Theoretical Computer Science最新文献

英文中文

Independent set reconfiguration under bounded-hop token jumping 有界跳令牌跳跃下的独立集合重构

IF 1 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2025-11-25 DOI: 10.1016/j.tcs.2025.115651

Hiroki Hatano , Naoki Kitamura , Taisuke Izumi , Takehiro Ito , Toshimitsu Masuzawa

The independent set reconfiguration problem (ISReconf) is the problem of determining, for two given independent sets of a graph, whether one can be transformed into the other by repeatedly applying a prescribed reconfiguration rule. There are two well-studied reconfiguration rules, called the Token Sliding (TS) rule and the Token Jumping (TJ) rule, and it is known that the complexity status of ISReconf differs between the TS and TJ rules for some graph classes. In this paper, we analyze how changes in reconfiguration rules affect the computational complexity of ISReconf. To this end, we generalize the TS and TJ rules to a unified reconfiguration rule, called the k-Jump rule, which removes one vertex from a current independent set and adds a vertex within distance k from the removed vertex to obtain another independent set having the same cardinality. We give the following three results: First, we show that the reconfigurability of any ISReconf instance does not change for all k ≥ 3. Second, we present a polynomial-time algorithm to solve ISReconf under the 2-Jump rule for split graphs. Third, we consider the shortest variant of ISReconf, which determines whether there is a transformation of at most ℓ steps, for a given integer ℓ ≥ 0. We prove that this shortest variant under the k-Jump rule is NP-complete for chordal graphs of diameter at most

2 k + 1

, for any k ≥ 3.

独立集重构问题（ISReconf）是对给定的两个图的独立集，通过重复应用规定的重构规则，确定其中一个能否转化为另一个的问题。有两种重新配置规则，称为令牌滑动（TS）规则和令牌跳跃（TJ）规则，众所周知，对于某些图类，ISReconf在TS和TJ规则之间的复杂性状态是不同的。本文分析了重构规则的变化对ISReconf计算复杂度的影响。为此，我们将TS和TJ规则推广为一个统一的重构规则，称为k- jump规则，该规则从当前独立集中删除一个顶点，并在距离被删除顶点k的距离内添加一个顶点，以获得具有相同基数的另一个独立集。我们给出了以下三个结果：首先，我们证明了对于所有k ≥ 3，任何ISReconf实例的可重构性都不会改变。其次，我们提出了一个多项式时间算法来求解分割图的2-Jump规则下的ISReconf。第三，我们考虑ISReconf的最短变体，它决定了对于给定的整数（ ≥ 0），是否存在最多步长的变换。我们证明了在k- jump规则下，对于直径不超过2k+1的弦图，对于任意k ≥ 3，这个最短变体是np完全的。

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引用次数: 0

#P-Hardness proofs of matrix immanants evaluated on restricted matrices 在受限矩阵上求矩阵内变量的硬度证明

IF 1 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2025-11-25 DOI: 10.1016/j.tcs.2025.115660

Istvan Miklos , Cordian Riener

We establish the #P-hardness of computing a broad class of immanants, even when restricted to specific categories of matrices. Concretely, we prove that computing λ-immanants of

0 - 1

matrices is #P-hard whenever the partition λ contains a sufficiently large domino-tileable region, subject to certain technical conditions.

We also give hardness proofs for some λ-immanants of weighted adjacency matrices of planar directed graphs, such that the shape

λ = (1 + λ_{d})

has size n such that

| λ_{d} | = n^{ε}

for some

0 < ε < \frac{1}{2}

, and such that for some w, the shape λ_d/(w) is tileable with 1 × 2 dominos.

我们建立了计算广义内变量的# p -硬度，即使局限于特定类别的矩阵。具体地，我们证明了在一定的技术条件下，当划分λ包含一个足够大的多米诺骨牌区域时，计算0−1矩阵的λ-内积是#P-hard的。我们还给出了平面有向图的加权邻接矩阵的一些λ-内量的硬度证明，使得形状λ=(1+λd)的大小为n，使得对于某些0<；ε<12，形状λd/(w)可以铺成1 × 2个多米诺骨牌。

引用次数: 0

Causal reversibility in nondeterministic process calculi extended with time or probabilities 随时间或概率扩展的不确定性过程演算中的因果可逆性

IF 1 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2025-11-25 DOI: 10.1016/j.tcs.2025.115646

Marco Bernardo, Claudio A. Mezzina, Andrea Esposito

In addition to forward computations, a reversible system also features backward computations along which the effects of forward ones can be undone. This is accomplished by reverting executed actions starting from the last one. Since the last performed action may not be uniquely identifiable in a concurrent setting, Danos and Krivine proposed causal reversibility: an executed action can be undone provided that all of its consequences have been undone already. Phillips and Ulidowski then showed how to define nondeterministic process calculi that meet causal reversibility by construction. Lanese, Phillips, and Ulidowski subsequently classified the basic properties that ensure causal reversibility. In this paper we investigate the extent to which those techniques apply to reversible nondeterministic process calculi that include quantitative aspects. Firstly, we consider the introduction of time described via numeric delays with action execution separated from time passing like in the calculus of Moller and Tofts, where actions can be lazy or eager and time is subject to time determinism and time additivity. Secondly, we address the introduction of probabilities like in the calculus of Hansson and Jonsson, in which action execution and probabilistic choices alternate. We show that both resulting reversible calculi satisfy causal reversibility provided that suitable variants of the aforementioned techniques are developed to guarantee the proper forward and backward interplay of nondeterminism and quantitative aspects. The use of the former calculus is illustrated on a timeout mechanism, whereas the use of the latter is exemplified on quantum teleportation.

除了向前计算，可逆系统还具有向后计算的特点，向前计算的影响可以撤消。这是通过从最后一个动作开始恢复已执行的动作来实现的。由于最后执行的操作在并发设置中可能不是唯一可识别的，因此Danos和Krivine提出了因果可逆性：如果已执行的操作的所有结果都已撤消，则可以撤消该操作。Phillips和uldowski随后展示了如何通过构造来定义满足因果可逆性的不确定性过程演算。Lanese、Phillips和uldowski随后对确保因果可逆性的基本属性进行了分类。在本文中，我们研究了这些技术在包括定量方面的可逆不确定性过程演算中的应用程度。首先，我们考虑通过数值延迟来描述时间的引入，动作执行与时间流逝分离，就像Moller和Tofts的微积分一样，其中动作可以是懒惰的或渴望的，并且时间服从时间决定论和时间可加性。其次，我们介绍了概率的引入，就像汉森和约翰逊的微积分一样，其中行动执行和概率选择交替进行。我们表明，这两种可逆演算都满足因果可逆性，前提是开发了上述技术的适当变体，以保证不确定性和定量方面的适当向前和向后相互作用。前一种演算的使用是在一个超时机制上说明的，而后者的使用是在量子隐形传态上举例说明的。

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引用次数: 0

Towards new characterizations of small circuit classes via discrete ordinary differential equations 用离散常微分方程描述小电路类的新特性

IF 1 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2025-11-25 DOI: 10.1016/j.tcs.2025.115655

Melissa Antonelli , Arnaud Durand , Juha Kontinen

Implicit computational complexity is a lively area of theoretical computer science, which aims to provide machine-independent characterizations of relevant complexity classes. One of the seminal works in this field appeared in the 1960s, when Cobham introduced a function algebra closed under bounded recursion on notation to capture polynomial time computable functions (FP). Later on, several complexity classes have been characterized using limited recursion schemas. In this context, an original approach has been recently introduced, showing that ordinary differential equations (ODEs) offer a natural tool for algorithmic design and providing a characterization of FP by a new ODE-schema. In the present paper we generalize this approach by presenting original ODE-characterizations for the small circuit classes FAC⁰ and FTC⁰.

隐式计算复杂性是理论计算机科学的一个活跃领域，旨在提供与机器无关的相关复杂性类的表征。该领域的一个开创性工作出现在20世纪60年代，当时Cobham在符号上引入了一个在有界递归下闭合的函数代数来捕获多项式时间可计算函数（FP）。稍后，使用有限的递归模式描述了几个复杂性类。在这种背景下，最近引入了一种新颖的方法，表明常微分方程（ode）为算法设计提供了一种天然的工具，并通过新的ode模式提供了FP的表征。在本文中，我们通过提出小电路类FAC0和FTC0的原始ode特征来推广这种方法。

引用次数: 0

Penalty-enhanced quantum approximate optimization algorithm framework for maximization and minimization problems 最大化和最小化问题的惩罚增强量子近似优化算法框架

IF 1 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2025-11-22 DOI: 10.1016/j.tcs.2025.115649

Hao Zhong , Qi Zhang

The Quantum Approximate Optimization Algorithm (QAOA for short) has demonstrated great potential in solving NP-hard combinatorial optimization problems. This study proposes a penalty-enhanced QAOA framework for addressing both maximization and minimization problems. By uniformly setting penalty coefficients, the framework provides general support for both types of problems. It ensures the feasibility of output solutions and improves the quality of approximate solutions by adjusting the objective function and the construction of the Hamiltonian. We apply this framework to the Minimum Vertex Cover problem (as a minimization task) and the Maximum Independent Set problem (as a maximization task), designing corresponding quantum Hamiltonians and penalty terms.

量子近似优化算法（QAOA，简称QAOA）在求解NP-hard组合优化问题方面显示出巨大的潜力。本研究提出了一个惩罚增强的质量质量评估框架，以解决最大化和最小化问题。通过统一设置惩罚系数，该框架为这两种类型的问题提供了通用支持。通过调整目标函数和构造哈密顿算子，保证了输出解的可行性，提高了近似解的质量。我们将此框架应用于最小顶点覆盖问题（作为最小化任务）和最大独立集问题（作为最大化任务），设计相应的量子哈密顿量和惩罚项。

引用次数: 0

Parameterized algorithms for the spanning forest isomorphism and containment on tree 生成森林同构和树上约束的参数化算法

IF 1 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2025-11-22 DOI: 10.1016/j.tcs.2025.115652

Jingyi Liu , Xian Chen , Yicheng Zheng , Jianxin Wang , Feng Shi

The Minimum Tree Cut/Paste Distance problem is a well-known NP-hard problem in comparative genomics and phylogenetics. However, its fixed-parameter tractability (FPT) with respect to the distance remains open. Within the paper, we study a simplified variant, the Rooted Spanning Forest Isomorphism on Tree problem (RSFITP), which asks whether a rooted forest F is a spanning forest of a rooted target tree T*. This problem is NP-hard but FPT with respect to the number k of trees in F. We present several FPT algorithms for RSFITP and its generalizations. First, we improve the best-known algorithm for RSFITP, reducing the runtime from 2^O(klog k)n³ to

O (4^{k} k^{2} n^{2} + n^{3})

, where n is the size of the input instance. Second, we introduce the Rooted Spanning Forest Containment problem, which asks whether F contains k trees forming a spanning forest of T*, and provide an FPT algorithm with runtime O(25.6^kkn⁴), further improving it to

2^{3.03 k + 120 \log^{2} k} n^{O (1)}

when T* is binary. Third, we study a variant where trees in F can be “used” infinitely many times and solve it in runtime

n^{2 + o (1)}

. Besides the above work, we extend these algorithms to the unrooted versions of these problems with similar time complexity.

最小树剪切/粘贴距离问题是比较基因组学和系统遗传学中一个著名的np难题。然而，其相对于距离的固定参数可跟踪性（FPT）仍然是开放的。在本文中，我们研究了一个简化的变体，即有根生成林同构树问题（RSFITP），该问题是关于有根树F是否是有根目标树T*的生成林的问题。这个问题是np困难的，但是是关于f中树的个数k的FPT问题。我们提出了几种针对RSFITP的FPT算法及其推广。首先，我们改进了最著名的RSFITP算法，将运行时间从2O(klog k)n3减少到O(4kk2n2+n3)，其中n是输入实例的大小。其次，我们引入了扎根生成森林遏制问题，即F是否包含k棵树形成T*的生成森林，并提供了运行时间为0 （25.6kkn4）的FPT算法，进一步将其改进为T*为二进位时的23.03k+120log2knO(1)。第三，我们研究了一种变体，其中F中的树可以被“使用”无限次，并在运行时间n2+o(1)内解决它。除了上述工作之外，我们还将这些算法扩展到具有相似时间复杂度的这些问题的无根版本。

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引用次数: 0

Set cover, hitting set, and independent set problems for some restricted classes of geometric objects 一类受限几何对象的集覆盖、命中集和独立集问题

IF 1 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2025-11-21 DOI: 10.1016/j.tcs.2025.115657

Minati De , Ratnadip Mandal , Subhas C. Nandy

We consider the well-known set cover, hitting set, and independent set problems for some restricted classes of geometric objects. We present an 8-approximation algorithm for the unweighted set cover problem of boundary rectangles. When objects are translated copies of a convex object touching a line, we prove that both the weighted set cover and hitting set problems can be solved in polynomial time. On the other hand, when objects are translated copies of a 3-dimensional ball touching a plane, we obtain a PTAS for the unweighted version, and an O(1)-approximation randomized algorithm for the weighted version of both the set cover and hitting set problems. Furthermore, we propose a parameterized exact algorithm for hitting similarly sized homothetic copies of a convex object intersecting a line using points from

R^{2}

. Finally, we present an exact algorithm for the independent set problem of similarly sized α-fat objects intersecting a line.

考虑了一类受限几何对象的集覆盖、命中集和独立集问题。针对边界矩形的未加权集覆盖问题，提出了一种8逼近算法。当目标是与直线接触的凸目标的平移副本时，我们证明了加权集覆盖和命中集问题都可以在多项式时间内解决。另一方面，当物体是三维球接触平面的平移副本时，我们得到了未加权版本的PTAS，以及集覆盖和击球集问题的加权版本的O(1)近似随机化算法。此外，我们提出了一种参数化的精确算法，用于使用R2中的点命中与直线相交的凸物体的相似大小的同构副本。最后，我们给出了求解相似大小的α-脂肪物体与直线相交的独立集问题的精确算法。

引用次数: 0

Distance-restricted firefighting on finite graphs 有限图上的距离限制灭火

IF 1 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2025-11-21 DOI: 10.1016/j.tcs.2025.115658

Andrea C. Burgess , John Hawkin , Alexander Howse , John Marcoux , David A. Pike

In the classic version of the game of firefighter, on the first turn a fire breaks out on a vertex in a graph G and then b firefighters protect b vertices. On each subsequent turn, the fire spreads to the collective unburned neighbourhood of all the burning vertices and the firefighters again protect b vertices. Once a vertex has been burned or protected it remains that way for the rest of the game. In distance-restricted firefighting the firefighters’ movement is restricted so they can only move up to some fixed distance d and they may or may not be permitted to move through burning vertices. In this paper we establish the NP-completeness of the distance-restricted versions of b-Firefighter and present an integer program for computing the exact value. We also discuss some interesting properties of the Expected Damage function.

在经典版本的消防员游戏中，在第一个回合中，图G中的一个顶点发生火灾，然后b名消防员保护b个顶点。在随后的每一个回合中，火势蔓延到所有燃烧点的未燃烧区域，消防员再次保护b个点。一旦一个顶点被烧毁或保护，它就会在游戏的剩余时间里保持这种状态。在限制距离的消防中，消防员的行动受到限制，因此他们只能移动到某个固定的距离d，他们可能被允许或不被允许移动通过燃烧的顶点。本文建立了b-消防员距离限制版本的np完备性，并给出了计算精确值的整数程序。我们还讨论了期望损害函数的一些有趣的性质。

引用次数: 0

An operational quantum information framework for experimental studies on color perception 色彩感知实验研究的可操作量子信息框架

IF 1 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2025-11-21 DOI: 10.1016/j.tcs.2025.115650

Roberto Leporini , Edoardo Provenzi , Michel Berthier

Starting from the foundational axiomatization of the perceptual color space initiated by Schrödinger in 1920 and eventually refined by Resnikoff in 1974, Berthier, Provenzi and their collaborators have recently proposed a reformulation of perceptual color attributes within the framework of quantum information. Their work is based on the Jordan algebra formalism of quantum theories and, more specifically, on a quantum system described by a spin factor over the field of real numbers. This theoretical framework is not that of ordinary quantum mechanics, mainly because it requires dealing with rebits, whereas the latter uses qubits. The aim of this paper is to show that this difference in no way hinders the implementation of experimental protocols for testing the validity of the predictions of the color perception model. In particular, we show how to compute the quantum information based perceptual attributes of perceived colors in terms of qubit density matrices.

从1920年Schrödinger提出的感知色彩空间的基本公理化开始，最终由Resnikoff在1974年完善，Berthier， Provenzi及其合作者最近提出了在量子信息框架内对感知色彩属性的重新表述。他们的工作是基于量子理论的约旦代数形式，更具体地说，是基于一个由实数场上的自旋因子描述的量子系统。这个理论框架不是普通量子力学的，主要是因为它需要处理比特，而后者使用量子位。本文的目的是表明这种差异不会妨碍测试颜色感知模型预测有效性的实验协议的实施。特别是，我们展示了如何根据量子比特密度矩阵计算基于感知颜色感知属性的量子信息。

引用次数: 0

Time hierarchies for sublogarithmic-space quantum computation 次对数空间量子计算的时间层次

IF 1 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Theoretical Computer Science

Pub Date : 2025-11-19 DOI: 10.1016/j.tcs.2025.115639

A. C. Cem Say

We present new results on the landscape of problems that can be solved by quantum Turing machines (QTM’s) employing severely limited amounts of memory. In this context, we demonstrate two infinite time hierarchies of complexity classes within the “small space” regime: For all i ≥ 0, there is a language that can be recognized by a constant-space machine in

2^{O (n^{1 / 2^{i}})}

time, but not by any sublogarithmic-space QTM in

2^{O (n^{1 / 2^{i + 1}})}

time. For quantum machines operating within o(log log n) space, there exists another hierarchy, each level of which corresponds to an expected runtime of

2^{O ({(\log n)}^{i})}

for a different positive integer i. We also improve a quantum advantage result, demonstrating a language that can be recognized by a polynomial-time constant-space QTM, but not by any classical machine using o(log log n) space, regardless of the time budget. The implications of our findings for quantum space-time tradeoffs are discussed.

我们提出了一些问题的新结果，这些问题可以通过使用有限内存的量子图灵机（QTM）来解决。在这种情况下，我们证明了在“小空间”状态下复杂度类的两个无限时间层次结构：对于所有i ≥ 0，存在一种语言可以在2O（n1/2i）时间内被常数空间机器识别，但不能在2O（n1/2i+1）时间内被任何次对数空间QTM识别。对于在o（log logn）空间内运行的量子机器，存在另一个层次结构，每一层对应于不同正整数i的20 （(logn)i）的预期运行时间。我们还改进了量子优势结果，证明了一种语言可以被多项式时间常数空间QTM识别，但不能被任何使用o（log logn）空间的经典机器识别，无论时间预算如何。讨论了我们的发现对量子时空权衡的影响。

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