{"title":"The complexity of boolean failure identification","authors":"Nicola Galesi , Fariba Ranjbar","doi":"10.1016/j.tcs.2025.115536","DOIUrl":"10.1016/j.tcs.2025.115536","url":null,"abstract":"<div><div>We consider the problem of identifying failure nodes in networks under the <em>Boolean Network Tomography</em> (<span><math><mi>BNT</mi></math></span>) approach, which is based on end-to-end measurements routed in a network along paths and producing a boolean (failure/not-failure) outcome. Such end-to-end measurements paths are usually described by an incidence boolean matrix <span><math><mi>M</mi></math></span> with <span><math><mi>m</mi></math></span> rows (the measurements paths) and <span><math><mi>n</mi></math></span> columns (the nodes of the network). A key notion used in practice in this approach is that of <span><math><mi>k</mi></math></span>-<em>identifiability</em>. Loosely speaking, a set of <span><math><mi>m</mi></math></span> boolean measurements paths over <span><math><mi>n</mi></math></span> nodes is <span><math><mi>k</mi></math></span>-identifiable, where <span><math><mi>k</mi></math></span> is a non-negative integer, if, whenever there are fewer than <span><math><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></math></span> failures, it is always possible to identify unambiguously and uniquely which nodes are failing.</div><div>Following the focus of some recent results analyzing maximal identifiability from a theoretical point of view, this work establishes the complexity of the optimization problem that determines the <em>maximal</em> <span><math><mi>k</mi></math></span> for which a set of measurement paths is <span><math><mi>k</mi></math></span>-identifiable (<span><math><mi>MID</mi></math></span>). We prove that such problem is <span><math><mi>NP</mi></math></span>-hard by a reduction from the <em>Minimum Hitting Set</em> problem and we prove that its decision version is in <span><math><mi>NP</mi></math></span>.</div><div>We further consider the following extremal combinatoric question, which is also of practical relevance: given the number <span><math><mi>n</mi></math></span> of nodes of the network and a non-negative integer value <span><math><mi>k</mi></math></span> for the identifiability, what is the minimal number <span><math><mi>m</mi></math></span> of measurement paths over the <span><math><mi>n</mi></math></span> nodes to consider in such a way that the maximal identifiability is at least <span><math><mi>k</mi></math></span>? A folklore result shows that to have maximal identifiability at least 1, then <span><math><mrow><mi>m</mi><mo>≥</mo><mi>log</mi><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span> (or, equivalently, that if <span><math><mrow><mi>n</mi><mo>></mo><msup><mn>2</mn><mi>m</mi></msup><mo>−</mo><mn>1</mn></mrow></math></span>, then the maximal identifiability is less than or equal 0). In this work we answer this question for each <span><math><mrow><mi>n</mi><mo>∈</mo><mi>N</mi></mrow></math></span> and for each <span><math><mrow><mi>k</mi><mo>≥</mo><mn>2</mn></mrow></math></span>, proving that, there is constant <span><math><mi>C</mi></math></span> such that if <span><math><","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1056 ","pages":"Article 115536"},"PeriodicalIF":1.0,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145095610","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":"Asymptotic analysis of weighted fair division","authors":"Pasin Manurangsi , Warut Suksompong , Tomohiko Yokoyama","doi":"10.1016/j.tcs.2025.115533","DOIUrl":"10.1016/j.tcs.2025.115533","url":null,"abstract":"<div><div>Several resource allocation settings involve agents with unequal entitlements represented by weights. We analyze weighted fair division from an asymptotic perspective: if <span><math><mi>m</mi></math></span> items are divided among <span><math><mi>n</mi></math></span> agents whose utilities are independently sampled from a probability distribution, when is it likely that a fair allocation exist? We show that if the ratio between the weights is bounded, a weighted envy-free allocation exists with high probability provided that <span><math><mrow><mi>m</mi><mo>=</mo><mstyle><mi>Ω</mi></mstyle><mo>(</mo><mi>n</mi><mi>log</mi><mi>n</mi><mo>/</mo><mi>log</mi><mi>log</mi><mi>n</mi><mo>)</mo></mrow></math></span>, generalizing a prior unweighted result. For weighted proportionality, we establish a sharp threshold of <span><math><mrow><mi>m</mi><mo>=</mo><mi>n</mi><mo>/</mo><mo>(</mo><mn>1</mn><mo>−</mo><mi>μ</mi><mo>)</mo></mrow></math></span> for the transition from non-existence to existence, where <span><math><mrow><mi>μ</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></math></span> denotes the mean of the distribution. In addition, we prove that for two agents, a weighted envy-free (and weighted proportional) allocation is likely to exist if <span><math><mrow><mi>m</mi><mo>=</mo><mi>ω</mi><mo>(</mo><msqrt><mi>r</mi></msqrt><mo>)</mo></mrow></math></span>, where <span><math><mi>r</mi></math></span> denotes the ratio between the two weights.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115533"},"PeriodicalIF":1.0,"publicationDate":"2025-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145057236","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}
Jeremy Chizewer , Stephen Melczer , J. Ian Munro , Ava Pun
{"title":"Succinct encodings of binary trees with application to AVL trees","authors":"Jeremy Chizewer , Stephen Melczer , J. Ian Munro , Ava Pun","doi":"10.1016/j.tcs.2025.115537","DOIUrl":"10.1016/j.tcs.2025.115537","url":null,"abstract":"<div><div>We use a novel decomposition to create succinct data structures – supporting a wide range of operations on static trees in constant time – for a variety tree classes, extending results of Munro, Nicholson, Benkner, and Wild. Motivated by the class of AVL trees, we further derive asymptotics for the information-theoretic lower bound on the number of bits needed to store tree classes whose generating functions satisfy certain functional equations. In particular, we prove that AVL trees require approximately 0.938 bits per node to encode.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1056 ","pages":"Article 115537"},"PeriodicalIF":1.0,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145018560","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":"Max-SAT with cardinality constraint parameterized by the number of clauses","authors":"Pallavi Jain , Lawqueen Kanesh , Fahad Panolan , Souvik Saha , Abhishek Sahu , Saket Saurabh , Anannya Upasana","doi":"10.1016/j.tcs.2025.115540","DOIUrl":"10.1016/j.tcs.2025.115540","url":null,"abstract":"<div><div><span>Max-SAT</span> with cardinality constraint (<span>CC-Max-SAT</span>) is one of the classical <span>NP</span>-complete problems. In this problem, given a CNF-formula <span><math><mstyle><mi>Φ</mi></mstyle></math></span> on <span><math><mi>n</mi></math></span> variables, positive integers <span><math><mi>k</mi></math></span> and <span><math><mi>t</mi></math></span>, the goal is to find an assignment <span><math><mi>β</mi></math></span> with at most <span><math><mi>k</mi></math></span> variables set to true (also called a weight <span><math><mi>k</mi></math></span>-assignment) such that the number of clauses satisfied by <span><math><mi>β</mi></math></span> is at least <span><math><mi>t</mi></math></span>. The problem is known to be <span><math><mrow><mi>W</mi><mo>[</mo><mn>2</mn><mo>]</mo></mrow></math></span>-hard with respect to the parameter <span><math><mi>k</mi></math></span>. In this paper, we study the problem with respect to the parameter <span><math><mi>t</mi></math></span>. The special case of <span>CC-Max-SAT</span>, when all the clauses contain only positive literals (known as <span>Maximum Coverage</span>), is known to admit a <span><math><mrow><msup><mn>2</mn><mrow><mi>O</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></msup><msup><mi>n</mi><mrow><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msup></mrow></math></span> algorithm. We present a <span><math><mrow><msup><mn>2</mn><mrow><mi>O</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></msup><msup><mi>n</mi><mrow><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msup></mrow></math></span> algorithm for the general case, <span>CC-Max-SAT</span>. We further study the problem through the lens of kernelization. Since <span>Maximum Coverage</span> does not admit polynomial kernel with respect to the parameter <span><math><mi>t</mi></math></span>, we focus our study on <span><math><msub><mi>K</mi><mrow><mi>d</mi><mo>,</mo><mi>d</mi></mrow></msub></math></span>-free formulas (that is, the clause-variable incidence bipartite graph of the formula that excludes <span><math><msub><mi>K</mi><mrow><mi>d</mi><mo>,</mo><mi>d</mi></mrow></msub></math></span> as a subgraph). Recently, in [Jain et al., SODA 2023], an <span><math><mrow><mi>O</mi><mo>(</mo><mi>d</mi><msup><mi>t</mi><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></math></span> kernel has been designed for the <span>Maximum Coverage</span> problem on <span><math><msub><mi>K</mi><mrow><mi>d</mi><mo>,</mo><mi>d</mi></mrow></msub></math></span>-free incidence graphs. We extend this result to <span>CC-Max-SAT</span> on <span><math><msub><mi>K</mi><mrow><mi>d</mi><mo>,</mo><mi>d</mi></mrow></msub></math></span>-free formulas and design an <span><math><mrow><mi>O</mi><mo>(</mo><mi>d</mi><msup><mn>4</mn><msup><mi>d</mi><mn>2</mn></msup></msup><msup><mi>t</mi><mrow><mi>d</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></math></span> kernel.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1056 ","pages":"Article 115540"},"PeriodicalIF":1.0,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145049070","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}
Jasine Babu , K. Murali Krishnan , Veena Prabhakaran , Nandini J. Warrier
{"title":"Computing eternal vertex cover number of maximal outerplanar graphs in linear time","authors":"Jasine Babu , K. Murali Krishnan , Veena Prabhakaran , Nandini J. Warrier","doi":"10.1016/j.tcs.2025.115530","DOIUrl":"10.1016/j.tcs.2025.115530","url":null,"abstract":"<div><div>Eternal vertex cover problem is a variant of the classical vertex cover problem modeled as a two player attacker-defender game. Computing the eternal vertex cover number of graphs is known to be NP-hard in general and even for bipartite graphs. There is a quadratic complexity algorithm known for this problem for chordal graphs. Maximal outerplanar graphs form a subclass of chordal graphs, for which no algorithm of sub-quadratic time complexity is known. In this paper, we obtain a linear time recursive algorithm for computing eternal vertex cover number of maximal outerplanar graphs.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1056 ","pages":"Article 115530"},"PeriodicalIF":1.0,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144911891","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}
Anthony Bonato, Caleb Jones, Trent G. Marbach, Teddy Mishura, Zhiyuan Zhang
{"title":"Hypergraph burning, matchings, and zero forcing","authors":"Anthony Bonato, Caleb Jones, Trent G. Marbach, Teddy Mishura, Zhiyuan Zhang","doi":"10.1016/j.tcs.2025.115529","DOIUrl":"10.1016/j.tcs.2025.115529","url":null,"abstract":"<div><div>Lazy burning is a recently introduced variation of burning where only one set of vertices is chosen to burn during the first round. In hypergraphs, lazy burning spreads when all but one vertex in a hyperedge is burned. The lazy burning number is the minimum number of initially burned vertices that eventually burn all vertices. We give several equivalent characterizations of lazy burning on hypergraphs using matchings and zero forcing, and then apply these to establish new bounds and complexity results.</div><div>We prove that the lazy burning number of a hypergraph <em>H</em> equals its order minus the maximum cardinality of a certain matching on its incidence graph. Using this characterization, we give a formula for the lazy burning number of a dual hypergraph and give new bounds on the lazy burning number based on various hypergraph parameters. We show that the lazy burning number of a hypergraph may be characterized by a maximal subhypergraph that results from iteratively deleting vertices in singleton hyperedges.</div><div>We prove that lazy burning on a hypergraph is equivalent to zero forcing on its incidence graph and show an equivalence between skew zero forcing on a graph and lazy burning on its neighborhood hypergraph. As a result, we show that the decision problem of computing the lazy burning number of a hypergraph is NP-complete, which solves an open problem in <span><span>[12]</span></span>. By applying the results found for lazy burning, we show that the decision problem of computing the skew zero forcing number for bipartite graphs is NP-complete. We finish with open problems.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1056 ","pages":"Article 115529"},"PeriodicalIF":1.0,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144904642","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}
Laurent Feuilloley , Jan Janoušek , Jan Matyáš Křišťan , Josef Erik Sedláček
{"title":"Decreasing verification radius in local certification","authors":"Laurent Feuilloley , Jan Janoušek , Jan Matyáš Křišťan , Josef Erik Sedláček","doi":"10.1016/j.tcs.2025.115520","DOIUrl":"10.1016/j.tcs.2025.115520","url":null,"abstract":"<div><div>This paper deals with <em>local certification</em>, specifically locally checkable proofs: given a <em>graph property</em>, the task is to certify whether a graph satisfies the property. The verification of this certification needs to be done <em>locally</em> without the knowledge of the whole graph. More precisely, a distributed algorithm, called a <em>verifier</em>, is executed on each vertex. The verifier observes the local neighborhood up to a constant distance and either accepts or rejects.</div><div>We examine the trade-off between the visibility radius and the size of certificates. We describe a procedure that decreases the radius by encoding the neighborhood of each vertex into its certificate. We also provide a corresponding lower bound on the required certificate size increase, showing that such an approach is close to optimal.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1056 ","pages":"Article 115520"},"PeriodicalIF":1.0,"publicationDate":"2025-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144904641","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":"Hybrid encryption in correlated randomness model and KEM combiners","authors":"Somnath Panja , Setareh Sharifian , Shaoquan Jiang , Reihaneh Safavi-Naini","doi":"10.1016/j.tcs.2025.115518","DOIUrl":"10.1016/j.tcs.2025.115518","url":null,"abstract":"<div><div>Hybrid encryption (HE) is an efficient public key encryption system for messages of unrestricted length. Like public key encryption, it does not require the establishment of a shared key, while benefiting from the efficiency and flexibility of symmetric key encryption systems in encrypting messages without length restrictions. An HE system consists of a public key component, called <em>key encapsulation mechanism (KEM)</em>, and a symmetric key component, called <em>data encapsulation mechanism (DEM)</em>. In HE encryption, KEM is used to generate a random key that will be used by DEM algorithm to encrypt the message, and they generate a ciphertext. HE decryption uses the ciphertext to first recover the random key, and then use it to decrypt the message. The KEM/DEM composition theorem proves that if the KEM and DEM components satisfy certain security properties, then the resulting HE will satisfy the well-established security notions of public key encryption systems. KEM/DEM paradigm has been widely studied and used for securing communication over the Internet.</div><div>We motivate and introduce HE in <em>correlated randomness</em> setting where, instead of public and private key, the HE encryption and decryption algorithms have their respective <em>private correlated random</em> values that are partially leaked to the adversary. We define two types of KEMs, <em>iKEM with information theoretic security</em> and <em>cKEM with computational security</em>, and prove a composition theorem for each of these KEMs and a <em>DEM with computational security.</em> This results in efficient and secure HEs with proved computational CPA (Chosen Plaintext Attack) and CCA (Chosen Ciphertext Attack) security, and in the case of iKEM, without relying on specific computational hardness assumptions beyond general ones, such as the existence of one-way hash functions, or practical assumptions, such as the security of AES. We construct two iKEMs, based on an information theoretic secure one-message key agreement protocol, and prove their security against passive and active adversaries, respectively. The iKEMs are used to construct two efficient quantum-resistant HEs, with <em>post-quantum security</em>, using an AES based DEM.</div><div>To combine the new KEM/DEM paradigm of HE with the traditional public key based paradigm, we extend <em>KEM combiners</em> to combine a public-key KEM with an iKEM such that the resulting KEM is as secure as any of the two component KEMs. We discuss our results and their applications, and outline directions for future work.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1054 ","pages":"Article 115518"},"PeriodicalIF":1.0,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144894802","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}
Vittorio Bilò , Marios Mavronicolas , Paul G. Spirakis
{"title":"The contest game for crowdsourcing reviews","authors":"Vittorio Bilò , Marios Mavronicolas , Paul G. Spirakis","doi":"10.1016/j.tcs.2025.115516","DOIUrl":"10.1016/j.tcs.2025.115516","url":null,"abstract":"<div><div>We consider a <em>contest game</em> with discrete strategies, modelling a contest where reviews for a <em>proposal</em> are crowdsourced from <em>n players</em>. Player <em>i</em> has a <em>skill</em> <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>, strategically chooses a <em>quality</em> <span><math><mi>q</mi><mo>∈</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>Q</mi><mo>}</mo></math></span> for her review and pays an <em>effort</em> <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>≥</mo><mn>0</mn></math></span>, strictly increasing with <em>q</em>. Under <em>voluntary participation,</em> a player may opt to not write a review, paying zero effort; <em>mandatory participation</em> excludes this option. For her effort, she is awarded a <em>payment</em> per her <em>payment function</em>, which is either <em>player-invariant</em>, like, e.g., the popular <em>proportional allocation</em>, or <em>player-specific</em>; it is <em>oblivious</em> when it does not depend on the loads on other qualities. The <em>utility</em> to player <em>i</em> is the difference between her payment and her <em>cost,</em> calculated by a <em>skill-effort</em> function <span><math><mi>Λ</mi><mo>(</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>q</mi></mrow></msub><mo>)</mo></math></span>. Skills may vary for <em>arbitrary players</em>; when players are <em>anonymous</em>, <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mn>1</mn></math></span> for each player <em>i</em>. In a <em>pure Nash equilibrium,</em> no player could increase her utility by unilaterally switching to another quality. We show the following results about the (in)existence and the computation of a pure Nash equilibrium:<ul><li><span>•</span><span><div>A contest game with arbitrary players and player-invariant and oblivious payments is an unweighted <em>congestion game with player-specific constants</em> on parallel links <span><span>[42]</span></span>; so it has a generalized ordinal potential, the <em>Finite Improvement Property</em> (<em>FIP</em>) and a pure Nash equilibrium, which can be computed in <span><math><mi>PLS</mi></math></span>. However, under the assumption that the payment function is monotonically nonincreasing, a pure Nash equilibrium can be computed efficiently by resorting to <span><span>[44, Theorem 2]</span></span>.</div><div>In contrast, a pure Nash equilibrium might not exist for <em>(i)</em> anonymous players and player-invariant but not oblivious payments, <em>(ii)</em> arbitrary players and proportionally allocated payments, and <em>(iii)</em> anonymous players and player-specific and oblivious payments; in the latter case, it is <span><math><mi>NP</mi></math></span>-hard to decide existence even if players are anonymous. These counterexamples prove the tightness of our existence r","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1055 ","pages":"Article 115516"},"PeriodicalIF":1.0,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144921828","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 minimal components of substitution subshifts","authors":"Raphaël Henry","doi":"10.1016/j.tcs.2025.115517","DOIUrl":"10.1016/j.tcs.2025.115517","url":null,"abstract":"<div><div>In this paper we study substitutions on <span><math><msup><mrow><mi>A</mi></mrow><mrow><mi>Z</mi></mrow></msup></math></span> where <em>A</em> is a finite alphabet. We precisely characterize the minimal components of substitution subshifts, give an optimal bound for their number and describe their dynamics. The explicitness of these results provides a method to algorithmically compute and count the minimal components of a given substitution subshift.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1056 ","pages":"Article 115517"},"PeriodicalIF":1.0,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144890951","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}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
