Theoretical Computer Science最新文献

{"title":"TCS B Editorial","authors":"","doi":"10.1016/j.tcs.2025.115348","DOIUrl":"10.1016/j.tcs.2025.115348","url":null,"abstract":"","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1047 ","pages":"Article 115348"},"PeriodicalIF":0.9,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144168970","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":"Decision trees with short explainable rules","authors":"Victor F.C. Souza ,&nbsp;Ferdinando Cicalese ,&nbsp;Eduardo Sany Laber ,&nbsp;Marco Molinaro","doi":"10.1016/j.tcs.2025.115344","DOIUrl":"10.1016/j.tcs.2025.115344","url":null,"abstract":"<div><div>Decision trees are widely used in many settings where interpretable models are preferred or required. As confirmed by recent empirical studies, the interpretability/explainability of a decision tree critically depends on some of its structural parameters, like size and the average/maximum depth of its leaves. There is indeed a vast literature on the design and analysis of decision tree algorithms that aim at optimizing these parameters.</div><div>This paper contributes to this important line of research: we propose as a novel criterion of measuring the interpretability of a decision tree, the sparsity of the set of attributes that are required to explain the classification of the examples. We give a tight characterization of the best possible guarantees achievable by a decision tree built to optimize both our new measure (which we call the <em>explanation size</em>) and the more classical measures of worst-case and average depth. We also show that from our characterizations it is possible to obtain polynomial algorithms that guarantee <span><math><mi>O</mi><mo>(</mo><mi>ln</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span>-approximation (hence optimal if <span><math><mi>P</mi><mo>≠</mo><mi>N</mi><mi>P</mi></math></span>) for the minimization of both the average/worst-case explanation size and the average/worst-case depth.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1047 ","pages":"Article 115344"},"PeriodicalIF":0.9,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144138118","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":"Editorial: A Personal Journey with TCS","authors":"","doi":"10.1016/j.tcs.2025.115347","DOIUrl":"10.1016/j.tcs.2025.115347","url":null,"abstract":"","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1047 ","pages":"Article 115347"},"PeriodicalIF":0.9,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144168969","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":"Compatibility of convergence algorithms for autonomous mobile robots","authors":"Yuichi Asahiro ,&nbsp;Masafumi Yamashita","doi":"10.1016/j.tcs.2025.115328","DOIUrl":"10.1016/j.tcs.2025.115328","url":null,"abstract":"<div><div>We investigate a swarm of anonymous oblivious mobile robots under the semi-synchronous (<span><math><mi>SSYNC</mi></math></span>) scheduler. Each robot has a function called <em>target function</em> to decide the destination from the robots' positions, and operates in Look-Compute-Move cycles, i.e., identifies the robots' positions, computes the destination by the target function, and then moves there. Robots may have different target functions. Let Φ and Π be a set of target functions and a problem, respectively. If the robots whose target functions are chosen from Φ always solve Π, we say that Φ is compatible with respect to Π. If Φ is compatible with respect to Π, every target function <span><math><mi>ϕ</mi><mo>∈</mo><mi>Φ</mi></math></span> is an algorithm for Π (in the conventional sense). Note that even if both <em>ϕ</em> and <span><math><msup><mrow><mi>ϕ</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> are algorithms for Π, <span><math><mo>{</mo><mi>ϕ</mi><mo>,</mo><msup><mrow><mi>ϕ</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>}</mo></math></span> may not be compatible with respect to Π.</div><div>From the view point of compatibility, we investigate the convergence, the fault tolerant (<span><math><mi>n</mi><mo>,</mo><mi>f</mi></math></span>)-convergence (FC(<em>f</em>)), the fault tolerant (<span><math><mi>n</mi><mo>,</mo><mi>f</mi></math></span>)-convergence to <em>f</em> points (FC(<em>f</em>)-PO), the fault tolerant (<span><math><mi>n</mi><mo>,</mo><mi>f</mi></math></span>)-convergence to a convex <em>f</em>-gon (FC(<em>f</em>)-CP), and the gathering problems, assuming crash failures. As a result, we see that these problems are classified into three groups: The convergence, the FC(1), the FC(1)-PO, and the FC(<em>f</em>)-CP compose the first group: <strong>Every</strong> set of target functions which always shrink the convex hull of a configuration is compatible. The second group is composed of the gathering and the FC(<em>f</em>)-PO for <span><math><mi>f</mi><mo>≥</mo><mn>2</mn></math></span>: <strong>No</strong> set of target functions which always shrink the convex hull of a configuration is compatible. The third group, the FC(<em>f</em>) for <span><math><mi>f</mi><mo>≥</mo><mn>2</mn></math></span>, is placed in between. Thus, the FC(1) and the FC(2), the FC(1)-PO and the FC(2)-PO, and the FC(2) and the FC(2)-PO are respectively in different groups, despite that the FC(1) and the FC(1)-PO are in the first group.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1048 ","pages":"Article 115328"},"PeriodicalIF":0.9,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144167910","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":"Largest convex hulls for convex-hull disjoint clusters with bounded size","authors":"Xuehou Tan ,&nbsp;Rong Chen","doi":"10.1016/j.tcs.2025.115345","DOIUrl":"10.1016/j.tcs.2025.115345","url":null,"abstract":"<div><div>A <em>cluster</em> is a set of points, with a predefined similarity measure. In this paper, we study the problem of computing the largest possible convex hulls, measured by length and by area, of the points that are selected from a set of <em>convex-hull disjoint</em> clusters, one per cluster. We show that the largest convex hulls for convex-hull disjoint clusters with <em>bounded size</em>, measured by length or area, can be computed in <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>)</mo></math></span> time, where <em>n</em> is the number of given clusters. Our solution of either problem for arbitrarily given points relies on the convex hull of all points. Moreover, for a set of the clusters, whose all points are in convex position, its solution can be reduced to several instances of the problem of computing the single-source shortest-paths in a weighted graph. Not only our results significantly improve upon the known time bound <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>9</mn></mrow></msup><mo>)</mo></math></span>, but also the obtained solutions are unified and simple. Moreover, our algorithms can be used to improve the known results on several other variants of the considered problem.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1047 ","pages":"Article 115345"},"PeriodicalIF":0.9,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116623","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":"Characterization of locally most split reliable graphs","authors":"Pablo Romero","doi":"10.1016/j.tcs.2025.115327","DOIUrl":"10.1016/j.tcs.2025.115327","url":null,"abstract":"&lt;div&gt;&lt;div&gt;A two-terminal graph is a graph equipped with two distinguished vertices, called terminals. Let &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; be the set of all nonisomorphic connected simple two-terminal graphs on &lt;em&gt;n&lt;/em&gt; vertices and &lt;em&gt;m&lt;/em&gt; edges. Let &lt;em&gt;G&lt;/em&gt; be any two-terminal graph in &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt;. For every number &lt;em&gt;p&lt;/em&gt; in &lt;span&gt;&lt;math&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; we let each of the edges in &lt;em&gt;G&lt;/em&gt; be independently deleted with probability &lt;span&gt;&lt;math&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt;. The &lt;em&gt;split reliability&lt;/em&gt; &lt;span&gt;&lt;math&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; is the probability that the resulting spanning subgraph has precisely 2 connected components, each one including one terminal. The two-terminal graph &lt;em&gt;G&lt;/em&gt; is &lt;em&gt;uniformly most split reliable&lt;/em&gt; if &lt;span&gt;&lt;math&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; for each &lt;em&gt;H&lt;/em&gt; in &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and every &lt;em&gt;p&lt;/em&gt; in &lt;span&gt;&lt;math&gt;&lt;mo&gt;[&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;]&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;. We say &lt;em&gt;G&lt;/em&gt; is &lt;em&gt;locally most split reliable&lt;/em&gt; if there exists &lt;span&gt;&lt;math&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;mo&gt;&gt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt; such that &lt;span&gt;&lt;math&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;G&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;mo&gt;≥&lt;/mo&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;p&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt; for each &lt;em&gt;H&lt;/em&gt; in &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and every &lt;em&gt;p&lt;/em&gt; in &lt;span&gt;&lt;math&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;δ&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/span&gt;.&lt;/div&gt;&lt;div&gt;Brown and McMullin showed that there exists uniformly most split reliable graphs in each class &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; such that &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;, &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, or &lt;span&gt;&lt;math&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/span&gt;. The authors also proved that there is no uniformly most split reliable two-terminal graph in &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;T&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1047 ","pages":"Article 115327"},"PeriodicalIF":0.9,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144124219","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":"Axiomatising weak bisimulation congruences over CCS with left merge and communication merge","authors":"Luca Aceto ,&nbsp;Valentina Castiglioni ,&nbsp;Anna Ingólfsdóttir ,&nbsp;Bas Luttik","doi":"10.1016/j.tcs.2025.115325","DOIUrl":"10.1016/j.tcs.2025.115325","url":null,"abstract":"<div><div>Classic weak bisimulation-based congruences are not finitely axiomatisable over (the recursion, relabelling, and restriction free fragment of) CCS. Motivated by these negative results, this paper studies the role of auxiliary operators in the finite equational characterisation of CCS parallel composition modulo those congruences. Firstly, we consider CCS with interleaving and left merge. We provide finite equational bases for this language modulo branching, <em>η</em>, delay, and weak bisimulation congruence. In particular, the completeness proofs for <em>η</em>, delay, and weak bisimulation congruence are obtained by reduction to the completeness result for branching bisimulation congruence. Then we extend the language with full merge and communication merge. In this case we provide an equational basis modulo branching bisimulation congruence under the assumption that the set of action names is infinite.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1047 ","pages":"Article 115325"},"PeriodicalIF":0.9,"publicationDate":"2025-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107650","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":"Similarity metrics, metrics, and conditionally negative definite functions","authors":"Daniel Alpay ,&nbsp;Liora Mayats-Alpay","doi":"10.1016/j.tcs.2025.115326","DOIUrl":"10.1016/j.tcs.2025.115326","url":null,"abstract":"<div><div>We give an example of a similarity metric which is not positive definite, and present a general theorem which provides a large family of similarity metrics which are positive definite.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1047 ","pages":"Article 115326"},"PeriodicalIF":0.9,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107644","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 expressibility of the reconstructional color refinement","authors":"V. Arvind ,&nbsp;Johannes Köbler ,&nbsp;Oleg Verbitsky","doi":"10.1016/j.tcs.2025.115321","DOIUrl":"10.1016/j.tcs.2025.115321","url":null,"abstract":"<div><div>In this note we explore the color refinement procedure — also known as the 1-dimensional Weisfeiler-Leman procedure, well-studied in connection with the Graph Isomorphism problem — in the context of the Graph Reconstruction conjecture of Ulam. A basic fact about the Ulam reconstruction conjecture is that the connectedness of a graph is determined by the deck of its vertex-deleted subgraphs, which are considered up to isomorphism. We strengthen this result by proving that connectedness of a graph can even be determined from the deck of its vertex-deleted subgraphs given only by their stable colorings (i.e., up to equivalence under color refinement). It follows as a consequence that connectedness is recognizable by Reconstruction Graph Neural Networks, which is a recently introduced GNN architecture inspired by the reconstruction conjecture (Cotta, Morris, Ribeiro 2021).</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1047 ","pages":"Article 115321"},"PeriodicalIF":0.9,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107649","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 discrete linear order with non-dense punctual degrees","authors":"Kai Jun Khoo,&nbsp;Heer Tern Koh,&nbsp;Keng Meng Ng","doi":"10.1016/j.tcs.2025.115324","DOIUrl":"10.1016/j.tcs.2025.115324","url":null,"abstract":"<div><div>This paper contributes to a systematic study of <em>punctual structures</em>, which are structures computable without delay. The (punctual) degree structure induced by treating “being primitive recursively isomorphic” as a reduction provides insight into the different speeds of enumerations of a given structure. In this paper, we work towards a classification of density of the punctual degrees for linear orders. More specifically, we construct a discrete linear order whose punctual degrees are not dense.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1047 ","pages":"Article 115324"},"PeriodicalIF":0.9,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144107645","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}