Theory of Computing Systems最新文献_第4页

New Results on the Remote Set Problem and Its Applications in Complexity Study 远程集问题的新成果及其在复杂性研究中的应用

IF 0.5 4区计算机科学

Theory of Computing Systems Pub Date : 2024-03-05 DOI: 10.1007/s00224-024-10162-2

Yijie Chen, Kewei Lv

{"title":"New Results on the Remote Set Problem and Its Applications in Complexity Study","authors":"Yijie Chen, Kewei Lv","doi":"10.1007/s00224-024-10162-2","DOIUrl":"https://doi.org/10.1007/s00224-024-10162-2","url":null,"abstract":"In 2015, Haviv introduced the Remote set problem (RSP) and studied the complexity of the covering radius problem (CRP), which is a classical problem in lattices. The RSP aims to identify a set containing a point that is sufficiently distant from a given lattice (pmb {mathcal {L}}). It introduced a new method for analyzing the complexity of CRP. An open question in RSP is whether we can obtain the approximation factor (gamma =1/2). This paper investigates this question and proposes a probabilistic polynomial-time algorithm for RSP with an approximation factor of (1/2-1/(clambda ^{(p)}_n)), where (cin mathbb {Z}^{+}) and (lambda ^{(p)}_n) is the n-th successive minima in lattice under (l_p)-norm. For a given lattice (pmb {mathcal {L}}) with rank n and positive integer d, our algorithm outputs a set S of size d in polynomial time. This set S includes a point at least ((frac{1}{2}-frac{1}{clambda ^{(p)}_n}){{rho }^{(p)}}(pmb {mathcal {L}})) from lattice (pmb {mathcal {L}}) with a probability greater than (1-1/2^d). Here, c is a positive integer and (rho ^{(p)}(pmb {mathcal {L}})) denotes the covering radius of (pmb {mathcal {L}}) in (l_p)-norm((1le ple infty )). Based on this, we obtain that (text {GAPCRP}_{2+1/2^{O(n)}}) belongs to the complexity class coRP, and we provide new reductions from GAPCRP to GAPCVP.","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":"65 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140034561","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}

引用次数: 0

On Non-principal Arithmetical Numberings and Families 论非主流算术级数和族

IF 0.5 4区计算机科学

Theory of Computing Systems Pub Date : 2024-02-23 DOI: 10.1007/s00224-024-10165-z

Marat Faizrahmanov

{"title":"On Non-principal Arithmetical Numberings and Families","authors":"Marat Faizrahmanov","doi":"10.1007/s00224-024-10165-z","DOIUrl":"https://doi.org/10.1007/s00224-024-10165-z","url":null,"abstract":"The paper studies (varvec{Sigma ^0_n})-computable families ((varvec{ngeqslant 2})) and their numberings. It is proved that any non-trivial (varvec{Sigma ^0_n})-computable family has a complete with respect to any of its elements (varvec{Sigma ^0_n})-computable non-principal numbering. It is established that if a (varvec{Sigma ^0_n})-computable family is not principal, then any of its (varvec{Sigma ^0_n})-computable numberings has a minimal cover and, if the family is infinite, is incomparable with one of its minimal (varvec{Sigma ^0_n})-computable numberings. It is also shown that for any (varvec{Sigma ^0_n})-computable numbering (varvec{nu }) of a (varvec{Sigma ^0_n})-computable non-principal family there exists its (varvec{Sigma ^0_n})-computable numbering that is incomparable with (varvec{nu }). If a non-trivial (varvec{Sigma ^0_n})-computable family contains the least and greatest elements under inclusion, then for any of its (varvec{Sigma ^0_n})-computable non-principal non-least numberings (varvec{nu }) there exists a (varvec{Sigma ^0_n})-computable numbering of the family incomparable with (varvec{nu }). In particular, this is true for the family of all (varvec{Sigma ^0_n})-sets and for the families consisting of two inclusion-comparable (varvec{Sigma ^0_n})-sets (semilattices of the (varvec{Sigma ^0_n})-computable numberings of such families are isomorphic to the semilattice of (varvec{m})-degrees of (varvec{Sigma ^0_n})-sets).","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":"7 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139955332","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}

引用次数: 0

Complexity of the (Connected) Cluster Vertex Deletion Problem on H-free Graphs 无 H 图上（连接）簇顶点删除问题的复杂性

IF 0.5 4区计算机科学

Theory of Computing Systems Pub Date : 2024-02-23 DOI: 10.1007/s00224-024-10161-3

Hoang-Oanh Le, Van Bang Le

{"title":"Complexity of the (Connected) Cluster Vertex Deletion Problem on H-free Graphs","authors":"Hoang-Oanh Le, Van Bang Le","doi":"10.1007/s00224-024-10161-3","DOIUrl":"https://doi.org/10.1007/s00224-024-10161-3","url":null,"abstract":"The well-known Cluster Vertex Deletion problem (cluster-vd) asks for a given graph G and an integer k whether it is possible to delete a set S of at most k vertices of G such that the resulting graph (G-S) is a cluster graph (a disjoint union of cliques). We give a complete characterization of graphs H for which cluster-vd on H-free graphs is polynomially solvable and for which it is (textsf{NP})-complete. Moreover, in the (textsf{NP})-completeness cases, cluster-vd cannot be solved in sub-exponential time in the vertex number of the H-free input graphs unless the Exponential-Time Hypothesis fails. We also consider the connected variant of cluster-vd, the Connected Cluster Vertex Deletion problem (connected cluster-vd), in which the set S has to induce a connected subgraph of G. It turns out that connected cluster-vd admits the same complexity dichotomy for H-free graphs. Our results enlarge a list of rare dichotomy theorems for well-studied problems on H-free graphs.","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":"41 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139955176","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}

引用次数: 0

On the Decidability of Infix Inclusion Problem 论无穷包含问题的可判定性

IF 0.5 4区计算机科学

Theory of Computing Systems Pub Date : 2024-01-13 DOI: 10.1007/s00224-023-10160-w

{"title":"On the Decidability of Infix Inclusion Problem","authors":"","doi":"10.1007/s00224-023-10160-w","DOIUrl":"https://doi.org/10.1007/s00224-023-10160-w","url":null,"abstract":"<h3>Abstract</h3> We introduce the infix inclusion problem of two languages S and T that decides whether or not S is a subset of the set of all infixes of T. This problem is motivated by the need for identifying malicious computation patterns according to their semantics, which are often disguised with additional sub-patterns surrounding information. In other words, malicious patterns are embedded as an infix of the whole pattern. We examine the infix inclusion problem for the case where a source S and a target T are finite, regular or context-free languages. We prove that the problem is 1) co-NP-complete when one of the languages is finite, 2) PSPACE-complete when both S and T are regular, 3) EXPTIME-complete when S is context-free and T is regular, 4) undecidable when S is either regular or context-free and T is context-free and 5) undecidable when one of S and T is in a language class where the emptiness of its languages is undecidable, even if the other is finite. We, furthermore, explore the infix inclusion problem for visibly pushdown languages, a subclass of context-free languages.","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":"31 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139459373","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}

引用次数: 0

Farkas Bounds on Horn Constraint Systems 角约束系统的法卡斯界值

IF 0.5 4区计算机科学

Theory of Computing Systems Pub Date : 2024-01-06 DOI: 10.1007/s00224-023-10156-6

K. Subramani, Piotr Wojciechowki, Alvaro Velasquez

{"title":"Farkas Bounds on Horn Constraint Systems","authors":"K. Subramani, Piotr Wojciechowki, Alvaro Velasquez","doi":"10.1007/s00224-023-10156-6","DOIUrl":"https://doi.org/10.1007/s00224-023-10156-6","url":null,"abstract":"In this paper, we analyze the copy complexity of unsatisfiable Horn constraint systems, under the ADD refutation system. Recall that a linear constraint of the form (sum _{i=1}^{n} a_{i}cdot x_{i} ge b), is said to be a horn constraint if all the (a_{i} in {0,1,-1}) and at most one of the (a_{i})s is positive. A conjunction of such constraints is called a Horn constraint system (HCS). Horn constraints arise in a number of domains including, but not limited to, program verification, power systems, econometrics, and operations research. The ADD refutation system is both sound and complete. Additionally, it is the simplest and most natural refutation system for refuting the feasibility of a system of linear constraints. The copy complexity of an infeasible linear constraint system (not necessarily Horn) in a refutation system, is the minimum number of times each constraint needs to be replicated, in order to obtain a read-once refutation. We show that for an HCS with n variables and m constraints, the copy complexity is at most (2^{n-1}), in the ADD refutation system. Additionally, we analyze bounded-width HCSs from the perspective of copy complexity. Finally, we provide an empirical analysis of an integer programming formulation of the copy complexity problem in HCSs. (An extended abstract was published in FroCos 2021 [26].)","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":"4 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139373777","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}

引用次数: 0

On Polynomial Recursive Sequences. 论多项式递推序列。

IF 0.6 4区计算机科学

Theory of Computing Systems Pub Date : 2024-01-01 Epub Date: 2021-06-02 DOI: 10.1007/s00224-021-10046-9

Michaël Cadilhac, Filip Mazowiecki, Charles Paperman, Michał Pilipczuk, Géraud Sénizergues

引用次数: 0

Rational Index of Languages Defined by Grammars with Bounded Dimension of Parse Trees 解析树维度有界的语法所定义语言的有理索引

IF 0.5 4区计算机科学

Theory of Computing Systems Pub Date : 2023-12-20 DOI: 10.1007/s00224-023-10159-3

Ekaterina Shemetova, Alexander Okhotin, Semyon Grigorev

{"title":"Rational Index of Languages Defined by Grammars with Bounded Dimension of Parse Trees","authors":"Ekaterina Shemetova, Alexander Okhotin, Semyon Grigorev","doi":"10.1007/s00224-023-10159-3","DOIUrl":"https://doi.org/10.1007/s00224-023-10159-3","url":null,"abstract":"The rational index (rho _L) of a language L is an integer function, where (rho _L(n)) is the maximum length of the shortest string in (L cap R), over all regular languages R recognized by n-state nondeterministic finite automata (NFA). This paper investigates the rational index of languages defined by grammars with bounded parse tree dimension: this is a numerical measure of the amount of branching in a tree (with trees in a linear grammar having dimension 1). For context-free grammars, a grammar with tree dimension bounded by d has rational index at most (O(n^{2d})), and it is known from the literature that there exists a grammar with rational index (Theta (n^{2d})). In this paper, it is shown that for multi-component grammars with at most k components (k-MCFG) and with a tree dimension bounded by d, the rational index is at most (O(n^{2kd})), where the constant depends on the grammar, and there exists such a grammar with rational index (frac{k}{2^{kd^2 - kd -2k -1} cdot (8k+1)^{2kd}} n^{2kd}). Also, for the case of ordinary context-free grammars, a more precise lower bound (frac{1}{2^{d^2 + d - 3} 3^{2d}} n^{2d}) is established.","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":"10 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138818090","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}

引用次数: 0

Improved Bounds for Matching in Random-Order Streams 随机排序流中匹配的改进边界

IF 0.5 4区计算机科学

Theory of Computing Systems Pub Date : 2023-12-12 DOI: 10.1007/s00224-023-10155-7

Aaron Bernstein

{"title":"Improved Bounds for Matching in Random-Order Streams","authors":"Aaron Bernstein","doi":"10.1007/s00224-023-10155-7","DOIUrl":"https://doi.org/10.1007/s00224-023-10155-7","url":null,"abstract":"We study the problem of computing an approximate maximum cardinality matching in the semi-streaming model when edges arrive in a random order. In the semi-streaming model, the edges of the input graph (G = (V,E)) are given as a stream (e_1, ldots , e_m), and the algorithm is allowed to make a single pass over this stream while using (O(ntext {polylog}(n))) space ((m = |E|) and (n = |V|)). If the order of edges is adversarial, a simple single-pass greedy algorithm yields a 1/2-approximation in O(n) space; achieving a better approximation in adversarial streams remains an elusive open question. A line of recent work shows that one can improve upon the 1/2-approximation if the edges of the stream arrive in a random order. The state of the art for this model is two-fold: Assadi et al. [SODA 2019] show how to compute a (frac{2}{3}) ((sim .66))-approximate matching, but the space requirement is (O(n^{1.5}text {polylog}(n))). Very recently, Farhadi et al. [SODA 2020] presented an algorithm with the desired space usage of (O(ntext {polylog}(n))), but a worse approximation ratio of (frac{6}{11}) ((sim .545)), or (frac{3}{5}) ((=.6)) in bipartite graphs. In this paper, we present an algorithm that computes a (frac{2}{3}(sim .66))-approximate matching using only (O(nlog (n))) space, improving upon both results above. We also note that for adversarial streams, a lower bound of Kapralov [SODA 2013] shows that any algorithm that achieves a (1-frac{1}{e})((sim .63))-approximation requires ((n^{1+Omega (1/log log (n))})) space; recent follow-up work by the same author improved this lower bound to (1+ln (2) sim .59) [SODA 2021]. As a consequence, both our result and the earlier result of Farhadi et al. prove that the problem of computing a maximum matching is strictly easier in random-order streams than in adversarial ones.","PeriodicalId":22832,"journal":{"name":"Theory of Computing Systems","volume":"31 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138573618","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}

引用次数: 0

Beyond the Existential Theory of the Reals 超越现实存在论

IF 0.5 4区计算机科学

Theory of Computing Systems Pub Date : 2023-12-12 DOI: 10.1007/s00224-023-10151-x

Marcus Schaefer, Daniel Štefankovič

引用次数: 0

Upper Bounds on Communication in Terms of Approximate Rank 近似等级的通信上限

IF 0.5 4区计算机科学

Theory of Computing Systems Pub Date : 2023-12-12 DOI: 10.1007/s00224-023-10158-4

Anna Gál, Ridwan Syed

引用次数: 0