Theoretical Computer Science最新文献

{"title":"Probabilistic cluster fault diagnosis for multiprocessor systems","authors":"","doi":"10.1016/j.tcs.2024.114837","DOIUrl":"10.1016/j.tcs.2024.114837","url":null,"abstract":"<div><p>As high performance computing systems consisting of multiple processors play an important role in big data analytics, we are motivated to focus on the research of reliability, design-for-test, fault diagnosis and detection of large-scale multiprocessor interconnected systems. System-level diagnosis theory, which originates from the testing of VLSI and Wafer, aims to identify faulty processors in these systems by means of analyzing the test results among the processors, while diagnosability as well as diagnosis accuracy are two important indices. The probabilistic fault diagnostic strategy seeks to correctly diagnose processors with high probability under the assumption that each processor has a certain failing probability. In this work, based on the probabilistic diagnosis algorithm with consideration of fault clustering, we specialize in the local diagnostic capability to establish the probability that any processor in a discrete status is diagnosed correctly. Subsequently, we investigate the global performance evaluation of multiprocessor systems under various significant fault distributions including Poisson distribution, Exponential distribution and Binomial distribution. In addition, we directly apply our results to the data center network <span><math><mi>H</mi><mi>S</mi><mi>D</mi><mi>C</mi></math></span> and <span><math><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></math></span>-star network. Numerical simulations are performed to verify the established results, which reveal the relationship between the accuracy of correct diagnosis and regulatory parameters.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142168383","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":"Restriction on cut rule in cyclic-proof system for symbolic heaps","authors":"","doi":"10.1016/j.tcs.2024.114854","DOIUrl":"10.1016/j.tcs.2024.114854","url":null,"abstract":"<div><p>Symbolic heaps, which are a restricted class of separation logic formulas, with inductive definitions are a suitable language in automated verification systems for memory-manipulating programs. In this context, some related problems, e.g., the entailment problem, have been studied theoretically. In addition, several solvers for the entailment problem based on the proof-search algorithm in cyclic-proof systems, which are proof systems in sequent calculus style with cyclic structure, have been proposed. However, the cut-elimination property generally does not hold for cyclic-proof systems of symbolic heaps with inductive definitions, which means that searching for a cut-free proof is insufficient. In other words, we hope to find a reasonable proof-search algorithm considering the cut rule or we give up on obtaining a complete proof-search procedure. This paper investigates this issue and demonstrates a limit to the challenge of the restrictions on the cut rule in a cyclic-proof system for symbolic heaps. We propose a restricted cut rule, referred to as the presumable cut, which is a relaxed variant of the analytic cut, in which the cut formula must be a subformula of the bottom sequent. This paper demonstrates that the provability of the cyclic-proof system for symbolic heaps becomes strictly weaker by restricting the cut rule to the presumable cut.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304397524004717/pdfft?md5=08f063fdecac881a6031c44144f640a6&pid=1-s2.0-S0304397524004717-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142163029","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":"Threshold sampling","authors":"","doi":"10.1016/j.tcs.2024.114847","DOIUrl":"10.1016/j.tcs.2024.114847","url":null,"abstract":"<div><p>We consider the problem of sampling elements with some desired property from a large set, without testing the property of interest, but with the (probabilistic) assurance to have at least one match among the random sample. Like in ranked set sampling (RSS), we consider an infinite population under study, whose properties of interest are too expensive and/or time-consuming to measure. Unlike RSS, we are void of a ranking mechanism, so our sampling is done entirely blind. We show how it is nonetheless doable to assure, with controllably large likelihood, to either have at least one of the interesting elements in a random sample, or, contrarily, sample with the likewise assurance of not having one of the interesting elements in the sample. Our technique utilizes density bounds for distributions and threshold functions from random graph theory.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S030439752400464X/pdfft?md5=26ceab1a448b5baf958ad0b8d3b32343&pid=1-s2.0-S030439752400464X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142163028","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":"A new similarity in clustering through users' interest and social relationship","authors":"","doi":"10.1016/j.tcs.2024.114833","DOIUrl":"10.1016/j.tcs.2024.114833","url":null,"abstract":"<div><p>Clustering is a basic technology in data mining, and similarity measurement plays a crucial role in it. The existing clustering algorithms, especially those for social networks, pay more attention to users' properties while ignoring the global measurement across social relationships. In this paper, a new clustering algorithm is proposed, which not only considers the distance of users' properties but also considers users' social influence. Social influence can be further divided into mutual influence and self influence. With mutual influence, we can deal with users' interests and measure their similarities by introducing areas and activities, thus better weighing the influence between them in an indirect way. Separately, we formulate a new propagation model, PR-Threshold++, by merging the PageRank algorithm and Linear Threshold model, to model the self influence. Based on that, we design a novel similarity by exploiting users' distance, mutual influence, and self influence. Finally, we adjust K-medoids according to our similarity and use real-world datasets to evaluate their performance in intensive simulations.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142158432","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":"High fault-tolerant performance of the divide-and-swap cube network","authors":"","doi":"10.1016/j.tcs.2024.114834","DOIUrl":"10.1016/j.tcs.2024.114834","url":null,"abstract":"<div><p>Two crucial metrics used to evaluate the fault tolerance of interconnection networks are connectivity and diagnosability. By improving the connectivity and diagnosability of the interconnection network, its fault tolerance can be enhanced. In this paper, we focus on determining the <em>g</em>-extra connectivity <span><math><mo>(</mo><mn>0</mn><mo>≤</mo><mi>g</mi><mo>≤</mo><mn>10</mn><mo>)</mo></math></span> of the divide-and-swap cube <span><math><mi>D</mi><mi>S</mi><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, as well as its diagnosability based on the pessimistic diagnosis strategy and <em>g</em>-extra precise diagnosis strategy, under the PMC and MM* models. The research analysis suggests that compared with some other connectivity and diagnosability of <span><math><mi>D</mi><mi>S</mi><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>, such as classical connectivity, structure connectivity, super connectivity, and classical diagnosability, the extra connectivity/diagnosability and pessimistic diagnosability of <span><math><mi>D</mi><mi>S</mi><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> enable it to have a higher fault tolerance. Moreover, we propose two <span><math><mi>O</mi><mo>(</mo><mi>N</mi><msub><mrow><mi>log</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>⁡</mo><mi>N</mi><mo>)</mo></math></span> effective diagnosis algorithms of <span><math><mi>D</mi><mi>S</mi><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>: the <em>g</em>-extra diagnosis algorithm (EX-Diagnosis<span><math><msub><mrow></mrow><mrow><mi>D</mi><mi>S</mi><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></msub></math></span>) and the pessimistic diagnosis algorithm (PE-Diagnosis<span><math><msub><mrow></mrow><mrow><mi>D</mi><mi>S</mi><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></msub></math></span>), where the EX-Diagnosis<span><math><msub><mrow></mrow><mrow><mi>D</mi><mi>S</mi><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></msub></math></span> algorithm can accurately diagnose the state of all processors in <span><math><mi>D</mi><mi>S</mi><msub><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142163043","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":"Partial key exposure attacks on Prime Power RSA with non-consecutive blocks","authors":"","doi":"10.1016/j.tcs.2024.114845","DOIUrl":"10.1016/j.tcs.2024.114845","url":null,"abstract":"<div><p>Partial key exposure attacks pose a significant threat to RSA-type cryptosystems. These attacks factorize the RSA modulus by utilizing partial knowledge of the decryption exponent, which is typically revealed by side-channel attacks, cold boot attacks, etc. Such partial information is often located in non-consecutive blocks. However, the majority of the proposed attacks on Prime Power RSA have only considered a single unexposed block. Meanwhile, related attacks are incapable of being expanded to multiple unexposed blocks or achieving optimal results.</p><p>In this paper, we propose partial key exposure attacks on Prime Power RSA modulus <span><math><mi>N</mi><mo>=</mo><msup><mrow><mi>p</mi></mrow><mrow><mi>r</mi></mrow></msup><msup><mrow><mi>q</mi></mrow><mrow><mi>l</mi></mrow></msup></math></span> with <em>n</em> unknown blocks, where <span><math><mi>n</mi><mo>≥</mo><mn>2</mn></math></span>. We reduce this extended attack to solving multivariate linear modular equations and apply lattice-based approaches, including Herrmann-May's method (ASIACRYPT'08), Takayasu-Kunihiro's method (ACISP'13), and Lu-Zhang-Peng-Lin's method (ASIACRYPT'15), to solve them. Furthermore, we improve Lu et al.'s method by adding helpful polynomials and removing unhelpful polynomials to construct a better lattice basis. We also extend Lu et al.'s method by introducing a new parameter to make the lattice basis construction more flexible. Our improved and extended methods can be used for attacks when <span><math><mi>l</mi><mo>=</mo><mn>1</mn></math></span> and <span><math><mi>l</mi><mo>≥</mo><mn>1</mn></math></span>, respectively. These new attacks require less partial information than previous methods. For example, in the case where <span><math><mi>n</mi><mo>=</mo><mn>2</mn></math></span>, we reduce the amount of partial information needed from 80.7% to 77.8% when <span><math><mi>r</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>l</mi><mo>=</mo><mn>1</mn></math></span>, and from 64.0% to 44.9% when <span><math><mi>r</mi><mo>=</mo><mn>3</mn><mo>,</mo><mi>l</mi><mo>=</mo><mn>2</mn></math></span>.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142163044","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 complexity trichotomy for k-regular asymmetric spin systems with complex edge functions","authors":"","doi":"10.1016/j.tcs.2024.114835","DOIUrl":"10.1016/j.tcs.2024.114835","url":null,"abstract":"<div><p>We prove a complexity trichotomy theorem for a class of partition functions over <em>k</em>-regular graphs, where the signature is complex valued and not necessarily <em>symmetric</em>. In details, we establish explicit criteria, according to which the partition functions of all such systems are classified into three classes: For every parameter setting in <span><math><mi>C</mi></math></span> for the spin system, the partition function is either (1) computable in polynomial time for every graph, or (2) #P-hard for general graphs but computable in polynomial time for planar graphs, or (3) #P-hard even for planar graphs.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142172866","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":"Observation routes and external watchman routes","authors":"","doi":"10.1016/j.tcs.2024.114818","DOIUrl":"10.1016/j.tcs.2024.114818","url":null,"abstract":"<div><p>We introduce the Observation Route Problem (<span>ORP</span>) defined as follows: Given a set of <em>n</em> pairwise disjoint obstacles (regions) in the plane, find a shortest tour (route) such that an observer walking along this tour can see (observe) each obstacle from some point of the tour. The observer does <em>not</em> need to see the entire boundary of an obstacle. The tour is <em>not</em> allowed to intersect the interior of any region (i.e., the regions are obstacles and therefore out of bounds). The problem exhibits similarity to both the Traveling Salesman Problem with Neighborhoods (<span>TSPN</span>) and the External Watchman Route Problem (<span>EWRP</span>). We distinguish two variants: the range of visibility is either limited to a bounding rectangle, or unlimited. We obtain the following results:</p><p>(I) Given a family of <em>n</em> disjoint convex bodies in the plane, computing a shortest observation route does not admit a <span><math><mo>(</mo><mi>c</mi><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span>-approximation unless <span><math><mi>P</mi><mo>=</mo><mrow><mi>NP</mi></mrow></math></span> for an absolute constant <span><math><mi>c</mi><mo>&gt;</mo><mn>0</mn></math></span>. (This holds for both limited and unlimited vision.)</p><p>(II) Given a family of disjoint convex bodies in the plane, computing a shortest external watchman route is <span><math><mi>NP</mi></math></span>-hard. (This holds for both limited and unlimited vision; and even for families of axis-aligned squares.)</p><p>(III) Given a family of <em>n</em> disjoint fat convex polygons in the plane, an observation tour whose length is at most <span><math><mi>O</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> times the optimal can be computed in polynomial time. (This holds for limited vision.)</p><p>(IV) For every <span><math><mi>n</mi><mo>≥</mo><mn>5</mn></math></span>, there exists a convex polygon with <em>n</em> sides and all angles obtuse such that its perimeter is <em>not</em> a shortest external watchman route. This refutes a conjecture by Absar and Whitesides (2006).</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0304397524004353/pdfft?md5=8156a2411321e5e2d23ab419a17b5976&pid=1-s2.0-S0304397524004353-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142163027","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":"An algorithmic construction of union-intersection-bounded families","authors":"","doi":"10.1016/j.tcs.2024.114817","DOIUrl":"10.1016/j.tcs.2024.114817","url":null,"abstract":"<div><p>In this paper, we present lower bounds and algorithmic constructions of union-intersection-bounded families of sets. The lower bound is established using the Lovász Local Lemma. This bound matches the best known bound for the size of union-intersection-bounded families of sets. We then use the variable framework for the Lovász Local Lemma, to discuss an algorithm that outputs explicit constructions that attain the lower bound. The algorithm has polynomial complexity in the number of points in the family.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142136033","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 fixed-parameter algorithm for dominance drawings of DAGs","authors":"","doi":"10.1016/j.tcs.2024.114819","DOIUrl":"10.1016/j.tcs.2024.114819","url":null,"abstract":"<div><p>A weak dominance drawing Γ of a DAG <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> is a <em>d</em>-dimensional drawing such that <span><math><mi>D</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>&lt;</mo><mi>D</mi><mo>(</mo><mi>v</mi><mo>)</mo></math></span> for every dimension <em>D</em> of Γ if there is a directed path from a vertex <em>u</em> to a vertex <em>v</em> in <em>G</em>, where <span><math><mi>D</mi><mo>(</mo><mi>w</mi><mo>)</mo></math></span> is the coordinate of vertex <span><math><mi>w</mi><mo>∈</mo><mi>V</mi></math></span> in dimension <em>D</em> of Γ. If <span><math><mi>D</mi><mo>(</mo><mi>u</mi><mo>)</mo><mo>&lt;</mo><mi>D</mi><mo>(</mo><mi>v</mi><mo>)</mo></math></span> for every dimension <em>D</em> of Γ, but there is no path from <em>u</em> to <em>v</em>, we have a <em>falsely implied path (fip)</em>. Minimizing the number of fips is an important theoretical and practical problem. Computing 2-dimensional weak dominance drawings with minimum number of fips is NP-hard. We show that this problem is FPT parameterized by the dimension <em>d</em> and the modular width <em>mw</em>. A key ingredient of our proof is the <span>Compaction Lemma</span>, where we show an interesting property of any weak dominance drawing of <em>G</em> with the minimum number of fips. This FPT result in weak dominance, which is interesting by itself because the fip-minimization problem is NP-hard, is used to prove our main contributions. Computing the dominance dimension of <em>G</em>, that is, the minimum number of dimensions <em>d</em> for which <em>G</em> has a <em>d</em>-dimensional dominance drawing (a weak dominance drawing with 0 fips), is a well-known NP-hard problem. We show that the dominance dimension of <em>G</em> is bounded by <span><math><mfrac><mrow><mi>m</mi><mi>w</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> (or <em>mw</em>, if <span><math><mi>m</mi><mi>w</mi><mo>&lt;</mo><mn>4</mn></math></span>) and that computing the dominance dimension of <em>G</em> is an FPT problem with parameter <em>mw</em>. As far as we know, this the first FPT-algorithm to compute the dominance dimension of a DAG.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142168385","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}