Information and Computation最新文献

{"title":"Finite-state relative dimension, dimensions of A. P. subsequences and a finite-state van Lambalgen's theorem","authors":"Satyadev Nandakumar,&nbsp;Subin Pulari,&nbsp;Akhil S","doi":"10.1016/j.ic.2024.105156","DOIUrl":"10.1016/j.ic.2024.105156","url":null,"abstract":"<div><p>Finite-state dimension, introduced by Dai, Lathrop, Lutz and Mayordomo quantifies the information rate in an infinite sequence as measured by finite-state automata. In this paper, we define a relative version of finite-state dimension. The finite-state relative dimension <span><math><msubsup><mrow><mi>dim</mi></mrow><mrow><mi>F</mi><mi>S</mi></mrow><mrow><mi>Y</mi></mrow></msubsup><mo>(</mo><mi>X</mi><mo>)</mo></math></span> of a sequence <em>X</em> relative to <em>Y</em> is the finite-state dimension of <em>X</em> measured using the class of finite-state gamblers with oracle access to <em>Y</em>. We show its mathematical robustness by equivalently characterizing this notion using the relative block entropy rate of <em>X</em> conditioned on <em>Y</em>.</p><p>We derive inequalities relating the dimension of a sequence to the relative dimension of its subsequences along any arithmetic progression (A. P.). These enable us to obtain a strengthening of Wall's Theorem on the normality of A. P. subsequences of a normal sequence, in terms of relative dimension. In contrast to the original theorem, this stronger version has an exact converse yielding a new characterization of normality.</p><p>We also obtain finite-state analogues of van Lambalgen's theorem on the symmetry of relative normality.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"298 ","pages":"Article 105156"},"PeriodicalIF":1.0,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140056136","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":"r-indexing the eBWT","authors":"Christina Boucher ,&nbsp;Davide Cenzato ,&nbsp;Zsuzsanna Lipták ,&nbsp;Massimiliano Rossi ,&nbsp;Marinella Sciortino","doi":"10.1016/j.ic.2024.105155","DOIUrl":"10.1016/j.ic.2024.105155","url":null,"abstract":"<div><p>The extended Burrows-Wheeler Transform (eBWT) [Mantaci et al. TCS 2007] is a variant of the BWT, introduced for collections of strings. In this paper, we present the <em>extended r-index</em>, an analogous data structure to the <em>r</em>-index [Gagie et al. JACM 2020]. It occupies <span><math><mi>O</mi><mo>(</mo><mi>r</mi><mo>)</mo></math></span> words, with <em>r</em> the number of runs of the eBWT, and offers the same functionalities as the <em>r</em>-index. We also show how to efficiently support finding maximal exact matches (MEMs). We implemented the extended <em>r</em>-index and tested it on circular bacterial genomes and plasmids, comparing it to five state-of-the-art compressed text indexes. While our data structure maintains similar time and memory requirements for answering pattern matching queries as the original <em>r</em>-index, it is the only index in the literature that can naturally be used for both circular and linear input collections. This is an extended version of [Boucher et al., <em>r-indexing the</em> eBWT, SPIRE 2021].</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"298 ","pages":"Article 105155"},"PeriodicalIF":1.0,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0890540124000208/pdfft?md5=473e3c991b33dac12225d2a9ce2daad7&pid=1-s2.0-S0890540124000208-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140056199","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":"Monomial Boolean functions with large high-order nonlinearities","authors":"Jinjie Gao ,&nbsp;Haibin Kan ,&nbsp;Yuan Li ,&nbsp;Jiahua Xu ,&nbsp;Qichun Wang","doi":"10.1016/j.ic.2024.105152","DOIUrl":"10.1016/j.ic.2024.105152","url":null,"abstract":"<div><p>Exhibiting an explicit Boolean function with a large high-order nonlinearity is an important problem in cryptography, coding theory, and computational complexity. We prove lower bounds on the second-order, third-order, and higher order nonlinearities of some monomial Boolean functions.</p><p>We prove lower bounds on the second-order nonlinearities of functions <span><math><msub><mrow><mi>tr</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>7</mn></mrow></msup><mo>)</mo></math></span> and <span><math><msub><mrow><mi>tr</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>r</mi></mrow></msup><mo>+</mo><mn>3</mn></mrow></msup><mo>)</mo></math></span> where <span><math><mi>n</mi><mo>=</mo><mn>2</mn><mi>r</mi></math></span>. Among all monomial Boolean functions, our bounds match the best second-order nonlinearity lower bounds by Carlet [IEEE Transactions on Information Theory 54(3), 2008] and Yan and Tang [Discrete Mathematics 343(5), 2020] for odd and even <em>n</em>, respectively. We prove a lower bound on the third-order nonlinearity for functions <span><math><msub><mrow><mi>tr</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>15</mn></mrow></msup><mo>)</mo></math></span>, which is the best third-order nonlinearity lower bound. For any <em>r</em>, we prove that the <em>r</em>-th order nonlinearity of <span><math><msub><mrow><mi>tr</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>r</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></math></span> is at least <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>−</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>(</mo><mn>1</mn><mo>−</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>−</mo><mi>r</mi></mrow></msup><mo>)</mo><mi>n</mi><mo>+</mo><mfrac><mrow><mi>r</mi></mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>r</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></mfrac><mo>−</mo><mn>1</mn></mrow></msup><mo>−</mo><mi>O</mi><mo>(</mo><msup><mrow><mn>2</mn></mrow><mrow><mfrac><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo>)</mo></math></span>. For <span><math><mi>r</mi><mo>≪</mo><msub><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⁡</mo><mi>n</mi></math></span>, this is the best lower bound among all explicit functions.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"297 ","pages":"Article 105152"},"PeriodicalIF":1.0,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139889415","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":"Constructing and indexing the bijective and extended Burrows–Wheeler transform","authors":"Hideo Bannai,&nbsp;Juha Kärkkäinen,&nbsp;Dominik Köppl,&nbsp;Marcin Pia̧tkowski","doi":"10.1016/j.ic.2024.105153","DOIUrl":"10.1016/j.ic.2024.105153","url":null,"abstract":"<div><p>The Burrows–Wheeler transform (BWT) is a permutation whose applications are prevalent in data compression and text indexing. The <em>bijective BWT</em> is a bijective variant of it that has not yet been studied for text indexing applications. We fill this gap by proposing a self-index built on the bijective BWT. The self-index applies the backward search technique of the FM-index to find a pattern <em>P</em> with <span><math><mi>O</mi><mo>(</mo><mo>|</mo><mi>P</mi><mo>|</mo><mi>lg</mi><mo>⁡</mo><mo>|</mo><mi>P</mi><mo>|</mo><mo>)</mo></math></span> backward search steps. Additionally, we propose the first linear-time construction algorithm that is based on SAIS, improving the best known result of <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>lg</mi><mo>⁡</mo><mi>n</mi><mo>/</mo><mi>lg</mi><mo>⁡</mo><mi>lg</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> time to linear.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"297 ","pages":"Article 105153"},"PeriodicalIF":1.0,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139813409","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":"Minimal session types for the π-calculus","authors":"Alen Arslanagić,&nbsp;Jorge A. Pérez,&nbsp;Anda-Amelia Palamariuc","doi":"10.1016/j.ic.2024.105148","DOIUrl":"10.1016/j.ic.2024.105148","url":null,"abstract":"<div><p>Session types are a type-based approach to correct message-passing programs. A session type specifies a channel's protocol as <em>sequences</em> of exchanges. Aiming to uncover the essential notions of session-based concurrency, prior work defined <em>minimal</em> session types (MSTs), a formulation of session types without the sequentiality construct, and showed a <em>minimality result</em>: every process typable with standard session types can be transformed into a process typable using MSTs. Such a minimality result was proven for a higher-order session <em>π</em>-calculus, in which values are abstractions (functions from names to processes).</p><p>In this paper, we study MSTs but now for the session <em>π</em>-calculus, the (first-order) language in which values are names and for which session types have been more widely studied. We first show that a new minimality result can be obtained by composing known results. Then, we develop optimizations of this new minimality result and prove also a dynamic correctness guarantee.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"297 ","pages":"Article 105148"},"PeriodicalIF":1.0,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0890540124000130/pdfft?md5=dca6052b3b897a7e1a5f44fb0794f9e3&pid=1-s2.0-S0890540124000130-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139578405","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":"Solving mean-payoff games via quasi dominions","authors":"Massimo Benerecetti ,&nbsp;Daniele Dell'Erba ,&nbsp;Fabio Mogavero","doi":"10.1016/j.ic.2024.105151","DOIUrl":"10.1016/j.ic.2024.105151","url":null,"abstract":"<div><p>We propose a novel algorithm for the solution of <em>mean-payoff games</em> that merges together two seemingly unrelated concepts introduced in the context of parity games, namely <em>small progress measures</em> and <em>quasi dominions</em>. We show that the integration of the two notions can be highly beneficial and significantly speeds up convergence to the problem solution. Experiments show that the resulting algorithm performs orders of magnitude better than the asymptotically-best solution algorithm currently known, without sacrificing on the worst-case complexity.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"297 ","pages":"Article 105151"},"PeriodicalIF":1.0,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0890540124000166/pdfft?md5=306a43f9ff3894332e824e402752e4b7&pid=1-s2.0-S0890540124000166-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139578549","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":"Constructions of several special classes of cubic bent functions outside the completed Maiorana-McFarland class","authors":"Fengrong Zhang ,&nbsp;Enes Pasalic ,&nbsp;Amar Bapić ,&nbsp;Baocang Wang","doi":"10.1016/j.ic.2024.105149","DOIUrl":"10.1016/j.ic.2024.105149","url":null,"abstract":"<div><p>We show that the direct sum, under more relaxed conditions compared to those of Polujan and Pott (2020), can generate bent functions provably outside the completed Maiorana-McFarland class (<span><math><msup><mrow><mi>MM</mi></mrow><mrow><mi>#</mi></mrow></msup></math></span>). We also show that the indirect sum method of generating bent functions, by imposing certain conditions (which are completely absent if only the bentness of the resulting function is required) on the initial bent functions, can be employed in the design of bent functions outside <span><math><msup><mrow><mi>MM</mi></mrow><mrow><mi>#</mi></mrow></msup></math></span>. Furthermore, applying this method to suitably chosen bent functions we construct several generic classes of homogeneous cubic bent functions (considered as a difficult problem) that might possess additional properties (namely without affine derivatives and/or outside <span><math><msup><mrow><mi>MM</mi></mrow><mrow><mi>#</mi></mrow></msup></math></span>). Our results significantly improve upon the best known instances of this type of bent functions given by Polujan and Pott (2020), and additionally we provide a solution to an open problem presented in their paper.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"297 ","pages":"Article 105149"},"PeriodicalIF":1.0,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139560114","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 the directed path partition problem","authors":"Yong Chen ,&nbsp;Zhi-Zhong Chen ,&nbsp;Curtis Kennedy ,&nbsp;Guohui Lin ,&nbsp;Yao Xu ,&nbsp;An Zhang","doi":"10.1016/j.ic.2024.105150","DOIUrl":"10.1016/j.ic.2024.105150","url":null,"abstract":"<div><p>Given a digraph <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span>, the <em>k</em>-path partition problem aims to find a minimum collection of vertex-disjoint directed paths, of order at most <em>k</em>, to cover all the vertices. The problem has various applications. Its special case on undirected graphs is NP-hard when <span><math><mi>k</mi><mo>≥</mo><mn>3</mn></math></span>, and has received much study recently from the approximation algorithm perspective. However, the general problem on digraphs is seemingly untouched in the literature. We fill the gap with the first <span><math><mi>k</mi><mo>/</mo><mn>2</mn></math></span>-approximation algorithm, based on a novel concept of enlarging walk to minimize the number of singletons. Secondly, for <span><math><mi>k</mi><mo>=</mo><mn>3</mn></math></span>, we define a second novel kind of enlarging walks to greedily reduce the number of 2-paths in the 3-path partition and propose an improved 13/9-approximation algorithm. Lastly, for any <span><math><mi>k</mi><mo>≥</mo><mn>7</mn></math></span>, we present an improved <span><math><mo>(</mo><mi>k</mi><mo>+</mo><mn>2</mn><mo>)</mo><mo>/</mo><mn>3</mn></math></span>-approximation algorithm built on the maximum path-cycle cover followed by a careful 2-cycle elimination process.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"297 ","pages":"Article 105150"},"PeriodicalIF":1.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0890540124000154/pdfft?md5=0dde1df73fe58468b9370f19cea306f4&pid=1-s2.0-S0890540124000154-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139495707","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":"Projection theorems using effective dimension","authors":"Neil Lutz ,&nbsp;D.M. Stull","doi":"10.1016/j.ic.2024.105137","DOIUrl":"10.1016/j.ic.2024.105137","url":null,"abstract":"<div><p>In this paper we use the theory of computing to study fractal dimensions of projections in Euclidean spaces. A fundamental result in fractal geometry is Marstrand's projection theorem, which states that for every analytic set <em>E</em>, for almost every line <em>L</em>, the Hausdorff dimension of the orthogonal projection of <em>E</em> onto <em>L</em> is maximal.</p><p>We use Kolmogorov complexity to give two new results on the Hausdorff and packing dimensions of orthogonal projections onto lines. The first shows that the conclusion of Marstrand's theorem holds whenever the Hausdorff and packing dimensions agree on the set <em>E</em>, even if <em>E</em> is not analytic. Our second result gives a lower bound on the packing dimension of projections of arbitrary sets. Finally, we give a new proof of Marstrand's theorem using the theory of computing.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"297 ","pages":"Article 105137"},"PeriodicalIF":1.0,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139495704","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":"The reflective higher-order calculus: Encodability, typability and separation","authors":"Stian Lybech","doi":"10.1016/j.ic.2024.105138","DOIUrl":"10.1016/j.ic.2024.105138","url":null,"abstract":"<div><p>The <em>ρ</em>-calculus (Reflective Higher-Order Calculus) of Meredith and Radestock is a <em>π</em>-calculus-like language with unusual features, notably, structured names, runtime generation of free names, and the lack of a scoping operator. These features pose interesting difficulties for proofs of encodability, type system soundness and separation results. We describe two errors in a previous attempt to encode the <em>π</em>-calculus in the <em>ρ</em>-calculus by Meredith and Radestock. Then we give a new encoding and prove its correctness, using a set of encodability criteria close to those of Gorla, and discuss the adaptations necessary to work with a calculus with runtime generation of structured names. We create a simple type system for the <em>ρ</em>-calculus to show that the encoding is well-typed, and discuss the limitations that must be imposed when working with structured names. Lastly we prove a separation result, showing that the <em>ρ</em>-calculus cannot be encoded in the <em>π</em>-calculus.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"297 ","pages":"Article 105138"},"PeriodicalIF":1.0,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139459973","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}