Journal of Computer and System Sciences最新文献

{"title":"Parameterized analysis of the cops and robber problem","authors":"Harmender Gahlawat ,&nbsp;Meirav Zehavi","doi":"10.1016/j.jcss.2026.103781","DOIUrl":"10.1016/j.jcss.2026.103781","url":null,"abstract":"<div><div><em>Pursuit-evasion games</em> have been intensively studied for several decades due to their numerous applications in artificial intelligence, robot motion planning, database theory, distributed computing, and algorithmic theory. <span>Cops and Robber</span> (<span>CnR</span>) is one of the most well-known pursuit-evasion games played on graphs, where multiple <em>cops</em> pursue a single <em>robber</em>. The aim is to compute the <em>cop number</em> of a graph, <em>k</em>, which is the minimum number of cops that ensures the <em>capture</em> of the robber. From the viewpoint of parameterized complexity, <span>CnR</span> is W[2]-hard parameterized by <em>k</em> (Fomin et al. (2010) <span><span>[39]</span></span>). Thus, we study structural parameters of the input graph. We begin with the <em>vertex cover number</em> (<span><math><mi>vcn</mi></math></span>). First, we establish that <span><math><mi>k</mi><mo>≤</mo><mfrac><mrow><mi>vcn</mi></mrow><mrow><mn>3</mn></mrow></mfrac><mo>+</mo><mn>1</mn></math></span>. Second, we prove that <span>CnR</span> parameterized by <span><math><mi>vcn</mi></math></span> is <span><math><mi>FPT</mi></math></span> by designing an exponential kernel. We complement this result by showing that it is unlikely for <span>CnR</span> parameterized by <span><math><mi>vcn</mi></math></span> to admit a polynomial compression. We extend our exponential kernels to the parameters <em>cluster vertex deletion number</em> and <em>deletion to stars number</em>, and design a linear vertex kernel for <em>neighborhood diversity</em>. Additionally, we extend all of our results to several well-studied variations of <span>CnR</span>.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"158 ","pages":"Article 103781"},"PeriodicalIF":0.9,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"Kernelization for orthogonality dimension","authors":"Ishay Haviv,&nbsp;Dror Rabinovich","doi":"10.1016/j.jcss.2026.103757","DOIUrl":"10.1016/j.jcss.2026.103757","url":null,"abstract":"<div><div>The orthogonality dimension of a graph over <span><math><mi>R</mi></math></span> is the smallest integer <em>d</em> for which one can assign to every vertex a nonzero vector in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> such that every two adjacent vertices receive orthogonal vectors. For an integer <em>d</em>, the <figure><img></figure> problem asks to decide whether the orthogonality dimension of a given graph over <span><math><mi>R</mi></math></span> is at most <em>d</em>. We prove that for every integer <span><math><mi>d</mi><mo>≥</mo><mn>3</mn></math></span>, the <figure><img></figure> problem parameterized by the vertex cover number <em>k</em> admits a kernel with <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>k</mi></mrow><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>)</mo></math></span> vertices and bit-size <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>k</mi></mrow><mrow><mi>d</mi><mo>−</mo><mn>1</mn></mrow></msup><mo>⋅</mo><mi>log</mi><mo>⁡</mo><mi>k</mi><mo>)</mo></math></span>. We complement this result by a nearly matching lower bound, showing that for any <span><math><mi>ε</mi><mo>&gt;</mo><mn>0</mn></math></span>, the problem admits no kernel of bit-size <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>k</mi></mrow><mrow><mi>d</mi><mo>−</mo><mn>1</mn><mo>−</mo><mi>ε</mi></mrow></msup><mo>)</mo></math></span> unless <span><math><mrow><mi>NP</mi></mrow><mo>⊆</mo><mrow><mi>coNP</mi><mo>/</mo><mi>poly</mi></mrow></math></span>. We further study the kernelizability of orthogonality dimension problems in additional settings, including over general fields and under various structural parameterizations.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"157 ","pages":"Article 103757"},"PeriodicalIF":0.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"A divide and conquer algorithm for deciding group cellular automata dynamics","authors":"Niccolò Castronuovo ,&nbsp;Alberto Dennunzio ,&nbsp;Luciano Margara","doi":"10.1016/j.jcss.2025.103749","DOIUrl":"10.1016/j.jcss.2025.103749","url":null,"abstract":"<div><div>We prove that many dynamical properties of group cellular automata (GCA) can be decided by decomposing them into a set of much simpler GCA, provided those properties are decidable for such simpler GCA. Specifically, we provide a novel algorithmic technique that decomposes the GCA under investigation into a finite number of GCA, some defined on abelian groups, while others, if any, on products of simple non-abelian isomorphic groups. Importantly, the groups resulting from the decomposition depend only on the original group and are therefore completely independent of both the automaton and the considered property. Consequently, they do not inherit any aspect of the complexity of the automaton under investigation. We study the inheritance of the dynamical properties in the original GCA versus the same properties in the GCA obtained through decomposition. The latter turn out to be significantly easier to analyze than in the original GCA. Then, we show that injectivity, surjectivity, and equicontinuity/sensitivity to initial conditions can be decided by testing them in the smaller GCA produced by the decomposition. Moreover, we prove that the topological entropy of a GCA can be computed, provided one knows how to compute it for GCA defined on products of simple non-abelian isomorphic groups – for which we explicitly prove how to compute it in the surjective case – and on abelian groups. Finally, we prove that no strongly transitive, and therefore no positively expansive, GCA defined on non-abelian groups exist.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"157 ","pages":"Article 103749"},"PeriodicalIF":0.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145736654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"Approximation algorithms for two extensions of min-k-union","authors":"Hua Chen ,&nbsp;Lin Chen ,&nbsp;Shenghao Ye ,&nbsp;Guochuan Zhang","doi":"10.1016/j.jcss.2025.103750","DOIUrl":"10.1016/j.jcss.2025.103750","url":null,"abstract":"<div><div>In the min-<em>k</em>-union problem (M<em>k</em>U), given a ground set <em>N</em>, a collection <span><math><mi>S</mi></math></span> of <em>m</em> subsets of <em>N</em>, and an integer <em>k</em>, one needs to select <em>k</em> sets from <span><math><mi>S</mi></math></span> so that their union has the smallest size. In this paper, we study two extensions of M<em>k</em>U.</div><div>The first is the maximum coverage interdiction problem, where there is a leader with cardinality <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>l</mi></mrow></msub></math></span> and a follower with cardinality <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>f</mi></mrow></msub></math></span>. The leader's goal (as well as the problem) is to remove up to <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>l</mi></mrow></msub></math></span> sets from <span><math><mi>S</mi></math></span> so that the union size of the at most <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>f</mi></mrow></msub></math></span> sets selected by the follower from the remaining sets attains the minimum. We provide an <span><math><mover><mrow><mi>O</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><msqrt><mrow><mi>m</mi></mrow></msqrt><mo>)</mo></math></span>-approximation algorithm, while a lower bound of <span><math><mi>Ω</mi><mo>(</mo><msup><mrow><mi>m</mi></mrow><mrow><mn>1</mn><mo>/</mo><mn>4</mn></mrow></msup><mo>)</mo></math></span> under the “Dense versus Random” conjecture for M<em>k</em>U [Chlamtáč et al. '17] applies to our problem as well. When <span><math><msub><mrow><mi>k</mi></mrow><mrow><mi>l</mi></mrow></msub><mo>=</mo><mi>m</mi><mo>−</mo><msub><mrow><mi>k</mi></mrow><mrow><mi>f</mi></mrow></msub></math></span>, this problem becomes M<em>k</em>U.</div><div>The second problem deals with monotone submodular minimization with a cardinality constraint. Given a ground set <em>N</em> of <em>n</em> elements, a nonnegative monotone submodular function <em>f</em>, and an integer <em>k</em>, we are required to find a size-<em>k</em> set <span><math><mi>S</mi><mo>⊆</mo><mi>N</mi></math></span> that minimizes <span><math><mi>f</mi><mo>(</mo><mi>S</mi><mo>)</mo></math></span>. We propose a 2<span><math><msqrt><mrow><mi>n</mi></mrow></msqrt></math></span>-approximation algorithm, matching (up to a logarithmic factor) the lower bound of <span><math><mi>Ω</mi><mo>(</mo><msqrt><mrow><mfrac><mrow><mi>n</mi></mrow><mrow><mi>ln</mi><mo>⁡</mo><mi>n</mi></mrow></mfrac></mrow></msqrt><mo>)</mo></math></span> [Svitkina and Fleischer '11]. When <em>f</em> is a coverage function, this problem becomes M<em>k</em>U.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"157 ","pages":"Article 103750"},"PeriodicalIF":0.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145839599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"Morphing graph drawings in the presence of point obstacles","authors":"Oksana Firman,&nbsp;Tim Hegemann,&nbsp;Boris Klemz,&nbsp;Felix Klesen,&nbsp;Marie Diana Sieper,&nbsp;Alexander Wolff,&nbsp;Johannes Zink","doi":"10.1016/j.jcss.2026.103755","DOIUrl":"10.1016/j.jcss.2026.103755","url":null,"abstract":"<div><div>A crossing-free morph is a continuous deformation between two graph drawings that preserves straight-line pairwise noncrossing edges. Motivated by applications in 3D morphing problems, we initiate the study of morphing graph drawings in the plane in the presence of stationary point obstacles, which need to be avoided throughout the deformation. As our main result, we prove that it is NP-hard to decide whether such an obstacle-avoiding 2D morph between two given drawings of the same graph exists. In fact, this statement remains true even in the severely restricted special case where only three vertices have to change positions. This is in sharp contrast to the classical case without obstacles, where there is an efficiently verifiable (necessary and sufficient) criterion for the existence of a morph. Further, we provide several combinatorial results related to conditions under which the existence of a morph between two drawings of a graph can or cannot be prevented by the placement of a given number of point obstacles.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"157 ","pages":"Article 103755"},"PeriodicalIF":0.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976498","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"AdapBlinker: Robust adaptive median filter approach to detect subtle eye blinks","authors":"Hafsa Sidaq ,&nbsp;Lei Wang ,&nbsp;Jiancheng Chi ,&nbsp;Hussain Haider","doi":"10.1016/j.jcss.2025.103746","DOIUrl":"10.1016/j.jcss.2025.103746","url":null,"abstract":"<div><div>Nowadays, eye blink detection is gaining significant attention in human-computer interaction systems. Users are increasingly favoring interactions with their phones and computers through non-manual methods, underscoring the constraints of conventional touch interfaces. Wearable technology, such as electrooculography (EOG)-based approaches and infrared sensors (IR), can accurately detect eye blinks; nevertheless, they can be inconvenient after prolonged use. Despite this, the drawbacks of camera-based eye blink recognition techniques are blind spots and the lighting effect. Thus, this study proposes an acoustic signal-based eye blink detection system to overcome these constraints. Acoustic signals can perform fine-grained detection within localized range due to their high attenuation in the air medium. The main benefit of acoustic sensing over conventional methods is that it senses signals directly, so the user does not need to wear any sensors. The prevalence of speakers and microphones in devices is another advancement that supports acoustic sensing. In this research, we present AdapBlinker, which employs the HP ProBook 440 G5 laptop to generate acoustic signals, retrieve data, process acquired signals, and plot Fast Fourier transform (FFT) to extract eye blink signals. AdapBlinker uses an adaptive median filter that adapts to surroundings, eliminates intrusions, and detects subtle blinks. We tested AdapBlinker with thirty-four participants across three settings for five months, achieving an average eye blink detection accuracy of 97.2%.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"157 ","pages":"Article 103746"},"PeriodicalIF":0.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145924260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 the structure of Hamiltonian graphs with small independence number","authors":"Nikola Jedličková ,&nbsp;Jan Kratochvíl","doi":"10.1016/j.jcss.2025.103754","DOIUrl":"10.1016/j.jcss.2025.103754","url":null,"abstract":"<div><div>A Hamiltonian path (cycle) in a graph is a path (cycle, respectively) which passes through all of its vertices exactly once. The problems of deciding the existence of a Hamiltonian path and a Hamiltonian cycle in an input graph (called <span>Hamiltonian Path</span> resp. <span>Hamiltonian Cycle</span>) is well known to be NP-complete, and restricted classes of graphs which allow for their polynomial-time solutions are intensively investigated. Until very recently, the complexity was open even for graphs of independence number at most 3. Fomin, Golovach, Sagunov, and Simonov [arxiv 2024] showed that for every integer <em>k</em>, <span>Hamiltonian Path</span> and <span>Hamiltonian Cycle</span> are polynomial-time solvable in graphs of independence number bounded by <em>k</em>, and moreover, that these problems are in FPT when parameterized by the independence number of the input graph. As a companion structural result to these general algorithms, we determine explicit obstacles to the existence of a Hamiltonian path for small values of <em>k</em>, namely for graphs of independence number 2, 3, and 4. Identifying these obstacles in an input graph yields alternative polynomial-time algorithms for <span>Hamiltonian Path</span> and <span>Hamiltonian Cycle</span> with no large hidden multiplicative constants.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"157 ","pages":"Article 103754"},"PeriodicalIF":0.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145976510","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 the structural parameterized complexity of defective coloring","authors":"Sriram Bhyravarapu ,&nbsp;Pankaj Kumar ,&nbsp;Saket Saurabh","doi":"10.1016/j.jcss.2025.103736","DOIUrl":"10.1016/j.jcss.2025.103736","url":null,"abstract":"<div><div>In this paper, we consider the problem <span>Defective Coloring</span>. Given a graph <em>G</em> and two positive integers <em>k</em> and <span><math><msup><mrow><mi>Δ</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>, the objective is to determine whether it is possible to obtain a coloring (not necessarily proper) of the vertices of <em>G</em> using at most <em>k</em> colors such that each vertex has at most <span><math><msup><mrow><mi>Δ</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> neighbors in the same color class. <span>Defective Coloring</span> is a generalization of <span>Graph Coloring</span> with <span><math><msup><mrow><mi>Δ</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>=</mo><mn>0</mn></math></span>. The optimization variant of this problem, which aims to find the minimum number of colors <em>k</em>, is known to be <span>NP</span>-hard even for split graphs and cographs. Belmonte, Lampis, and Mitsou (SIDMA 2020) showed that <span>Defective Coloring</span> is <span>W[1]</span>-hard when parameterized by feedback vertex set or by treedepth, which implies <span>W[1]</span>-hardness for path-width and treewidth parameters. The problem is <span>W[1]</span>-hard parameterized by modular-width or clique-width as <span>Defective Coloring</span> is <span>NP</span>-hard on cographs. They asked whether <span>Defective Coloring</span> is fixed-parameter tractable (<span>FPT</span>) when parameterized by modular-width, neighborhood diversity or clique-width combined with either <em>k</em> or <span><math><msup><mrow><mi>Δ</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>. In an effort to address the question concerning modular-width, this study investigates the parameters neighborhood diversity and twin-cover, which are special cases of modular-width. We show that <span>Defective Coloring</span> is <span>FPT</span> when parameterized by twin-cover, distance to disjoint paths, or the combined parameters neighborhood diversity and <em>k</em>. The latter implies an FPT algorithm for complete-<em>d</em>-partite graphs, a subclass of cographs, parameterized by <em>d</em>. We present an algorithm for graphs with bounded distance to <em>d</em>-degree. We also present a 1-additive approximation algorithm for split graphs.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"157 ","pages":"Article 103736"},"PeriodicalIF":0.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 power of knowledge in linear search for an escaping target","authors":"Jared Coleman ,&nbsp;Dmitry Ivanov ,&nbsp;Evangelos Kranakis ,&nbsp;Danny Krizanc ,&nbsp;Oscar Morales-Ponce","doi":"10.1016/j.jcss.2025.103737","DOIUrl":"10.1016/j.jcss.2025.103737","url":null,"abstract":"<div><div>We consider linear search for an escaping target whose speed and/or initial distance from the origin may be unknown to the searcher. The searcher (an autonomous mobile agent) is initially placed at the origin of the real line and can move with maximum speed 1 in either direction along the line. The oblivious mobile target that is moving away from the origin with a constant speed <span><math><mi>v</mi><mo>&lt;</mo><mn>1</mn></math></span> is initially placed by an adversary on the infinite line at distance <em>d</em> from the origin in an unknown direction. We consider four cases, depending on whether <em>v</em> and/or <em>d</em> is known to the searcher. The main contributions of this paper are new lower bounds as well as algorithms leading to new upper bounds for search in these settings. We present tight bounds for the cases when <em>v</em> is known. For the cases where <em>v</em> is unknown, we prove an optimal (up to lower order terms in the exponent) competitive ratio in the case where <em>d</em> is known and improved upper and lower bounds for the case where <em>d</em> is unknown. These results solve an open problem proposed in Coleman et al. (2022) <span><span>[11]</span></span>.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"157 ","pages":"Article 103737"},"PeriodicalIF":0.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145736652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"A comparative study of the smallest probability intervals for which a binary sequence is random","authors":"Floris Persiau,&nbsp;Gert de Cooman,&nbsp;Jasper De Bock","doi":"10.1016/j.jcss.2025.103734","DOIUrl":"10.1016/j.jcss.2025.103734","url":null,"abstract":"<div><div>There are many randomness notions. Classically, many of them are about whether a given infinite binary sequence is random for some given probability, meaning that it is random for the i.i.d. process that assigns this probability to the outcome 1. In that case, if a sequence is random according to several randomness notions, then the probability for which it is random is the same for all these notions. Comparing randomness notions then amounts to finding out according to which of them a given sequence is random. This changes dramatically when we consider randomness for probability intervals, because here, a sequence is always random for at least one such interval, so the question is not if, but rather for which intervals, a sequence is random. We show that for many randomness notions thus generalised, every sequence has a smallest interval for which it is (almost) random. We study such smallest intervals and then use them as a way to compare the corresponding randomness notions. We establish conditions under which such smallest intervals coincide, and provide examples where they do not.</div></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"157 ","pages":"Article 103734"},"PeriodicalIF":0.9,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145571842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}