Theoretical Computer Science最新文献

{"title":"Locally-iterative (Δ + 1)-coloring in sublinear (in Δ) rounds","authors":"Xinyu Fu ,&nbsp;Yitong Yin ,&nbsp;Chaodong Zheng","doi":"10.1016/j.tcs.2025.115456","DOIUrl":"10.1016/j.tcs.2025.115456","url":null,"abstract":"<div><div>Distributed graph coloring is one of the most extensively studied problems in distributed computing. There is a canonical family of distributed graph coloring algorithms known as the <em>locally-iterative</em> coloring algorithms, first formalized in Szegedy and Vishwanathan (1993) <span><span>[6]</span></span>. In such algorithms, every vertex iteratively updates its own color according to a predetermined function of the current coloring of its local neighborhood. Due to the simplicity and naturalness of its framework, locally-iterative coloring algorithms are of great significance both in theory and practice.</div><div>In this paper, we give a locally-iterative <span><math><mo>(</mo><mi>Δ</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-coloring algorithm with runtime <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>Δ</mi></mrow><mrow><mn>3</mn><mo>/</mo><mn>4</mn></mrow></msup><mi>log</mi><mo>⁡</mo><mi>Δ</mi><mo>)</mo><mo>+</mo><msup><mrow><mi>log</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>⁡</mo><mi>n</mi></math></span>, using messages of size <span><math><mi>O</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> bits. This is the first locally-iterative <span><math><mo>(</mo><mi>Δ</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-coloring algorithm with sublinear-in-Δ runtime, and answers the main open question raised by previous best result (Barenboim et al. (2021) <span><span>[16]</span></span>). The key component of our algorithm is a new locally-iterative procedure that transforms an <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>-coloring to a <span><math><mo>(</mo><mi>Δ</mi><mo>+</mo><mi>O</mi><mo>(</mo><msup><mrow><mi>Δ</mi></mrow><mrow><mn>3</mn><mo>/</mo><mn>4</mn></mrow></msup><mi>log</mi><mo>⁡</mo><mi>Δ</mi><mo>)</mo><mo>)</mo></math></span>-coloring in <span><math><mi>o</mi><mo>(</mo><mi>Δ</mi><mo>)</mo></math></span> time. As an application of our result, we also devise a self-stabilizing algorithm for <span><math><mo>(</mo><mi>Δ</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-coloring with <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>Δ</mi></mrow><mrow><mn>3</mn><mo>/</mo><mn>4</mn></mrow></msup><mi>log</mi><mo>⁡</mo><mi>Δ</mi><mo>)</mo><mo>+</mo><msup><mrow><mi>log</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>⁡</mo><mi>n</mi></math></span> stabilization time, using <span><math><mi>O</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span>-bit messages. To the best of our knowledge, this is the first self-stabilizing algorithm for <span><math><mo>(</mo><mi>Δ</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-coloring in the CONGEST model with sublinear-in-Δ stabilization time.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1052 ","pages":"Article 115456"},"PeriodicalIF":0.9,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655292","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":"Computing the D-base and D-relation in finite closure systems","authors":"Kira Adaricheva ,&nbsp;Lhouari Nourine ,&nbsp;Simon Vilmin","doi":"10.1016/j.tcs.2025.115459","DOIUrl":"10.1016/j.tcs.2025.115459","url":null,"abstract":"<div><div>Implicational bases (IBs) are a common representation of finite closure systems and lattices, along with meet-irreducible elements. They appear in a wide variety of fields ranging from logic and databases to Knowledge Space Theory.</div><div>Different IBs can represent the same closure system. Therefore, several IBs have been studied, such as the canonical and canonical direct bases. In this paper, we investigate the <em>D</em>-base, a refinement of the canonical direct base. It is connected with the <em>D</em>-relation, an essential tool in the study of free lattices. The <em>D</em>-base demonstrates desirable algorithmic properties, and together with the <em>D</em>-relation, it conveys essential properties of the underlying closure system. Hence, computing the <em>D</em>-base and the <em>D</em>-relation of a closure system from another representation is crucial to enjoy its benefits. However, complexity results for this task are lacking.</div><div>In this paper, we give algorithms and hardness results for the computation of the <em>D</em>-base and <em>D</em>-relation. Specifically, we establish the <strong>NP</strong>-completeness of finding the <em>D</em>-relation from an arbitrary IB; we give an output-quasi-polynomial time algorithm to compute the <em>D</em>-base from meet-irreducible elements; and we obtain a polynomial-delay algorithm computing the <em>D</em>-base from an arbitrary IB. These results complete the picture regarding the complexity of identifying the <em>D</em>-base and <em>D</em>-relation of a closure system.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1052 ","pages":"Article 115459"},"PeriodicalIF":0.9,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655291","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":"Combinatorial characterizations and algorithms for trajectory planning of an articulated robotic probe in three dimensions","authors":"Ovidiu Daescu ,&nbsp;Ka Yaw Teo","doi":"10.1016/j.tcs.2025.115461","DOIUrl":"10.1016/j.tcs.2025.115461","url":null,"abstract":"<div><div>Consider a three-dimensional workspace that contains <em>n</em> disjoint triangular obstacles and a destination point. We define the problem of trajectory planning for a two-segment articulated probe as the task of computing a feasible path that allows the probe to reach the destination while avoiding collisions with obstacles. The articulated probe is constrained to a sequence of movements – a straight-line insertion possibly followed by a rotation of the end segment. A feasible probe trajectory is referred to as <em>extremal</em> when the probe or its path is in immediate contact with obstacles, effectively defining the boundaries of the probe trajectory. We prove that if there exists a feasible probe trajectory, then a finite set of extremal feasible trajectories must be present. Through careful case analysis, we show that these extremal trajectories can be represented by <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>)</mo></math></span> combinatorial events. We present a solution approach that enumerates and verifies these combinatorial events for feasibility in overall <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>4</mn><mo>+</mo><mi>ε</mi></mrow></msup><mo>)</mo></math></span> time using <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>4</mn><mo>+</mo><mi>ε</mi></mrow></msup><mo>)</mo></math></span> space, for any constant <span><math><mi>ε</mi><mo>&gt;</mo><mn>0</mn></math></span>. The enumeration algorithm is highly parallel, considering that each combinatorial event can be generated and verified for feasibility independently of the others. In the process of deriving our solution, we design the first data structure for addressing a special instance of circular sector emptiness queries among polyhedral obstacles in three-dimensional space, and provide a simplified data structure for the corresponding emptiness query problem in two dimensions.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1053 ","pages":"Article 115461"},"PeriodicalIF":0.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144653150","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":"On the intersection problem for quantum finite automata","authors":"Andrea Benso ,&nbsp;Flavio D'Alessandro ,&nbsp;Paolo Papi","doi":"10.1016/j.tcs.2025.115454","DOIUrl":"10.1016/j.tcs.2025.115454","url":null,"abstract":"<div><div>This paper continues the study of measure-once finite quantum automata building on work by Bertoni, Choffrut et al. We investigate conditions ensuring that, given a language recognized by such a device and a language generated by a grammar, it is decidable whether or not they have a nonempty intersection.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1053 ","pages":"Article 115454"},"PeriodicalIF":0.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144653222","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":"Computable formal contexts","authors":"Huishan Wu","doi":"10.1016/j.tcs.2025.115457","DOIUrl":"10.1016/j.tcs.2025.115457","url":null,"abstract":"<div><div>This paper studies effective aspects of mathematical structures in formal concept analysis from the standpoint of computability theory. Firstly, we consider the notion of formal concepts of formal contexts and prove that the first and second derivation of a subset of objects of a computable context are <span><math><msubsup><mrow><mi>Π</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>0</mn></mrow></msubsup></math></span>- and <span><math><msubsup><mrow><mi>Π</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>0</mn></mrow></msubsup></math></span>-complete, respectively. Secondly, we examine the complexity of two representative processes in finding reductions of a context. To study the complexity of the process of merging objects with the same object intents of a context, we define a natural equivalence relation on objects of the context and show that the object equivalence relation of a computable context is <span><math><msubsup><mrow><mi>Π</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>0</mn></mrow></msubsup></math></span>-complete. We directly formalize the other process of removing reducible objects of a context via reducible objects themselves and prove that the set of reducible objects of a computable context is <span><math><msubsup><mrow><mi>Π</mi></mrow><mrow><mn>3</mn></mrow><mrow><mn>0</mn></mrow></msubsup></math></span>-complete. The down-left arrow relation is a useful tool to find reducible objects of a context. Lastly, we show that the arrow relation of a computable context is <span><math><msubsup><mrow><mi>Π</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>0</mn></mrow></msubsup></math></span>-complete. By dealing with dual contexts, we obtain the same complexity results on corresponding structures based on attributes of contexts.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115457"},"PeriodicalIF":0.9,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655551","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":"Discriminating code and set cover with k-bend paths","authors":"Yu Yang,&nbsp;Cai-Xia Wang,&nbsp;Shou-Jun Xu","doi":"10.1016/j.tcs.2025.115458","DOIUrl":"10.1016/j.tcs.2025.115458","url":null,"abstract":"<div><div>In this paper, we explore geometric discriminating code and set cover problems with <em>k</em>-bend paths. We first demonstrate that both the discriminating code problem and the set cover problem with unit 0-bend paths are NP-hard. Additionally, we establish that the set cover problem is NP-hard with unit 1-bend paths restricted to type ⌜, where horizontal segments intersect a vertical line and vertical segments intersect a horizontal line. Furthermore, we show that the discriminating code problem remains NP-hard with unit 1-bend paths of type ⌜, where all vertical segments intersect a horizontal line. Finally, we provide approximation algorithms for these two problems, specifically for 0-bend paths of uniform length and for 1-bend paths of type ⌜, where all horizontal and vertical segments are of equal length.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115458"},"PeriodicalIF":0.9,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144633893","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":"Path cover using only short paths","authors":"Mingyang Gong ,&nbsp;Guangting Chen ,&nbsp;Zhi-Zhong Chen ,&nbsp;Guohui Lin ,&nbsp;Riki Uchida","doi":"10.1016/j.tcs.2025.115455","DOIUrl":"10.1016/j.tcs.2025.115455","url":null,"abstract":"<div><div>We study a variant of the well-known <em>Path Cover</em> problem where the candidate paths in a solution have orders up to a fixed integer <em>k</em>. In Path Cover, one finds a minimum number of vertex-disjoint paths in an input graph to cover all the vertices; in our variant, not all paths but only those short ones, i.e., containing up to <em>k</em> vertices, can be used as candidates. The problem is NP-hard when <span><math><mi>k</mi><mo>≥</mo><mn>3</mn></math></span>; in the literature, there exist quite a number of approximation algorithms, especially for small <em>k</em>'s. We present an improved <span><math><mfrac><mrow><mi>k</mi></mrow><mrow><mn>3</mn></mrow></mfrac></math></span>-approximation algorithm for <span><math><mi>k</mi><mo>∈</mo><mo>{</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>8</mn><mo>}</mo></math></span>, an improved <span><math><mfrac><mrow><mn>55</mn></mrow><mrow><mn>31</mn></mrow></mfrac></math></span>-approximation algorithm for <span><math><mi>k</mi><mo>=</mo><mn>5</mn></math></span>, and an improved <span><math><mfrac><mrow><mn>8</mn></mrow><mrow><mn>5</mn></mrow></mfrac></math></span>-approximation algorithm for <span><math><mi>k</mi><mo>=</mo><mn>4</mn></math></span>. The novelty inside these improved algorithms is observing a close connection between an optimal path cover and a certain polynomial-time computed edge set.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115455"},"PeriodicalIF":0.9,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614657","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":"Non finite axiomatisability of weak bisimulation-based congruences","authors":"Luca Aceto ,&nbsp;Valentina Castiglioni ,&nbsp;Anna Ingólfsdóttir ,&nbsp;Bas Luttik","doi":"10.1016/j.tcs.2025.115453","DOIUrl":"10.1016/j.tcs.2025.115453","url":null,"abstract":"<div><div>We study the axiomatisability of CCS parallel composition operator modulo weak bisimulation-based congruences. Specifically, we prove that all congruences that are coarser than rooted branching bisimilarity, and finer than rooted weak bisimilarity, do not admit a finite equational axiomatisation over the recursion, restriction, and relabelling free fragment of CCS.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115453"},"PeriodicalIF":0.9,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614827","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":"On the Weisfeiler algorithm of depth-1 stabilization","authors":"Gang Chen ,&nbsp;Qing Ren ,&nbsp;Ilia Ponomarenko","doi":"10.1016/j.tcs.2025.115460","DOIUrl":"10.1016/j.tcs.2025.115460","url":null,"abstract":"<div><div>An origin of the multidimensional Weisfeiler-Leman algorithm goes back to a refinement procedure of deep stabilization, introduced by B. Weisfeiler in a paper included in the collective monograph “On construction and identification of graphs” (1976). This procedure is recursive and the recursion starts from an algorithm of depth-1 stabilization, which has never been discussed in the literature.</div><div>A goal of the present paper is to show that a simplified algorithm of the depth-1 stabilization has the same power as the 3-dimensional Weisfeiler-Leman algorithm. It is proved that the class of coherent configurations obtained as the output of this simplified algorithm coincides with the class introduced earlier by the third author. As an application we also prove that if there exist at least two nonisomorphic projective planes of order <em>q</em>, then the Weisfeiler-Leman dimension of the incidence graph of any projective plane of order <em>q</em> is at least 4.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115460"},"PeriodicalIF":0.9,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614826","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":"Modular soundness checking of feature model evolution plans","authors":"Crystal Chang Din ,&nbsp;Charaf Eddine Dridi ,&nbsp;Ida Sandberg Motzfeldt ,&nbsp;Violet Ka I Pun ,&nbsp;Volker Stolz ,&nbsp;Ingrid Chieh Yu","doi":"10.1016/j.tcs.2025.115451","DOIUrl":"10.1016/j.tcs.2025.115451","url":null,"abstract":"<div><div>Feature model evolution plans (FMEPs) describe how feature models for software product lines (SPLs) evolve over time. While different feature models can exist for different points in time over the lifetime of the product line, an FMEP describes how to compute a feature model for a given time point. SPLs capitalise on the variability and reusability of the software through combining optional and mandatory features. As business requirements change over time, FMEPs should support intermediate update. A plan hence contains updates to an initial model by adding, deleting, moving or changing elements at different points in time, in line with the evolving business requirements on the SPL, potentially affecting feature models that should be derived in the future from the plan.</div><div>A recurring challenge in maintaining FMEPs is that updates may lead to inconsistent intermediate feature models, most notably so-called paradoxes. A paradox may not materialise at the first point in time an update on the plan is performed to obtain a particular feature model, but may only in combination with a later modification prescribed by the plan create a structurally invalid model. Correspondingly, a single modification to a plan may require multiple checks over the liftetime of the affected elements to rule out paradoxes.</div><div>Current approaches require the analysis from the point in time an update is applied to an FMEP throughout the entire lifetime of the plan. In this paper, we define a so-called interval-based feature model (IBFM) to represent FMEPs, with a precise definition of spatial and temporal scopes that narrow the time interval and the sub-models that an update can affect. We propose a rule system for updating IBFMs, and also prove the soundness of the proposed rules and show their modularity, i.e., that each rule operates strictly within its temporal and spatial scopes. We have conducted a detailed evaluation on our modular approach and present the experimental results, which show that we outperform an existing linear approach.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115451"},"PeriodicalIF":0.9,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632958","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}