Information and Computation最新文献

{"title":"Maximal diameter of integral circulant graphs","authors":"Milan Bašić ,&nbsp;Aleksandar Ilić ,&nbsp;Aleksandar Stamenković","doi":"10.1016/j.ic.2024.105208","DOIUrl":"10.1016/j.ic.2024.105208","url":null,"abstract":"<div><p>Integral circulant graphs are proposed as models for quantum spin networks enabling perfect state transfer. Understanding the potential information transfer between nodes in such networks involves calculating the maximal graph diameter. The integral circulant graph <span><math><msub><mrow><mi>ICG</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>D</mi><mo>)</mo></math></span> has vertex set <span><math><msub><mrow><mi>Z</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>}</mo></math></span>, with vertices <em>a</em> and <em>b</em> adjacent if <span><math><mi>gcd</mi><mo>⁡</mo><mo>(</mo><mi>a</mi><mo>−</mo><mi>b</mi><mo>,</mo><mi>n</mi><mo>)</mo><mo>∈</mo><mi>D</mi></math></span>, where <span><math><mi>D</mi><mo>⊆</mo><mo>{</mo><mi>d</mi><mo>:</mo><mi>d</mi><mo>|</mo><mi>n</mi><mo>,</mo><mspace></mspace><mn>1</mn><mo>≤</mo><mi>d</mi><mo>&lt;</mo><mi>n</mi><mo>}</mo></math></span>. Building on the upper bound <span><math><mn>2</mn><mo>|</mo><mi>D</mi><mo>|</mo><mo>+</mo><mn>1</mn></math></span> for the diameter provided by Saxena, Severini, and Shparlinski, we prove that the maximal diameter of <span><math><msub><mrow><mi>ICG</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>D</mi><mo>)</mo></math></span> for a given order <em>n</em> with prime factorization <span><math><msubsup><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow><mrow><msub><mrow><mi>α</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msubsup><mo>⋯</mo><msubsup><mrow><mi>p</mi></mrow><mrow><mi>k</mi></mrow><mrow><msub><mrow><mi>α</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></msubsup></math></span> is <span><math><mi>r</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> or <span><math><mi>r</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>+</mo><mn>1</mn></math></span>, where <span><math><mi>r</mi><mo>(</mo><mi>n</mi><mo>)</mo><mo>=</mo><mi>k</mi><mo>+</mo><mo>|</mo><mo>{</mo><mi>i</mi><mspace></mspace><mo>|</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>&gt;</mo><mn>1</mn><mo>,</mo><mspace></mspace><mn>1</mn><mo>≤</mo><mi>i</mi><mo>≤</mo><mi>k</mi><mo>}</mo><mo>|</mo></math></span>. We show that a divisor set <em>D</em> with <span><math><mo>|</mo><mi>D</mi><mo>|</mo><mo>≤</mo><mi>k</mi></math></span> achieves this bound. We calculate the maximal diameter for graphs of order <em>n</em> and divisor set cardinality <span><math><mi>t</mi><mo>≤</mo><mi>k</mi></math></span>, identifying all extremal graphs and improving the previous upper bound.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105208"},"PeriodicalIF":0.8,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944897","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":"Rational weighted tree languages with storage","authors":"Frederic Dörband ,&nbsp;Zoltán Fülöp ,&nbsp;Heiko Vogler","doi":"10.1016/j.ic.2024.105205","DOIUrl":"10.1016/j.ic.2024.105205","url":null,"abstract":"<div><p>We define the class of rational weighted tree languages with storage over complete, not necessarily commutative, semirings and we repeat its characterization by weighted regular tree grammars with storage. Moreover, we show an alternative proof of the fact that the class of rational weighted tree languages with storage is closed under the rational operations, i.e., top-concatenation, scalar multiplication, sum, tree concatenation, and Kleene-star, where the latter two closure results require that the storage has a reset instruction.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105205"},"PeriodicalIF":0.8,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944900","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":"Zeroing neural network based on the equation AXA = A","authors":"Marko D. Petković,&nbsp;Predrag S. Stanimirović","doi":"10.1016/j.ic.2024.105207","DOIUrl":"10.1016/j.ic.2024.105207","url":null,"abstract":"<div><p>According to available scientific research, there is no information that Zeroing Neural Network (ZNN) models for calculating the matrix inverse and generalized inverses have been studied on the basis of Penrose equations. Our intention is to present a new ZNN design which defined on the Penrose matrix equations and whose intention is to find the time-variant matrix inverse and pseudoinverse. We propose a novel Zeroing function (ZF) based on the first Penrose equation <span><math><mi>A</mi><mi>X</mi><mi>A</mi><mo>=</mo><mi>A</mi></math></span>. The initiated ZNN design for computing the time-varying inverse and the pseudoinverse is defined and investigated. An explicit form of the defined model is also proposed. The convergence properties of the proposed explicit dynamics are investigated in both the time-invariant and time-varying case. Illustrative simulation results are given in order to verify the obtained theoretical results.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105207"},"PeriodicalIF":0.8,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944896","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":"Strategy synthesis for zero-sum neuro-symbolic concurrent stochastic games","authors":"Rui Yan ,&nbsp;Gabriel Santos ,&nbsp;Gethin Norman ,&nbsp;David Parker ,&nbsp;Marta Kwiatkowska","doi":"10.1016/j.ic.2024.105193","DOIUrl":"10.1016/j.ic.2024.105193","url":null,"abstract":"<div><p>Neuro-symbolic approaches to artificial intelligence, which combine neural networks with classical symbolic techniques, are growing in prominence, necessitating formal approaches to reason about their correctness. We propose a novel modelling formalism called neuro-symbolic concurrent stochastic games (NS-CSGs), which comprise two probabilistic finite-state agents interacting in a shared continuous-state environment. Each agent observes the environment using a neural perception mechanism, which converts inputs such as images into symbolic percepts, and makes decisions symbolically. We focus on the class of NS-CSGs with Borel state spaces and prove the existence and measurability of the value function for zero-sum discounted cumulative rewards under piecewise-constant restrictions. To compute values and synthesise strategies, we first introduce a Borel measurable piecewise-constant (B-PWC) representation of value functions and propose a B-PWC value iteration. Second, we introduce two novel representations for the value functions and strategies, and propose a minimax-action-free policy iteration based on alternating player choices.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"300 ","pages":"Article 105193"},"PeriodicalIF":0.8,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0890540124000580/pdfft?md5=324958787cd624f11d92ad65e9802849&pid=1-s2.0-S0890540124000580-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944830","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":"Quantum temporal logic and reachability problems of matrix semigroups","authors":"Nengkun Yu","doi":"10.1016/j.ic.2024.105197","DOIUrl":"10.1016/j.ic.2024.105197","url":null,"abstract":"<div><p>We study the reachability problems of a quantum finite automaton. More precisely, we introduce quantum temporal logic (QTL) that specifies the time-dependent behavior of quantum finite automaton by presenting the time dependence of events temporal operators ◊ (eventually) and □ (always) and employing the projections on subspaces as atomic propositions. The satisfiability of QTL formulae corresponds to various reachability problems of matrix semigroups. We prove that the satisfiability problems for <span><math><mo>□</mo><msubsup><mrow><mo>∨</mo></mrow><mrow><mi>i</mi></mrow><mrow><mi>m</mi></mrow></msubsup><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>, <span><math><mo>◊</mo><mo>□</mo><msubsup><mrow><mo>∨</mo></mrow><mrow><mi>i</mi></mrow><mrow><mi>m</mi></mrow></msubsup><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> and <span><math><mo>□</mo><mo>◊</mo><msubsup><mrow><mo>∨</mo></mrow><mrow><mi>i</mi></mrow><mrow><mi>m</mi></mrow></msubsup><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> with atomic propositions <span><math><msub><mrow><mi>p</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> are decidable. This result solves the open problem of Li and Ying 2014. Notably, the decidability of <span><math><mo>□</mo><mo>◊</mo><mi>p</mi></math></span> can be interpreted as a generalization of Skolem-Mahler-Lech's celebrated theorem based on additive number theory. This paper's last part shows how the quantum finite automaton can model the general concurrent quantum programs, which may involve an arbitrary classical control flow.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"300 ","pages":"Article 105197"},"PeriodicalIF":0.8,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141844019","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":"Parameterized problems complete for nondeterministic FPT time and logarithmic space","authors":"Hans L. Bodlaender ,&nbsp;Carla Groenland ,&nbsp;Jesper Nederlof ,&nbsp;Céline Swennenhuis","doi":"10.1016/j.ic.2024.105195","DOIUrl":"10.1016/j.ic.2024.105195","url":null,"abstract":"<div><p>Let XNLP be the class of parameterized problems such that an instance of size <em>n</em> with parameter <em>k</em> can be solved nondeterministically in time <span><math><mi>f</mi><mo>(</mo><mi>k</mi><mo>)</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msup></math></span> and space <span><math><mi>f</mi><mo>(</mo><mi>k</mi><mo>)</mo><mi>log</mi><mo>⁡</mo><mo>(</mo><mi>n</mi><mo>)</mo></math></span> (for some computable function <em>f</em>). We give a wide variety of XNLP-complete problems, such as <span>List Coloring</span> and <span>Precoloring Extension</span> with pathwidth as parameter, <span>Scheduling of Jobs with Precedence Constraints</span>, with both number of machines and partial order width as parameter, <span>Bandwidth</span> and variants of <span>Weighted CNF-Satisfiability</span>. In particular, this implies that all these problems are <span><math><mi>W</mi><mo>[</mo><mi>t</mi><mo>]</mo></math></span>-hard for all <em>t</em>.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"300 ","pages":"Article 105195"},"PeriodicalIF":0.8,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0890540124000609/pdfft?md5=d0da8381d251320bbac6a22a5a72e28d&pid=1-s2.0-S0890540124000609-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141847856","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":"Secretive interaction","authors":"Eduardo Skapinakis","doi":"10.1016/j.ic.2024.105196","DOIUrl":"10.1016/j.ic.2024.105196","url":null,"abstract":"<div><p>We study the behaviour of <em>n</em> players engaged in a conversation, each attempting to predict the behaviour of the others. We prove that, under a certain notion of interaction, it is possible to learn all other players, but, generally, not without being learned back. We then focus on the interaction of two players and consider, for different methodological restrictions based on the philosophy of science, whether some form of secretive learning can be achieved.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"300 ","pages":"Article 105196"},"PeriodicalIF":0.8,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0890540124000610/pdfft?md5=52e993e68eec638d4166f04f3c0ed5ab&pid=1-s2.0-S0890540124000610-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141851783","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":"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}

{"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}

{"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}