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The number of spanning trees for Sierpiński graphs and data center networks 西尔皮斯基图和数据中心网络的生成树数量
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-07-17 DOI: 10.1016/j.ic.2024.105194
Xiaojuan Zhang , Gang Yang , Changxiang He , Ralf Klasing , Yaping Mao
{"title":"The number of spanning trees for Sierpiński graphs and data center networks","authors":"Xiaojuan Zhang ,&nbsp;Gang Yang ,&nbsp;Changxiang He ,&nbsp;Ralf Klasing ,&nbsp;Yaping Mao","doi":"10.1016/j.ic.2024.105194","DOIUrl":"10.1016/j.ic.2024.105194","url":null,"abstract":"<div><p>The number of spanning trees is an important graph invariant related to different topological and dynamic properties of the graph, such as its reliability, synchronization capability and diffusion properties. In 2007, Chang et al. proposed two conjectures on the number of spanning trees of Sierpiński triangle graphs and its spanning tree entropy. In this paper, we completely confirm these conjectures. For data center networks <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>k</mi><mo>,</mo><mi>n</mi></mrow></msub></math></span>, we get the exact formula for <span><math><mi>k</mi><mo>=</mo><mn>1</mn></math></span>, and upper and lower bounds for <span><math><mi>k</mi><mo>≥</mo><mn>2</mn></math></span>. Our results allow also the calculation of the spanning tree entropy of Sierpiński graphs and data center networks.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"300 ","pages":"Article 105194"},"PeriodicalIF":0.8,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141840476","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}
引用次数: 0
Depth-3 circuits for inner product 内积的深度-3 电路
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-07-15 DOI: 10.1016/j.ic.2024.105192
Mika Göös, Ziyi Guan, Tiberiu Mosnoi
{"title":"Depth-3 circuits for inner product","authors":"Mika Göös,&nbsp;Ziyi Guan,&nbsp;Tiberiu Mosnoi","doi":"10.1016/j.ic.2024.105192","DOIUrl":"10.1016/j.ic.2024.105192","url":null,"abstract":"<div><p>What is the <span><math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></msubsup></math></span>-circuit complexity (depth 3, bottom-fanin 2) of the 2<em>n</em>-bit inner product function? The complexity is known to be exponential <span><math><msup><mrow><mn>2</mn></mrow><mrow><msub><mrow><mi>α</mi></mrow><mrow><mi>n</mi></mrow></msub><mi>n</mi></mrow></msup></math></span> for some <span><math><msub><mrow><mi>α</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><mi>Ω</mi><mo>(</mo><mn>1</mn><mo>)</mo></math></span>. We show that the limiting constant <span><math><mi>α</mi><mo>≔</mo><mrow><mrow><mi>lim</mi></mrow><mspace></mspace><mrow><mi>sup</mi></mrow></mrow><mspace></mspace><msub><mrow><mi>α</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> satisfies<span><span><span><math><mn>0.847</mn><mo>.</mo><mo>.</mo><mo>.</mo><mspace></mspace><mo>≤</mo><mspace></mspace><mi>α</mi><mspace></mspace><mo>≤</mo><mspace></mspace><mn>0.965</mn><mo>.</mo><mo>.</mo><mo>.</mo><mspace></mspace><mo>.</mo></math></span></span></span> Determining <em>α</em> is one of the seemingly-simplest open problems about depth-3 circuits. The question was recently raised by Golovnev, Kulikov, and Williams (ITCS 2021) and Frankl, Gryaznov, and Talebanfard (ITCS 2022), who observed that <span><math><mi>α</mi><mo>∈</mo><mo>[</mo><mn>0.5</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>. To obtain our improved bounds, we analyse a covering LP that captures the <span><math><msubsup><mrow><mi>Σ</mi></mrow><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></msubsup></math></span>-complexity up to polynomial factors. In particular, our lower bound is proved by constructing a feasible solution to the dual LP.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"300 ","pages":"Article 105192"},"PeriodicalIF":0.8,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0890540124000579/pdfft?md5=d971ff1d4b55c2511084a32e393fcc6e&pid=1-s2.0-S0890540124000579-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141785105","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}
引用次数: 0
A generic type system for higher-order Ψ-calculi 高阶Ψ计算的通用类型系统
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-07-10 DOI: 10.1016/j.ic.2024.105190
Hans Hüttel , Stian Lybech , Alex R. Bendixen , Bjarke B. Bojesen
{"title":"A generic type system for higher-order Ψ-calculi","authors":"Hans Hüttel ,&nbsp;Stian Lybech ,&nbsp;Alex R. Bendixen ,&nbsp;Bjarke B. Bojesen","doi":"10.1016/j.ic.2024.105190","DOIUrl":"10.1016/j.ic.2024.105190","url":null,"abstract":"<div><p>The Higher-Order Ψ-calculus framework (HOΨ) by Parrow et al. is a generalisation of many first- and higher-order extensions of the <em>π</em>-calculus. In this paper we present a generic type system for HOΨ-calculi. It satisfies a subject reduction property and can be instantiated to yield both existing and new type systems for calculi, that can be expressed as HOΨ-calculi. In this paper, we consider the type system for termination in HO<em>π</em> by Demangeon et al. Moreover, we derive a new type system for the <em>ρ</em>-calculus of Meredith and Radestock and present a type system for non-interference for mobile code.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"300 ","pages":"Article 105190"},"PeriodicalIF":0.8,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0890540124000555/pdfft?md5=5e7315b62a66845496d085f24a5451e4&pid=1-s2.0-S0890540124000555-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719134","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}
引用次数: 0
Characterizing contrasimilarity through games, modal logic, and complexity 通过游戏、模态逻辑和复杂性表征相似性
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-07-10 DOI: 10.1016/j.ic.2024.105191
Benjamin Bisping, Luisa Montanari
{"title":"Characterizing contrasimilarity through games, modal logic, and complexity","authors":"Benjamin Bisping,&nbsp;Luisa Montanari","doi":"10.1016/j.ic.2024.105191","DOIUrl":"10.1016/j.ic.2024.105191","url":null,"abstract":"<div><p>We present the first game characterization of contrasimilarity, the weakest form of bisimilarity. It corresponds to an elegant modal characterization of nested trees of impossible future behavior. The game is exponential but finite for finite-state systems and can thus be used for contrasimulation equivalence checking, of which no tool has been capable to date. By reduction from weak trace equivalence, we establish that contrasimilarity is PSPACE-complete. A machine-checked Isabelle/HOL formalization backs our work and enables further use of contrasimilarity in verification contexts.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"300 ","pages":"Article 105191"},"PeriodicalIF":0.8,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0890540124000567/pdfft?md5=5d349cca73dcbd929167de5c7c879b9e&pid=1-s2.0-S0890540124000567-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141713198","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}
引用次数: 0
A computable and compositional semantics for hybrid systems 混合系统的可计算和组合语义
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-07-08 DOI: 10.1016/j.ic.2024.105189
Davide Bresolin , Pieter Collins , Luca Geretti , Roberto Segala , Tiziano Villa , Sanja Živanović Gonzalez
{"title":"A computable and compositional semantics for hybrid systems","authors":"Davide Bresolin ,&nbsp;Pieter Collins ,&nbsp;Luca Geretti ,&nbsp;Roberto Segala ,&nbsp;Tiziano Villa ,&nbsp;Sanja Živanović Gonzalez","doi":"10.1016/j.ic.2024.105189","DOIUrl":"10.1016/j.ic.2024.105189","url":null,"abstract":"<div><p>Hybrid Systems are systems having a mixed discrete and continuous behaviour that cannot be characterised faithfully using either discrete or continuous models only.</p><p>Due to the intrinsic complexity of hybrid systems, it is highly desirable to describe them compositionally, where large systems are seen as the composition of several simpler subparts that are studied independently. Furthermore, since several problems, including reachability, are undecidable for hybrid systems, the availability of approximate decision procedures is another important feature.</p><p>In this paper, we propose a purely behavioural formalism for hybrid systems that is compositional and supports approximate decision procedures. The formalism is abstract and sufficiently general to subsume or be a semantic framework for most of the concrete formalisms or languages proposed in the literature.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"300 ","pages":"Article 105189"},"PeriodicalIF":0.8,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141637812","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}
引用次数: 0
Pathwise-randomness and models of second-order arithmetic 路径随机性和二阶算术模型
IF 1 4区 计算机科学
Information and Computation Pub Date : 2024-05-24 DOI: 10.1016/j.ic.2024.105181
George Barmpalias , Wei Wang
{"title":"Pathwise-randomness and models of second-order arithmetic","authors":"George Barmpalias ,&nbsp;Wei Wang","doi":"10.1016/j.ic.2024.105181","DOIUrl":"10.1016/j.ic.2024.105181","url":null,"abstract":"<div><p>A tree is <em>pathwise-random</em> if all of its paths are Martin-Löf random. We show that: (a) no weakly 2-random real computes a perfect pathwise-random tree; it follows that the class of perfect pathwise-random trees is null, with respect to any computable measure; (b) there exists a positive-measure pathwise-random tree which does not compute any complete extension of Peano arithmetic; and (c) there exists a perfect pathwise-random tree which does not compute any tree of positive measure and finite randomness deficiency. We then obtain models of second-order arithmetic that separate principles below weak Königs lemma.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"299 ","pages":"Article 105181"},"PeriodicalIF":1.0,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141197156","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}
引用次数: 0
Spiking neural P systems with mute rules 具有静音规则的尖峰神经 P 系统
IF 1 4区 计算机科学
Information and Computation Pub Date : 2024-05-23 DOI: 10.1016/j.ic.2024.105179
Tingfang Wu , Luis Valencia-Cabrera , Mario J. Pérez-Jiménez , Linqiang Pan
{"title":"Spiking neural P systems with mute rules","authors":"Tingfang Wu ,&nbsp;Luis Valencia-Cabrera ,&nbsp;Mario J. Pérez-Jiménez ,&nbsp;Linqiang Pan","doi":"10.1016/j.ic.2024.105179","DOIUrl":"10.1016/j.ic.2024.105179","url":null,"abstract":"<div><p>Spiking neural P (SNP) systems are a class of neural network models that draw inspiration from the functioning of biological neurons. It was experimentally found that there exist autapses from neurons onto themselves in the brain, i.e., a neuron can transmit a signal back to itself through an autapse. In this work, inspired by the characteristics of autapses, a new variant of the SNP system, termed SNP systems with mute rules (SNPMR systems), is considered. Specifically, mute rules have no communication functioning, namely the execution of a mute rule only applies the change on the number of spikes within its residing neuron, rather than affecting other postsynaptic neurons. The computational power of SNPMR systems is examined by demonstrating that SNPMR systems achieve Turing universality with four or ten neurons. In addition, a simulator for SNPMR systems is developed to provide an experimental validation of the systems designed theoretically.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"299 ","pages":"Article 105179"},"PeriodicalIF":1.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141196976","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}
引用次数: 0
Special issue: Selected papers of the 9th International Conference on Algebraic Informatics, CAI 2022 特刊：第 9 届代数信息学国际会议（CAI 2022）论文选
IF 1 4区 计算机科学
Information and Computation Pub Date : 2024-05-22 DOI: 10.1016/j.ic.2024.105180
Dimitrios Poulakis, George Rahonis
{"title":"Special issue: Selected papers of the 9th International Conference on Algebraic Informatics, CAI 2022","authors":"Dimitrios Poulakis,&nbsp;George Rahonis","doi":"10.1016/j.ic.2024.105180","DOIUrl":"https://doi.org/10.1016/j.ic.2024.105180","url":null,"abstract":"","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"299 ","pages":"Article 105180"},"PeriodicalIF":1.0,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141091060","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}
引用次数: 0
Relative approximate bisimulations for fuzzy picture automata 模糊图象自动机的相对近似二拟合
IF 1 4区 计算机科学
Information and Computation Pub Date : 2024-05-15 DOI: 10.1016/j.ic.2024.105172
Chao Yang , Ruiling Wu , Xiaobing Sun , Qichao Wang , Yongming Li
{"title":"Relative approximate bisimulations for fuzzy picture automata","authors":"Chao Yang ,&nbsp;Ruiling Wu ,&nbsp;Xiaobing Sun ,&nbsp;Qichao Wang ,&nbsp;Yongming Li","doi":"10.1016/j.ic.2024.105172","DOIUrl":"10.1016/j.ic.2024.105172","url":null,"abstract":"<div><p>In this paper, we firstly give the notion of relative <em>ϵ</em>-approximate bisimulations between two fuzzy two-dimensional on-line tessellation automata (F2OTAs) and elaborate that the relative error between two F2OTAs, accompanying with a relative <em>ϵ</em>-approximate bisimulation between them, is less than or equal to <em>ϵ</em> where <span><math><mi>ϵ</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>. Moreover, if relative <em>ϵ</em>-approximate bisimulations between two F2OTAs are restricted to be surjective functional, then some properties are drawn and by which relative <em>ϵ</em>-approximate bisimulations on a F2OTA are defined. We construct the factor F2OTA of a F2OTA with respect to a relative <em>ϵ</em>-approximate bisimulation on it and describe the relationship between this factor automaton and the original F2OTA. Whereafter, we novelly design two algorithms to compute all maximal relative <em>ϵ</em>-approximate bisimulations on a given F2OTA. Finally, we discuss some interesting properties of bisimulations on F2OTAs.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"299 ","pages":"Article 105172"},"PeriodicalIF":1.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141041905","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}
引用次数: 0
Being an influencer is hard: The complexity of influence maximization in temporal graphs with a fixed source 成为有影响力的人很困难：具有固定来源的时序图中影响力最大化的复杂性
IF 1 4区 计算机科学
Information and Computation Pub Date : 2024-05-08 DOI: 10.1016/j.ic.2024.105171
Argyrios Deligkas , Michelle Döring , Eduard Eiben , Tiger-Lily Goldsmith , George Skretas
{"title":"Being an influencer is hard: The complexity of influence maximization in temporal graphs with a fixed source","authors":"Argyrios Deligkas ,&nbsp;Michelle Döring ,&nbsp;Eduard Eiben ,&nbsp;Tiger-Lily Goldsmith ,&nbsp;George Skretas","doi":"10.1016/j.ic.2024.105171","DOIUrl":"https://doi.org/10.1016/j.ic.2024.105171","url":null,"abstract":"<div><p>We consider the influence maximization problem over a temporal graph. We deviate from the standard model of influence maximization, where the goal is to choose the most influential vertices. In our model, we are given a fixed vertex and the goal is to find the best time steps to transmit so that the influence of this vertex is maximized. We frame this problem as a spreading process that follows a variant of the susceptible-infected-susceptible (SIS) model and focus on four objective functions. In the <span>MaxSpread</span> objective, the goal is to maximize the number of vertices that get infected at least once. In <span>MaxViral</span> and <span>MaxViralTstep</span>, the goal is to maximize the number of vertices that are infected at the same time step and at a given time step, respectively. Finally, in <span>MinNonViralTime</span>, the goal is to maximize the number of vertices that are infected in every <em>d</em> time-step window.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"299 ","pages":"Article 105171"},"PeriodicalIF":1.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141077859","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}
引用次数: 0
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