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Strategy synthesis for zero-sum neuro-symbolic concurrent stochastic games 零和神经符号并发随机博弈的策略合成
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-07-25 DOI: 10.1016/j.ic.2024.105193
Rui Yan , Gabriel Santos , Gethin Norman , David Parker , Marta Kwiatkowska
{"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}
引用次数: 0
Quantum temporal logic and reachability problems of matrix semigroups 量子时态逻辑与矩阵半群的可达性问题
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-07-23 DOI: 10.1016/j.ic.2024.105197
Nengkun Yu
{"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}
引用次数: 0
Parameterized problems complete for nondeterministic FPT time and logarithmic space 完成非确定性 FPT 时间和对数空间的参数化问题
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-07-19 DOI: 10.1016/j.ic.2024.105195
Hans L. Bodlaender , Carla Groenland , Jesper Nederlof , Céline Swennenhuis
{"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}
引用次数: 0
Secretive interaction 秘密互动
IF 0.8 4区 计算机科学
Information and Computation Pub Date : 2024-07-19 DOI: 10.1016/j.ic.2024.105196
Eduardo Skapinakis
{"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}
引用次数: 0
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
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