Information Processing Letters最新文献

{"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":"2025-06-16","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":"Rank-2 module-LIP with special matrices","authors":"Manoj Gyawali","doi":"10.1016/j.ipl.2025.106593","DOIUrl":"10.1016/j.ipl.2025.106593","url":null,"abstract":"<div><div>Lattice isomorphism problem (LIP) has been studied since 1990s. In 2023, a post-quantum signature scheme known as HAWK was submitted in the NIST standardization of additional signature scheme, which is based on the module lattice isomorphism problem (module-LIP). Module-LIP was formally defined by Mureau et al. at Eurocrypt'24 and Luo et al. reduced the problem of solving module-LIP over CM number fields to a problem of finding the special type of symplectic automorphism.</div><div>In this paper, we extend this idea further by establishing a reduction of the module-LIP to a problem of finding special types of matrices.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"191 ","pages":"Article 106593"},"PeriodicalIF":0.7,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144270237","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":"2025-06-03","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":"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":"2025-06-02","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":"A simple supercritical tradeoff between size and height in resolution","authors":"Sam Buss ,&nbsp;Neil Thapen","doi":"10.1016/j.ipl.2025.106589","DOIUrl":"10.1016/j.ipl.2025.106589","url":null,"abstract":"<div><div>We describe CNFs in <em>n</em> variables which, over a range of parameters, have small resolution refutations but are such that any small refutation must have height larger than <em>n</em> (even exponential in <em>n</em>), where the height of a refutation is the length of the longest path in it. This is called a <em>supercritical</em> tradeoff between size and height because, if we do not care about size, every CNF is refutable in height <em>n</em>. Our proof method uses a simple construction, based on or-ification and base <em>d</em> representations of integers, to reduce the number of variables. A similar result appeared in [Fleming, Pitassi and Robere, ITCS '22], for different formulas using a more complicated construction for reducing the number of variables.</div><div>Small refutations of our formula are necessarily highly irregular, making it a plausible candidate to separate resolution from pool resolution, which amounts to separating CDCL with restarts from CDCL without restarts. We are not able to show this. In the other direction, we show that a simpler version of our formula, with a similar irregularity property, <em>does</em> have polynomial size pool resolution refutations and thus does not provide such a separation for CDCL.</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"191 ","pages":"Article 106589"},"PeriodicalIF":0.7,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144125176","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":"2025-05-05","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":"2025-04-15","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":"Efficient Implementations of Square-root Vélu's Formulas","authors":"Jianming Lin ,&nbsp;Weize Wang ,&nbsp;Chang-An Zhao ,&nbsp;Yuhao Zheng","doi":"10.1016/j.ipl.2025.106580","DOIUrl":"10.1016/j.ipl.2025.106580","url":null,"abstract":"<div><div>In the implementation of isogeny-based cryptographic schemes, Vélu's formulas are essential for constructing and evaluating isogenies. Bernstein et al. proposed an approach known as √élu, which computes an <em>ℓ</em>-isogeny at a cost of <span><math><mover><mrow><mi>O</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>(</mo><msqrt><mrow><mi>ℓ</mi></mrow></msqrt><mo>)</mo></math></span> finite field operations. This paper presents two improvements to enhance the efficiency of the implementation of √élu as follows: optimizing the index system required in √élu and speeding up the computations of the sums of products used in polynomial multiplications over a finite field <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> with characteristic <em>p</em>. To optimize the index system, we modify it to enhance the utilization of <em>x</em>-coordinates and combine it with the technique of redundant representation, which can ultimately reduce the number of <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-multiplications. The speedup of the sums of products is to employ two techniques: lazy reduction (abbreviated as LZYR) and generalized interleaved Montgomery multiplication (abbreviated as INTL). These techniques aim to minimize the underlying operations. We provide an optimized C and assembly implementation of √élu. For the computational cost (in terms of <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-multiplications) of each isogeny involved in CTIDH2048 (resp. SQIsign), exploiting our modified index system (including the combination with redundant representation) obtains a saving up to 5.78% (resp. 5.39%) compared to the previous work. In terms of the performance (reported in CPU clock cycles) of isogeny computations in CTIDH512, applying our index system combined with INTL (resp. our index system combined with LZYR) offers an improvement up to 16.05% (resp. 10.96%) compared to the previous implementation. As for executing an isogeny group action in CTIDH512, our experimental results also demonstrate a reduction of 3.73% (resp. 1.83%) clock cycles by utilizing our index system combined with INTL (resp. our index system combined with LZYR).</div></div>","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"190 ","pages":"Article 106580"},"PeriodicalIF":0.7,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143833606","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":"2025-04-10","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":"Special issue on Economics and Computation","authors":"Argyrios Deligkas,&nbsp;Aris Filos-Ratsikas,&nbsp;Alexandros A. Voudouris","doi":"10.1016/j.ipl.2025.106578","DOIUrl":"10.1016/j.ipl.2025.106578","url":null,"abstract":"","PeriodicalId":56290,"journal":{"name":"Information Processing Letters","volume":"190 ","pages":"Article 106578"},"PeriodicalIF":0.7,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144068564","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}