{"title":"Efficient algorithm for stochastic rumor blocking problem in social networks during safety accident period","authors":"","doi":"10.1016/j.tcs.2024.114898","DOIUrl":"10.1016/j.tcs.2024.114898","url":null,"abstract":"<div><div>Rumor sources spread negative information throughout the network, which may cause unbelievable results in real society especially for social safety field. Propagating positive information from several “protector” users is an effective method for rumor blocking once the rumor is detected. Based on the probability of each user being a rumor, “protector” nodes need to be selected in order to prepare for rumor blocking. Given a social network <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>,</mo><mi>P</mi><mo>,</mo><mi>Q</mi><mo>)</mo></math></span>, where <span><math><msub><mrow><mi>P</mi></mrow><mrow><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></msub></math></span> is the probability that <em>v</em> is activated by <em>u</em> after <em>u</em> is activated, and <em>Q</em> is the weight function on node set <em>V</em>, <span><math><msub><mrow><mi>Q</mi></mrow><mrow><mi>v</mi></mrow></msub></math></span> is the probability that <em>v</em> will be a rumor source. Stochastic Rumor Blocking (SRB) problem is to select <em>k</em> nodes as “protector” such that the expected eventually influenced users by rumor is minimized. SRB will be proved to be NP-hard and the objective function is supermodular. We present a Compound Reverse Influence Set sampling method for estimation of the objective value which can be represented as a compound set function. A randomized greedy algorithm with theoretical analysis will be presented and other two different “protector” selection strategies will be proposed for comparison. Finally, we evaluate our algorithm on real world data sets and do comparison among different strategies.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434048","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":"Approximating decision trees with priority hypotheses","authors":"","doi":"10.1016/j.tcs.2024.114896","DOIUrl":"10.1016/j.tcs.2024.114896","url":null,"abstract":"<div><div>This paper addresses the problem of creating decision trees for identifying hypotheses, also known as entities, in a setting where the cost of an action is dependent on the true hypothesis. Specifically, we consider the scenario where <em>n</em> hypotheses are divided into <em>m</em> groups based on their priority levels. Taking an action on a higher priority hypothesis incurs a higher cost. This is relevant to many real-world applications where cost-sensitive decisions need to be made. For example, in a medical diagnosis task, the goal is to take a series of actions (such as medical tests) to identify a cause. Each action in this process requires conducting a test on the patient and observing the outcome, which can take anywhere from a few minutes to several weeks depending on the test. In this case, the cost (the result of waiting for the outcome) is higher if the true hypothesis is more time-sensitive. For example, if the true hypothesis is toxic chemical exposure (as opposed to a chronic disease such as diabetes), a delay of a few minutes could significantly increase the patient's risk of mortality. We propose a group greedy algorithm to solve this problem. We demonstrate that under worst-case scenarios, our algorithm has an approximation ratio of <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span>. Importantly, when <span><math><mi>m</mi><mo>=</mo><mn>1</mn></math></span>, meaning there is only one group of hypotheses, our result is consistent with the logarithmic approximation bound for the traditional optimal decision tree problem.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434047","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":"Algorithms for the thief orienteering problem on directed acyclic graphs","authors":"","doi":"10.1016/j.tcs.2024.114900","DOIUrl":"10.1016/j.tcs.2024.114900","url":null,"abstract":"<div><div>We consider the scenario of routing an agent called a <em>thief</em> through a weighted graph <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> from a start vertex <em>s</em> to an end vertex <em>t</em>. A set <em>I</em> of items each with weight <span><math><msub><mrow><mi>w</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> and profit <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> is distributed among <span><math><mi>V</mi><mo>∖</mo><mo>{</mo><mi>s</mi><mo>,</mo><mi>t</mi><mo>}</mo></math></span>. The thief, who has a knapsack of capacity <em>W</em>, must follow a simple path from <em>s</em> to <em>t</em> within a given time <em>T</em> while packing in the knapsack a set of items taken from the vertices along the path of total weight at most <em>W</em> and maximum profit. The travel time across an edge depends on the edge length and current knapsack load.</div><div>The thief orienteering problem (ThOP) is a generalization of the orienteering problem, the longest path problem, and the 0-1 knapsack problem. We prove that there exists no approximation algorithm for ThOP with constant approximation ratio unless <span><math><mtext>P</mtext><mo>=</mo><mtext>NP</mtext></math></span>, and we present a polynomial-time approximation scheme (PTAS) for a relaxed version of ThOP when <em>G</em> is directed and acyclic that produces solutions that use time at most <span><math><mi>T</mi><mo>(</mo><mn>1</mn><mo>+</mo><mi>ϵ</mi><mo>)</mo></math></span> for any constant <span><math><mi>ϵ</mi><mo>></mo><mn>0</mn></math></span>. We also present a fully polynomial-time approximation scheme (FPTAS) for ThOP on arbitrary undirected graphs where the travel time depends only on the lengths of the edges and <em>T</em> is the length of a shortest path from <em>s</em> to <em>t</em> plus a constant <em>K</em>. Finally, we present a FPTAS for a restricted version of the problem where the input graph is a clique.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142427852","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":"Verifiable attribute-based multi-keyword search scheme with sensitive information hiding for cloud-assisted e-healthcare sharing systems","authors":"","doi":"10.1016/j.tcs.2024.114895","DOIUrl":"10.1016/j.tcs.2024.114895","url":null,"abstract":"<div><div>Cloud-assisted e-healthcare sharing systems (EHSSs) play an increasingly pivotal role in the contemporary healthcare field. By outsourcing electronic medical records (EMRs) to the cloud, hospitals can alleviate local storage and management burdens while facilitating data sharing. Due to the highly sensitive nature of EMRs, encryption is necessary before storing them on the cloud. Attribute-based keyword search (ABKS) enables the privacy protection of EMRs with efficient search services. However, there remain some limitations in practical application. Firstly, most ABKS schemes only support single keyword queries, resulting in inaccurate results and wastage of computing and bandwidth resources. Secondly, since sensitive information within EMRs is encrypted as a whole, different data users (including internal doctors and external researchers) should have varying access rights to prevent leakage of this sensitive information. Thirdly, incorrect search results could lead to misdiagnosis or endanger patients' lives and affect researchers' decision-making processes. To effectively tackle these challenges, this paper proposes a verifiable attribute-based multi-keyword search scheme with sensitive information hiding (VABMKS-SIH) for cloud-assisted EHSSs, where we present a secure model for multi-keyword search with two-level access structure by incorporating an improved blindness filtering technique into ciphertext-policy attribute-based encryption (CP-ABE) within existing keyword search framework. Our scheme employs a super-increasing sequence to aggregate multiple filtered data blocks into one unified ciphertext, thereby greatly reducing communication overhead during the transmission phases of ciphertext. To check the correctness of returned results, we introduce a lightweight algebraic signature algorithm based on fundamental algebraic operations. A security analysis demonstrates that VABMKS-SIH is provably secure under the random oracle mode. Additionally, we also evaluate the proposed scheme's performance to demonstrate its utility in cloud-assisted EHSSs.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142427853","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":"Injective coloring of subclasses of chordal graphs","authors":"","doi":"10.1016/j.tcs.2024.114894","DOIUrl":"10.1016/j.tcs.2024.114894","url":null,"abstract":"<div><div>An injective <em>k</em>-coloring of a graph <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> is a function <span><math><mi>f</mi><mo>:</mo><mi>V</mi><mo>→</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>k</mi><mo>}</mo></math></span> such that for every pair of vertices <em>u</em> and <em>v</em> having a common neighbor, <span><math><mi>f</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>≠</mo><mi>f</mi><mo>(</mo><mi>v</mi><mo>)</mo></math></span>. The injective chromatic number <span><math><msub><mrow><mi>χ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> of a graph <em>G</em> is the minimum <em>k</em> for which <em>G</em> admits an injective <em>k</em>-coloring. Given a graph <em>G</em> and a positive integer <em>k</em>, <span>Decide Injective Coloring Problem</span> is to decide whether <em>G</em> admits an injective k-coloring. <span>Decide Injective Coloring Problem</span> is known to be NP-complete for chordal graphs. In this paper, we strengthen this result by proving that <span>Decide Injective coloring Problem</span> remains NP-complete for undirected path graphs, a proper subclass of chordal graphs. Moreover, we show that it is not possible to approximate the injective chromatic number of an undirected path graph within a factor of <span><math><msup><mrow><mi>n</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>3</mn><mo>−</mo><mi>ε</mi></mrow></msup></math></span> in polynomial time for every <span><math><mi>ε</mi><mo>></mo><mn>0</mn></math></span> unless ZPP = NP. On the positive side, we prove that the injective chromatic number of an interval graph is either <span><math><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> or <span><math><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>+</mo><mn>1</mn></math></span>, where <span><math><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is the maximum degree of <em>G</em>. We also characterize the interval graphs having <span><math><msub><mrow><mi>χ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and <span><math><msub><mrow><mi>χ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>+</mo><mn>1</mn></math></span>. As a consequence of this characterization, we obtain a linear time algorithm to find the injective chromatic number of an interval graph.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142427857","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":"String editing under pattern constraints","authors":"","doi":"10.1016/j.tcs.2024.114889","DOIUrl":"10.1016/j.tcs.2024.114889","url":null,"abstract":"<div><div>We introduce the novel Nearest Pattern Constrained String (NPCS) problem of finding a minimum set <span><math><mi>Q</mi></math></span> of character mutation, insertion, and deletion edit operations sufficient to modify a string <em>x</em> to contain all contiguous substrings in a pattern set <span><math><mi>P</mi></math></span> and no contiguous substrings in a forbidden pattern set <span><math><mi>F</mi></math></span>. Letting Σ be the alphabet of allowed characters, and letting <em>η</em> and ϒ be the longest string length and sum of all string lengths in <span><math><mi>P</mi><mo>∪</mo><mi>F</mi></math></span>, respectively, we show that NPCS is fixed-parameter tractable in <span><math><mo>|</mo><mi>P</mi><mo>|</mo></math></span> with time complexity <span><math><mi>O</mi><mrow><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>|</mo><mi>P</mi><mo>|</mo></mrow></msup><mo>⋅</mo><mi>ϒ</mi><mo>⋅</mo><mo>|</mo><mi>Σ</mi><mo>|</mo><mo>⋅</mo><mrow><mo>(</mo><mo>|</mo><mi>P</mi><mo>|</mo><mo>+</mo><mi>η</mi><mo>)</mo></mrow><mrow><mo>(</mo><mo>|</mo><mi>x</mi><mo>|</mo><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>)</mo></mrow></math></span>. Additionally, we consider a generalization of the NPCS problem in which we allow for constraints based on the membership of substrings in regular languages. In particular, we introduce a problem we denote String Editing under Substring in Language Constraints (StrEdit-SILC), where provided a wildcard-free string <span><math><mi>x</mi><mo>∈</mo><msup><mrow><mi>Σ</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>, a finite set of regular languages <span><math><mi>R</mi><mo>=</mo><mo>{</mo><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mo>…</mo><mo>}</mo></math></span>, and a regular language <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>F</mi></mrow></msub></math></span>, the objective is to find a minimum cost set of mutation, insertion, and deletion edit operations <span><math><mi>Q</mi></math></span> that suffice to convert the input string <em>x</em> into a string <span><math><msup><mrow><mi>x</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>∈</mo><msup><mrow><mi>Σ</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>, where no substring has membership in <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>F</mi></mrow></msub></math></span>, and <span><math><mo>∀</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>∈</mo><mi>R</mi></math></span>, there exists a substring in <span><math><msub><mrow><mi>L</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>. Here, letting Ψ and <em>ϖ</em> be the sum of all regular expression lengths and longest regular expression length for languages in <span><math><mi>R</mi><mo>∪</mo><mo>{</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>F</mi></mrow></msub><mo>}</mo></math></span>, respectively, and letting <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>m</mi><m","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Extremal polyphenyl chains with respect to the Kirchhoff index","authors":"","doi":"10.1016/j.tcs.2024.114893","DOIUrl":"10.1016/j.tcs.2024.114893","url":null,"abstract":"<div><div>Let <em>G</em> be a simple connected graph. The Kirchhoff index of a graph is the sum of the resistance distance between all vertex pairs in the graph <em>G</em>. The resistance distance in a graph is equivalent to the effective resistance between any node pairs in the electrical network obtained by replacing each edge in the graph <em>G</em> with a unit resistance. The polyphenyl chain <span><math><mi>P</mi><mi>L</mi><mo>(</mo><mi>S</mi><mo>)</mo></math></span> is a graph with <em>n</em> hexagons where each hexagon can be reduced to a vertex and connect to a path. In this paper, we characterize polyphenyl chains with maximal and minimal Kirchhoff index.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142427854","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 approximating partial scenario set cover","authors":"","doi":"10.1016/j.tcs.2024.114891","DOIUrl":"10.1016/j.tcs.2024.114891","url":null,"abstract":"<div><div>The <em>Partial Scenario Set Cover problem</em> (PSSC) generalizes the Partial Set Cover problem, which is itself a generalization of the classical Set Cover problem. We are given a finite ground set <em>Q</em>, a collection <span><math><mi>S</mi></math></span> of subsets of <em>Q</em> to choose from, each of which is associated with a nonnegative cost, and a second collection <span><math><mi>U</mi></math></span> of subsets of <em>Q</em> of which a given number <em>l</em> must be covered. The task is to choose a minimum cost sub-collection from <span><math><mi>S</mi></math></span> that covers at least <em>l</em> sets from <span><math><mi>U</mi></math></span>. PSSC is motivated by an application for locating emergency doctors.</div><div>We present two approximation approaches. The first one combines LP-based rounding with a greedy consideration of the scenarios. The other is a variant of the greedy set cover algorithm, and in each iteration tries to minimize the ratio of cost to number of newly covered scenarios. We show that this subproblem, which we call <em>Dense Scenario Set Cover</em> (DSSC), is itself as hard to approximate as Set Cover and NP-hard, even when there is only a single scenario and all sets contain at most three elements. Furthermore, we consider a special case of DSSC where the sets are pairwise disjoint and show that in this case DSSC can be solved in polynomial time. We also provide an approximation for the general case, which we use as a subroutine in the greedy algorithm to obtain an approximation for PSSC.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142427855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A further study on weak Byzantine gathering of mobile agents","authors":"","doi":"10.1016/j.tcs.2024.114892","DOIUrl":"10.1016/j.tcs.2024.114892","url":null,"abstract":"<div><div>The gathering of mobile agents in the presence of Byzantine faults is first studied by Dieudonné et al. Authors provide a polynomial time algorithm handling any number of weak Byzantine agents in the presence of at least one good agent considering start-up delays, i.e., the good agents may not wake up at the same time. Hirose et al. <span><span>[1]</span></span> come up with an algorithm considering start-up delays that use a strong team of at least <span><math><mn>4</mn><msup><mrow><mi>f</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>8</mn><mi>f</mi><mo>+</mo><mn>4</mn></math></span> many good agents but runs much faster than that of Dieudonné et al. Later, Hirose et al. <span><span>[2]</span></span> provided another polynomial time algorithm for gathering in the presence of at least <span><math><mn>7</mn><mi>f</mi><mo>+</mo><mn>7</mn></math></span> good agents. This algorithm works considering start-up delay and achieves simultaneous termination. However, this algorithm depends on the length of the largest ID in the system. We, in this work, provide an algorithm considering start-up delays of the good agents, reducing the number of good agents w.r.t. <span><span>[1]</span></span> to <span><math><msup><mrow><mi>f</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>4</mn><mi>f</mi><mo>+</mo><mn>9</mn></math></span>, and good agents achieve simultaneous termination. Our algorithm runs faster than <span><span>[2]</span></span> when the ID range of the good agents is significantly smaller in comparison to the ID range of all the agents. We also provide a much faster <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> time algorithm for trees using <span><math><mn>3</mn><mi>f</mi><mo>+</mo><mn>2</mn></math></span> agents handling start-up delays and guaranteeing simultaneous termination on a restricted ID range.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357995","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":"Intrinsic universality in automata networks III: On symmetry versus asynchrony","authors":"","doi":"10.1016/j.tcs.2024.114890","DOIUrl":"10.1016/j.tcs.2024.114890","url":null,"abstract":"<div><div>An automata network is a finite assembly of interconnected entities endowed with a set of local maps defined over a common finite alphabet. These relationships are represented through an interaction graph. Together with the local functions, an assignment known as an update scheme directs the evolution of the network by updating specific subsets of entities at discrete time steps. Despite the scrutiny of interaction graphs and update schemes, their profound impact on automata network dynamics remains largely open. This work investigates the intricate interplay between these aspects, with a focus on how update schemes can counterbalance constraints stemming from symmetric local interactions. This paper is the third of a series about intrinsic universality, a notion that assesses both dynamical and computational complexity, encompassing transient behaviors, attractors, and prediction or reachability problems. We consider four update modes—parallel, block-sequential, local clocks, and general periodic— along with several families of symmetric signed conjunctive boolean networks defined by local constraints on signs. Our main result is to show a diagonal complexity leap in this two-dimensional landscape: the stronger the local constraints the higher the level of asynchrony required to obtain intrinsic universality or increase in complexity. We also show how in some cases asynchronism allows to simulate directed interactions from undirected ones with the same local rules.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142357997","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}
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