Information Processing Letters最新文献

{"title":"Notes about the linear complexity of quaternary cyclotomic sequences of order four","authors":"Vladimir Edemskiy,&nbsp;Zeyu Cao","doi":"10.1016/j.ipl.2025.106595","DOIUrl":"10.1016/j.ipl.2025.106595","url":null,"abstract":"<div><div>In this paper, we study the linear complexity of quaternary cyclotomic sequences with period <em>p</em>, where <span><math><mi>p</mi><mo>&gt;</mo><mn>2</mn></math></span> is a prime. Considered sequences are based on classical cyclotomic classes of order four modulo <em>p</em>. We show that any balanced quaternary cyclotomic sequence of order four with period <em>p</em> has high linear complexity over finite ring of order four. Our results generalize those obtained earlier by other authors.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"191 ","pages":"Article 106595"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144633879","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 complexity of computing the period and the exponent of a digraph","authors":"Stefan Kiefer,&nbsp;Andrew Ryzhikov","doi":"10.1016/j.ipl.2025.106590","DOIUrl":"10.1016/j.ipl.2025.106590","url":null,"abstract":"<div><div>The period of a strongly connected digraph is the greatest common divisor of the lengths of all its cycles. The period of a digraph is the least common multiple of the periods of its strongly connected components. These notions play an important role in the theory of Markov chains and the analysis of powers of nonnegative matrices. While the time complexity of computing the period is well-understood, little is known about its space complexity. We show that the problem of computing the period of a digraph is <span>NL</span>-complete, even if all its cycles are contained in the same strongly connected component. However, if the digraph is strongly connected, we show that this problem becomes <span>L</span>-complete. For primitive digraphs (that is, strongly connected digraphs of period one), there always exists a number <em>m</em> such that there is a path of length exactly <em>m</em> between every two vertices. We show that computing the smallest such <em>m</em>, called the exponent of a digraph, is <span>NL</span>-complete. The exponent of a primitive digraph is a particular case of the index of convergence of a nonnegative matrix, which we also show to be computable in <span>NL</span>, and thus <span>NL</span>-complete.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"191 ","pages":"Article 106590"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144241718","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":"Logical characterization of branching bisimilarity over random processes","authors":"Xian Xu ,&nbsp;Wenbo Zhang","doi":"10.1016/j.ipl.2025.106596","DOIUrl":"10.1016/j.ipl.2025.106596","url":null,"abstract":"<div><div>Quantitative aspects like probabilities play an important role in concurrent processes. Providing a (modal) logic for a randomized concurrency model can augment the toolbox of analyzing probabilistic processes, and thus is a frequent topic in the field. In this paper, we are interested in logically characterizing uniformly randomized processes, whose semantical behavior is defined in a model-independent manner. Specifically, we present two modal logics for the uniformly randomized version of finite-state CCS (RCCS_fsfor short). Our logics extend the Hennessy-Milner logic, and one of them is equipped with the <em>μ</em> operator. Indeed, we prove that both logics characterize the branching bisimilarity for RCCS_fs, i.e., two RCCS_fsprocesses are branching bisimilar if and only if they are logically equivalent. To facilitate the proof, we also develop for RCCS_fsan up-to proof method, which may be of independent interest.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"191 ","pages":"Article 106596"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144679662","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":"On some families of binary codes","authors":"Zihui Liu","doi":"10.1016/j.ipl.2025.106591","DOIUrl":"10.1016/j.ipl.2025.106591","url":null,"abstract":"<div><div>We give further results on the weight distributions of the two families of binary codes recently constructed by simplicial complexes by (Wu, Lee, 2020), and show that the converse of the above results is also correct, that is, the binary codes with such weight distributions properties must be these two families of codes. Based on the above results, we also construct another family of binary self-orthogonal codes and present their separating properties and applications to the secret sharing scheme, cryptography and other aspects of information security.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"191 ","pages":"Article 106591"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144195768","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":"Finding the cyclic covers of a string","authors":"Roberto Grossi ,&nbsp;Costas S. Iliopoulos ,&nbsp;Jesper Jansson ,&nbsp;Zara Lim ,&nbsp;Wing-Kin Sung ,&nbsp;Wiktor Zuba","doi":"10.1016/j.ipl.2025.106594","DOIUrl":"10.1016/j.ipl.2025.106594","url":null,"abstract":"<div><div>We introduce the concept of cyclic covers, which generalizes the classical notion of covers in strings. Given any string <em>X</em>, a factor <em>W</em> of <em>X</em> is called a <em>cyclic cover</em> if each position of <em>X</em> belongs to an occurrence of a cyclic shift of <em>W</em> in <em>X</em>. Two cyclic covers are distinct if one is not a cyclic shift of the other. The <em>cyclic covers problem</em> asks for all distinct cyclic covers of an input string <em>X</em>. We present an algorithm that solves the cyclic covers problem in <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> time, where <em>n</em> is the length of <em>X</em>. It is based on finding a well-structured set of standard occurrences of a constant number of factors of a cyclic cover candidate <em>W</em>, computing the regions of <em>X</em> covered by cyclic shifts of <em>W</em>, extending those factors, and taking the union of the results.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"191 ","pages":"Article 106594"},"PeriodicalIF":0.7,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144298426","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":"An information theoretic proof of the Chernoff-Hoeffding inequality","authors":"Olivier Rioul ,&nbsp;Patrick Solé","doi":"10.1016/j.ipl.2025.106582","DOIUrl":"10.1016/j.ipl.2025.106582","url":null,"abstract":"<div><div>The Chernoff bound is a well-known upper bound on the tail of binomial distributions of parameter 1/2 involving the binary entropy function. Hoeffding's inequality (or the Chernoff-Hoeffding inequality) is a generalization for binomial distributions of parameter <span><math><mn>1</mn><mo>−</mo><mn>1</mn><mo>/</mo><mi>q</mi></math></span>, involving the <em>q</em>-ary entropy function (with <span><math><mi>q</mi><mo>≥</mo><mn>2</mn></math></span>), which can be written in terms of the Kullback-Leibler divergence and is related to the bound in Fano's inequality. We give an information theoretic proof of that bound, and sketch some applications to channel and source coding. We also derive a refined bound which is always sharper.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"190 ","pages":"Article 106582"},"PeriodicalIF":0.7,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143911475","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":"A PTAS for k-hop MST on the Euclidean plane: Improving dependency on k","authors":"Jittat Fakcharoenphol ,&nbsp;Nonthaphat Wongwattanakij","doi":"10.1016/j.ipl.2025.106581","DOIUrl":"10.1016/j.ipl.2025.106581","url":null,"abstract":"<div><div>For any <span><math><mi>ϵ</mi><mo>&gt;</mo><mn>0</mn></math></span>, Laue and Matijević [CCCG'07, IPL'08] give a PTAS for finding a <span><math><mo>(</mo><mn>1</mn><mo>+</mo><mi>ϵ</mi><mo>)</mo></math></span>-approximate solution to the <em>k</em>-hop MST problem in the Euclidean plane that runs in time <span><math><msup><mrow><mo>(</mo><mi>n</mi><mo>/</mo><mi>ϵ</mi><mo>)</mo></mrow><mrow><mi>O</mi><mo>(</mo><mi>k</mi><mo>/</mo><mi>ϵ</mi><mo>)</mo></mrow></msup></math></span>. In this paper, we present an algorithm that runs in time <span><math><msup><mrow><mo>(</mo><mi>n</mi><mo>/</mo><mi>ϵ</mi><mo>)</mo></mrow><mrow><mi>O</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>k</mi><mo>⋅</mo><msup><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mi>ϵ</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup><mo>⋅</mo><msup><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>⁡</mo><mo>(</mo><mn>1</mn><mo>/</mo><mi>ϵ</mi><mo>)</mo><mo>)</mo></mrow></msup></math></span>. This gives an improvement on the dependency on <em>k</em> on the exponent, while having a worse dependency on <em>ϵ</em>. As in Laue and Matijević, we follow the framework introduced by Arora for Euclidean TSP. Our key ingredients include exponential distance scaling and compression of dynamic programming state tables.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"190 ","pages":"Article 106581"},"PeriodicalIF":0.7,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143844295","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 longest common subsequence problem for small alphabets in the word RAM model","authors":"Rodrigo Alexander Castro Campos","doi":"10.1016/j.ipl.2025.106579","DOIUrl":"10.1016/j.ipl.2025.106579","url":null,"abstract":"<div><div>Given two strings of lengths <em>m</em> and <em>n</em>, with <span><math><mi>m</mi><mo>≤</mo><mi>n</mi></math></span>, the longest common subsequence problem consists of computing a common subsequence of maximum length by deleting symbols from both strings. While the <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mi>n</mi><mo>)</mo></math></span> algorithm devised in 1974 is optimal in the most general setting, algorithms that depend on parameters other than <em>m</em> and <em>n</em> have been proposed since then. In the word RAM model, let <em>w</em> be the word size, <em>s</em> be the alphabet size, <em>d</em> be the number of dominant symbol matches between the strings, and <em>p</em> be the length of the longest common subsequence. Fast algorithms for this problem have complexities <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mi>n</mi><mo>/</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span>, <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mi>n</mi><mo>/</mo><mi>w</mi><mo>)</mo></math></span>, <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>s</mi><mo>+</mo><mi>min</mi><mo>⁡</mo><mo>(</mo><mi>p</mi><mo>(</mo><mi>n</mi><mo>−</mo><mi>p</mi><mo>)</mo><mo>,</mo><mi>p</mi><mi>m</mi><mo>)</mo><mo>)</mo></math></span>, <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>s</mi><mo>+</mo><mi>d</mi><mi>log</mi><mo>⁡</mo><mi>log</mi><mo>⁡</mo><mi>min</mi><mo>⁡</mo><mo>(</mo><mi>d</mi><mo>,</mo><mi>m</mi><mi>n</mi><mo>/</mo><mi>d</mi><mo>)</mo><mo>)</mo></math></span>, <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>s</mi><mo>+</mo><mi>min</mi><mo>⁡</mo><mo>(</mo><mi>d</mi><mi>s</mi><mo>,</mo><mi>p</mi><mi>m</mi><mo>)</mo><mo>)</mo></math></span>, and <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>s</mi><mo>+</mo><mi>s</mi><msup><mrow><mo>!</mo></mrow><mrow><mn>2</mn></mrow></msup><mi>s</mi><mo>+</mo><mi>d</mi><mi>log</mi><mo>⁡</mo><mi>s</mi><mo>)</mo></math></span>. In this work, we present an <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>(</mo><mi>s</mi><mo>+</mo><msup><mrow><mi>log</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>⁡</mo><mi>n</mi><mo>)</mo><mo>+</mo><mi>min</mi><mo>⁡</mo><mo>(</mo><mi>d</mi><mi>log</mi><mo>⁡</mo><mi>s</mi><mo>,</mo><mi>p</mi><mi>m</mi><mo>)</mo><mo>)</mo></math></span> algorithm when <span><math><mi>s</mi><mo>∈</mo><mi>O</mi><mo>(</mo><mi>w</mi><mo>)</mo></math></span>, and also an <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>(</mo><mi>s</mi><mo>+</mo><msup><mrow><mi>log</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>⁡</mo><mi>n</mi><mo>)</mo><mo>+</mo><mi>d</mi><mo>)</mo></math></span> algorithm when <span><math><mi>s</mi><mo>≤</mo><mi>w</mi></math></span> which uses bitwise instructions that became recently available in modern processors.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"190 ","pages":"Article 106579"},"PeriodicalIF":0.7,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143833605","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":"On the complexity of some restricted variants of Quotient Pigeon and a weak variant of Kőnig","authors":"Takashi Ishizuka","doi":"10.1016/j.ipl.2025.106574","DOIUrl":"10.1016/j.ipl.2025.106574","url":null,"abstract":"<div><div>One of the most famous <span>TFNP</span> subclasses is <span>PPP</span>, which is the set of all search problems whose totality is guaranteed by the pigeonhole principle. The author's recent preprint <span><span>[1]</span></span> has introduced a <span>TFNP</span> problem related to the pigeonhole principle over a quotient set, called <span>Quotient Pigeon</span>, and shown that the problem <span>Quotient Pigeon</span> is not only <span>PPP</span>-hard but also <span>PLS</span>-hard. In this paper, we formulate other computational problems related to the pigeonhole principle over a quotient set via an explicit representation of the equivalence classes. Our new formulation introduces a non-trivial <span><math><mtext>PPP</mtext><mo>∩</mo><msub><mrow><mtext>PPA</mtext></mrow><mrow><mi>k</mi></mrow></msub></math></span>-complete problem for every <span><math><mi>k</mi><mo>≥</mo><mn>2</mn></math></span>. Furthermore, we consider the computational complexity of a computational problem related to Kőnig's lemma, which is a weaker variant of the problem formulated by Pasarkar et al. <span><span>[2]</span></span>. We show that our weaker variant is <span>PPAD</span>-hard and is in <span><math><mtext>PPP</mtext><mo>∩</mo><mtext>PPA</mtext></math></span>.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"190 ","pages":"Article 106574"},"PeriodicalIF":0.7,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143601479","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":"Lower bound proof for the size of BDDs representing a shifted addition","authors":"Jan Kleinekathöfer,&nbsp;Alireza Mahzoon,&nbsp;Rolf Drechsler","doi":"10.1016/j.ipl.2025.106571","DOIUrl":"10.1016/j.ipl.2025.106571","url":null,"abstract":"<div><div><em>Decision Diagrams</em> (DDs) are among the most popular representations for Boolean functions. They are widely used in the synthesis and verification of digital circuits. The size (i.e., number of nodes) and computation time (required time for performing operations) are two important parameters that determine the efficiency of a DD in different applications. It has been proven that some DDs can represent specific functions in polynomial space or perform certain operations in polynomial time. For example, <em>Binary Decision Diagrams</em> (BDDs) are capable of representing a wide variety of functions (e.g. integer addition) in polynomial space with respect to the input size. However, there are also some functions (e.g., integer multiplication) for which the exponential lower-bounds have been proven for the BDD sizes.</div><div>In this paper, we investigate the space complexity of representing an integer addition, where one of the operands is shifted to the right by an arbitrary value. We call this function the shifted addition. This function is widely used in many digital circuits, e.g., floating point adders. We prove that the size of the BDD representing a shifted addition has exponential space complexity with respect to the input size. It is an important step towards clarifying the reasons behind the failure of BDD-based verification and synthesis when they are applied to the circuits containing shifted addition, e.g., floating point adders.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"190 ","pages":"Article 106571"},"PeriodicalIF":0.7,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143427877","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}