{"title":"Weighted automata and logics meet computational complexity","authors":"Peter Kostolányi","doi":"10.1016/j.ic.2024.105213","DOIUrl":"10.1016/j.ic.2024.105213","url":null,"abstract":"<div><p>Complexity classes such as <span><math><mi>#</mi><mi>P</mi></math></span>, <span><math><mo>⊕</mo><mi>P</mi></math></span>, <strong>GapP</strong>, <strong>OptP</strong>, <strong>NPMV</strong>, or the class of fuzzy languages realised by polynomial-time fuzzy nondeterministic Turing machines, can all be described in terms of a class <span><math><mrow><mi>NP</mi></mrow><mo>[</mo><mi>S</mi><mo>]</mo></math></span> for a suitable semiring <em>S</em>, defined via weighted Turing machines over <em>S</em> similarly as <strong>NP</strong> is defined in the unweighted setting. Other complexity classes can be lifted to the quantitative world as well, the resulting classes relating to the original ones in the same way as weighted automata or logics relate to their unweighted counterparts. The article surveys these too-little-known connexions implicit in the existing literature and suggests a systematic approach to the study of weighted complexity classes. An extension of <span><math><mi>SAT</mi></math></span> to weighted propositional logic is proved to be complete for <span><math><mrow><mi>NP</mi></mrow><mo>[</mo><mi>S</mi><mo>]</mo></math></span> when <em>S</em> is finitely generated. Moreover, a class <span><math><mrow><mi>FP</mi></mrow><mo>[</mo><mi>S</mi><mo>]</mo></math></span> is introduced for each semiring <em>S</em> as a counterpart to <strong>P</strong>, and the relations between <span><math><mrow><mi>FP</mi></mrow><mo>[</mo><mi>S</mi><mo>]</mo></math></span> and <span><math><mrow><mi>NP</mi></mrow><mo>[</mo><mi>S</mi><mo>]</mo></math></span> are considered.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105213"},"PeriodicalIF":0.8,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141993489","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":"Modification problems toward proper (Helly) circular-arc graphs","authors":"Yixin Cao , Hanchun Yuan , Jianxin Wang","doi":"10.1016/j.ic.2024.105211","DOIUrl":"10.1016/j.ic.2024.105211","url":null,"abstract":"<div><p>We present a <span><math><msup><mrow><mn>9</mn></mrow><mrow><mi>k</mi></mrow></msup><mo>⋅</mo><msup><mrow><mi>n</mi></mrow><mrow><mi>O</mi><mo>(</mo><mn>1</mn><mo>)</mo></mrow></msup></math></span>-time algorithm for the proper circular-arc vertex deletion problem, resolving an open problem of van 't Hof and Villanger [Algorithmica 2013] and Crespelle et al. [Computer Science Review 2023]. Our structural study also implies parameterized algorithms for modification problems toward proper Helly circular-arc graphs.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105211"},"PeriodicalIF":0.8,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944893","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}
Giovanni Pagliarini , Simone Scaboro , Giuseppe Serra , Guido Sciavicco , Ionel Eduard Stan
{"title":"Neural-symbolic temporal decision trees for multivariate time series classification","authors":"Giovanni Pagliarini , Simone Scaboro , Giuseppe Serra , Guido Sciavicco , Ionel Eduard Stan","doi":"10.1016/j.ic.2024.105209","DOIUrl":"10.1016/j.ic.2024.105209","url":null,"abstract":"<div><p>Multivariate time series classification is an ubiquitous and widely studied problem. Due to their strong generalization capability, neural networks are suitable for this problem, but their intrinsic black-box nature often limits their applicability. Temporal decision trees are a relevant alternative to neural networks for the same task regarding classification performances while attaining higher levels of transparency and interpretability. In this work, we approach the problem of hybridizing these two techniques, and present three independent, natural hybridization solutions to study if, and in what measure, both the ability of neural networks to capture complex temporal patterns and the transparency and flexibility of temporal decision trees can be leveraged. To this end, we provide initial experimental results for several tasks in a binary classification setting, showing that our proposed neural-symbolic hybridization schemata may be a step towards accurate and interpretable models.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105209"},"PeriodicalIF":0.8,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0890540124000749/pdfft?md5=aee9f730063439e214c71730ad5c92be&pid=1-s2.0-S0890540124000749-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944895","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":"State complexity bounds for projection, shuffle, up- and downward closure and interior on commutative regular languages","authors":"Stefan Hoffmann","doi":"10.1016/j.ic.2024.105204","DOIUrl":"10.1016/j.ic.2024.105204","url":null,"abstract":"<div><div>We consider the state complexity of projection, shuffle, up- and downward closure and interior on commutative regular languages. We deduce the state complexity bound <span><math><msup><mrow><mi>n</mi></mrow><mrow><mo>|</mo><mi>Σ</mi><mo>|</mo></mrow></msup></math></span> for upward closure and downward interior, and <span><math><msup><mrow><mo>(</mo><mn>2</mn><mi>n</mi><mi>m</mi><mo>)</mo></mrow><mrow><mo>|</mo><mi>Σ</mi><mo>|</mo></mrow></msup></math></span>, <span><math><msup><mrow><mo>(</mo><mi>n</mi><mi>m</mi><mo>)</mo></mrow><mrow><mo>|</mo><mi>Σ</mi><mo>|</mo></mrow></msup></math></span>, <span><math><msup><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mi>m</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>|</mo><mi>Σ</mi><mo>|</mo></mrow></msup></math></span> and <span><math><msup><mrow><mo>(</mo><mi>n</mi><mo>+</mo><mi>m</mi><mo>−</mo><mn>2</mn><mo>)</mo></mrow><mrow><mo>|</mo><mi>Σ</mi><mo>|</mo></mrow></msup></math></span> for the shuffle on commutative regular, group, aperiodic and finite languages, respectively, with state complexities <em>n</em> and <em>m</em> over the alphabet Σ. We do not know whether these bounds are sharp. For projection, downward closure and upward interior, we give the sharp bound <em>n</em>. Our results are obtained by using the index and period vectors of a regular language, which we introduce in the present work and investigate w.r.t. the above operations and also union and intersection. Furthermore, we characterize the commutative aperiodic and commutative group languages in terms of these parameters and prove that a commutative regular language equals a finite union of shuffle products of commutative finite and commutative group languages.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105204"},"PeriodicalIF":0.8,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142416802","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":"Symbolic computation in algebra, geometry, and differential equations","authors":"Franz Winkler","doi":"10.1016/j.ic.2024.105200","DOIUrl":"10.1016/j.ic.2024.105200","url":null,"abstract":"<div><p>In this survey article we describe how symbolic computation in algebra and geometry leads to symbolic, i.e., formula solutions of algebraic differential equations. Symbolic solutions of algebraic differential equations can be derived from parametrizations of corresponding algebraic varieties. Such parametrizations in turn can be computed by elimination methods, i.e., methods for solving systems of polynomial equations.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105200"},"PeriodicalIF":0.8,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0890540124000658/pdfft?md5=0b04bde55234c483e1cb8b3d2f7312e3&pid=1-s2.0-S0890540124000658-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141979196","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":"Total (restrained) domination in unit disk graphs","authors":"Yu Yang , Cai-Xia Wang , Shou-Jun Xu","doi":"10.1016/j.ic.2024.105210","DOIUrl":"10.1016/j.ic.2024.105210","url":null,"abstract":"<div><p>The minimum total domination problem and the minimum total restrained domination problem are classical combinatorial optimization problems. In this paper, we first show that the decision versions of both the minimum total domination problem and the minimum total restrained domination problem are NP-complete for grid graphs (a subclass of unit disk graphs), thereby strengthening the result on the total domination decision problem in unit disk graphs established by Jena et al. (2021). Then, we present a linear-time 6.387-approximation algorithm for the minimum total domination problem in unit disk graphs, improving upon the previous algorithm with a ratio of 8 by Jena et al. (2021). Finally, we propose a linear-time 10.387-approximation algorithm and a PTAS for the minimum total restrained domination problem in unit disk graphs.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"300 ","pages":"Article 105210"},"PeriodicalIF":0.8,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944894","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 prime scenarios in qualitative spatial and temporal reasoning","authors":"Yakoub Salhi , Michael Sioutis","doi":"10.1016/j.ic.2024.105198","DOIUrl":"10.1016/j.ic.2024.105198","url":null,"abstract":"<div><p>The concept of prime implicant is a fundamental tool in Boolean algebra, which is used in Boolean circuit design and, recently, in explainable AI. This study investigates an analogous concept in qualitative spatial and temporal reasoning, called prime scenario. Specifically, we define a prime scenario of a qualitative constraint network (QCN) as a minimal set of decisions that can uniquely determine solutions of this QCN. We propose in this paper a collection of algorithms designed to address various problems related to prime scenarios, and also show how certain results can be useful for measuring the robustness of a QCN. In addition, we study the relationship between our notions in this paper and the notion of prime sub-QCN in the literature, and establish theoretical results in the process. Further, we devise a language based on the notion of prime scenario for knowledge compilation. Finally, an experimental evaluation is performed with instances of Allen's Interval Algebra and <span>RCC8</span> to assess the efficiency of our algorithms and, hence, also the difficulty of the newly introduced problems here.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"300 ","pages":"Article 105198"},"PeriodicalIF":0.8,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944901","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}
Anton Betten , Svetlana Topalova , Stela Zhelezova
{"title":"On parallelisms of PG(3,4) with automorphisms of order 2","authors":"Anton Betten , Svetlana Topalova , Stela Zhelezova","doi":"10.1016/j.ic.2024.105201","DOIUrl":"10.1016/j.ic.2024.105201","url":null,"abstract":"<div><p>Let <span><math><mrow><mi>PG</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span> be the <em>n</em>-dimensional projective space over the finite field <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>q</mi></mrow></msub></math></span>. A <em>spread</em> in <span><math><mrow><mi>PG</mi></mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span> is a set of mutually skew lines which partition the point set. A <em>parallelism</em> is a partition of the set of lines by spreads. The classification of parallelisms in small finite projective spaces is of interest for problems from projective geometry, design theory, network coding, error-correcting codes, and cryptography. All parallelisms of <span><math><mrow><mi>PG</mi></mrow><mo>(</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span> and <span><math><mrow><mi>PG</mi></mrow><mo>(</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></span> are known. Parallelisms of <span><math><mrow><mi>PG</mi></mrow><mo>(</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></span> which are invariant under automorphisms of odd prime orders have also been classified. The present paper contributes to the classification of parallelisms in <span><math><mrow><mi>PG</mi></mrow><mo>(</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></span> with automorphisms of even order. We focus on cyclic groups of order four and the group of order two generated by a Baer involution. We examine invariants of the parallelisms such as the full automorphism group, the type of spreads and questions of duality. The results given in this paper show that the number of parallelisms of <span><math><mrow><mi>PG</mi></mrow><mo>(</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></span> is at least 8675365. Some future directions of research are outlined.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105201"},"PeriodicalIF":0.8,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944902","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":"Detecting arrays for effects of multiple interacting factors","authors":"Charles J. Colbourn, Violet R. Syrotiuk","doi":"10.1016/j.ic.2024.105202","DOIUrl":"10.1016/j.ic.2024.105202","url":null,"abstract":"<div><p>Detecting arrays provide test suites for complex engineered systems in which many factors interact. The determination of which interactions have a significant impact on system behaviour requires not only that each interaction appear in a test, but also that its effect can be distinguished from those of other significant interactions. In this paper, compact representations of detecting arrays using vectors over the finite field are developed. Covering strong separating hash families exploit linear independence over the field, while the weaker elongated covering perfect hash families permit some linear dependence. For both, probabilistic analyses are employed to establish effective upper bounds on the number of tests needed in a detecting array for a wide variety of parameters. The analyses underlie efficient algorithms for the explicit construction of detecting arrays.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105202"},"PeriodicalIF":0.8,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141979194","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}
Marios Adamoudis , Konstantinos A. Draziotis , Dimitrios Poulakis
{"title":"Attacking (EC)DSA with partially known multiples of nonces","authors":"Marios Adamoudis , Konstantinos A. Draziotis , Dimitrios Poulakis","doi":"10.1016/j.ic.2024.105203","DOIUrl":"10.1016/j.ic.2024.105203","url":null,"abstract":"<div><p>In this paper, we introduce a series of attacks on DSA schemes that, under certain assumptions, can expose the secret key when one or more signed messages are accessible. By utilizing these signed messages, we construct a system of linear congruences with at most one solution smaller than a specific bound, which can be efficiently determined using Babai's Nearest Plane Algorithm. As a case study, we provide a successful attack on secp161k1, assuming that a particular multiple of an ephemeral key is 161 bits long.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"301 ","pages":"Article 105203"},"PeriodicalIF":0.8,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141944898","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}