is suitable for dealing with large-scale and high-dimensional datasets. We also conduct a set of experiments to evaluate the effectiveness of our proposed method on both synthetic and real datasets.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1057 ","pages":"Article 115538"},"PeriodicalIF":1.0,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110012","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}

{"title":"A new generalized lattice attack against a family of RSA-like cryptosystems","authors":"Michel Seck,&nbsp;Abdoul Aziz Ciss","doi":"10.1016/j.tcs.2025.115548","DOIUrl":"10.1016/j.tcs.2025.115548","url":null,"abstract":"<div><div>Recently, Cotan and Teşeleanu (NordSec 2023) published an RSA-like cryptosystem. While in RSA, the public exponent <span><math><mi>e</mi></math></span> and the private exponent <span><math><mi>d</mi></math></span> are related by the equation <span><math><mrow><mi>e</mi><mi>d</mi><mo>−</mo><mi>k</mi><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>(</mo><mi>q</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>=</mo><mn>1</mn></mrow></math></span>, in their scheme, <span><math><mi>e</mi></math></span> and <span><math><mi>d</mi></math></span> are related to the equation <span><math><mrow><mi>e</mi><mi>d</mi><mo>−</mo><mi>k</mi><mrow><mo>(</mo><msup><mi>p</mi><mi>n</mi></msup><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>(</mo><msup><mi>q</mi><mi>n</mi></msup><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mo>=</mo><mn>1</mn></mrow></math></span> for some positive integer <span><math><mi>n</mi></math></span>. Teşeleanu (CSCML 2024) showed that one can factor the modulus <span><math><mi>N</mi></math></span> using a lattice attack if <span><math><mi>d</mi></math></span> is small. In this paper, we extend his attack by showing that if the private exponent is either too small or too large, one can factor <span><math><mi>N</mi></math></span> in polynomial time by solving the generalized equation <span><math><mrow><mi>e</mi><mi>u</mi><mo>−</mo><mrow><mo>(</mo><msup><mi>p</mi><mi>n</mi></msup><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>(</mo><msup><mi>q</mi><mi>n</mi></msup><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mi>v</mi><mo>=</mo><mo>±</mo><mn>1</mn></mrow></math></span> using lattice reduction techniques.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1055 ","pages":"Article 115548"},"PeriodicalIF":1.0,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145095234","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}