{"title":"A categorical model for organic chemistry","authors":"Ella Gale , Leo Lobski , Fabio Zanasi","doi":"10.1016/j.tcs.2025.115084","DOIUrl":"10.1016/j.tcs.2025.115084","url":null,"abstract":"<div><div>We introduce a mathematical framework for organic chemistry, with three interrelated perspectives on chemical processes: reaction schemes, formal reactions and disconnection rules. We apply the framework to retrosynthetic analysis, an important research method in synthetic chemistry. Our approach represents molecules as labelled graphs, while the interactions between them are represented either as double pushout graph rewriting, partial bijections or local edge rewrite rules. In particular, we show that the formal reactions are generated by reaction schemes using double pushout rewriting, and that the disconnection rules are sound, complete and universal with respect to chemical reactions. The mathematical formulation of retrosynthesis is based on layered props – a recently introduced categorical model for partial explanations in scientific reasoning.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1032 ","pages":"Article 115084"},"PeriodicalIF":0.9,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143301910","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":"Visibility extension via reflection","authors":"Arash Vaezi , Bodhayan Roy , Mohammad Ghodsi","doi":"10.1016/j.tcs.2025.115083","DOIUrl":"10.1016/j.tcs.2025.115083","url":null,"abstract":"<div><div>This paper studies a variant of the Art Gallery problem in which the “walls” can be replaced by <em>reflecting edges</em>, which allows the guards to see further and thereby see a larger portion of the gallery. Given a simple polygon <span><math><mtext>P</mtext></math></span>, first, we consider one guard as a point viewer, and we intend to use reflection to add a certain amount of area to the visibility polygon of the guard. We study visibility with specular and diffuse reflections where the specular type of reflection is the mirror-like reflection, and in the diffuse type of reflection, the angle between the incident and reflected ray may assume all possible values between 0 and <em>π</em>. Lee and Aggarwal already proved that several versions of the general Art Gallery problem are <span><math><mtext>NP</mtext></math></span>-hard. We show that several cases of adding an area to the visible area of a given point guard are <span><math><mtext>NP</mtext></math></span>-hard, too.</div><div>Second,<span><span><sup>1</sup></span></span> we assume that all edges are reflectors, and we intend to decrease the minimum number of guards required to cover the whole gallery.</div><div>Chao Xu proved that even considering <em>r</em> specular reflections, one may need <span><math><mo>⌊</mo><mfrac><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></mfrac><mo>⌋</mo></math></span> guards to cover the polygon, let <em>r</em> be the maximum number of reflections of a guard's visibility ray.</div><div>In this work, we prove that considering <em>r diffuse</em> reflections, the minimum number of <em>vertex or boundary</em> guards required to cover a given simple polygon <span><math><mi>P</mi></math></span> decreases to <span><math><mo>⌈</mo><mfrac><mrow><mi>α</mi></mrow><mrow><mn>1</mn><mo>+</mo><mo>⌊</mo><mfrac><mrow><mi>r</mi></mrow><mrow><mn>8</mn></mrow></mfrac><mo>⌋</mo></mrow></mfrac><mo>⌉</mo></math></span>, where <em>α</em> indicates the minimum number of guards required to cover the polygon without reflection. We also generalize the <span><math><mi>O</mi><mo>(</mo><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span>-approximation ratio algorithm of the vertex guarding problem to work in the presence of reflection.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1031 ","pages":"Article 115083"},"PeriodicalIF":0.9,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143265846","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":"Powers of low rank sparse matrices","authors":"Keren Cohen","doi":"10.1016/j.tcs.2025.115082","DOIUrl":"10.1016/j.tcs.2025.115082","url":null,"abstract":"<div><div>Let <em>A</em> be a matrix of order <em>n</em> over an arbitrary field <em>F</em>, and let <em>k</em> be a positive integer. We present an algorithm that computes <span><math><msup><mrow><mi>A</mi></mrow><mrow><mi>k</mi></mrow></msup></math></span> which is faster than the known methods whenever <em>A</em> is sufficiently sparse and its rank is sufficiently small. In fact, already when <span><math><mi>r</mi><mi>a</mi><mi>n</mi><mi>k</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>1</mn><mo>−</mo><mi>ϵ</mi></mrow></msup><mo>)</mo></math></span> for a fixed <span><math><mi>ϵ</mi><mo>></mo><mn>0</mn></math></span> our method yields improved running times.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1032 ","pages":"Article 115082"},"PeriodicalIF":0.9,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143302051","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":"Recursive and iterative approaches to generate rotation Gray codes for stamp foldings and semi-meanders","authors":"Bowie Liu, Dennis Wong, Chan-Tong Lam, Marcus Im","doi":"10.1016/j.tcs.2024.115053","DOIUrl":"10.1016/j.tcs.2024.115053","url":null,"abstract":"<div><div>We first present a simple recursive algorithm that generates cyclic rotation Gray codes for stamp foldings and semi-meanders, where consecutive strings differ by a stamp rotation. These are the first known Gray codes for stamp foldings and semi-meanders, and we thus solve an open problem posted by Sawada and Li (2012) <span><span>[17]</span></span>. We then introduce an iterative algorithm that generates the same rotation Gray codes for stamp foldings and semi-meanders. Both the recursive and iterative algorithms generate stamp foldings and semi-meanders in constant amortized time and <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span>-amortized time per string respectively, using a linear amount of memory.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1031 ","pages":"Article 115053"},"PeriodicalIF":0.9,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143265811","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}
Bruno José S. Barros , Luiz Satoru Ochi , Rian Gabriel S. Pinheiro , Uéverton S. Souza
{"title":"On Conflict-Free Spanning Tree: Mapping tractable and hard instances through the lenses of graph classes","authors":"Bruno José S. Barros , Luiz Satoru Ochi , Rian Gabriel S. Pinheiro , Uéverton S. Souza","doi":"10.1016/j.tcs.2025.115081","DOIUrl":"10.1016/j.tcs.2025.115081","url":null,"abstract":"<div><div>A natural constraint in real-world applications is avoiding conflicting elements in problem solutions. Let <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> be a graph where each edge <span><math><mi>e</mi><mo>∈</mo><mi>E</mi></math></span> has a positive integer weight <span><math><mi>ω</mi><mo>(</mo><mi>e</mi><mo>)</mo></math></span>, and let <span><math><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>=</mo><mo>(</mo><mover><mrow><mi>V</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>,</mo><mover><mrow><mi>E</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>)</mo></math></span> be a conflict graph such that <span><math><mover><mrow><mi>V</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>⊆</mo><mi>E</mi></math></span> and each edge <span><math><mover><mrow><mi>e</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>=</mo><msub><mrow><mi>e</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mover><mrow><mi>E</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> represents a conflict between two edges <span><math><msub><mrow><mi>e</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>e</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mi>E</mi></math></span>. In the <span>Minimum Conflict-Free Spanning Tree (MCFST)</span> problem, we are asked to find a spanning tree avoiding pairs of conflicting edges (if such a tree exists) with minimum cost. In contrast to the polynomial-time solvability of <span>Minimum Spanning Tree</span>, to determine whether an instance <span><math><mo>(</mo><mi>G</mi><mo>,</mo><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>)</mo></math></span> of <span>MCFST</span> admits a feasible solution is an <span><math><mi>NP</mi></math></span>-complete problem. In this paper, we present a multivariate complexity analysis of <span>MCFST</span> by considering particular classes of graphs <em>G</em> and <span><math><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span>. We show that the problem of determining whether an instance <span><math><mo>(</mo><mi>G</mi><mo>,</mo><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>)</mo></math></span> of <span>MCFST</span> has a feasible solution is <span><math><mi>NP</mi></math></span>-complete even if <em>G</em> is a bipartite planar subcubic graph, and <span><math><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> is a disjoint union of paths with three vertices. Contrastingly, we show that when <em>G</em> is complete and <span><math><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></math></span> is bipartite, then a solution for <span><math><mo>(</mo><mi>G</mi><mo>,</mo><mover><mrow><mi>G</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>)</mo></math></span> can be found in linear time, while the problem of finding an optimal solution is <span><math><mi>NP</mi></math></span>-h","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1031 ","pages":"Article 115081"},"PeriodicalIF":0.9,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143265845","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":"Conflict-free coloring on subclasses of perfect graphs and bipartite graphs","authors":"Sriram Bhyravarapu , Subrahmanyam Kalyanasundaram , Rogers Mathew","doi":"10.1016/j.tcs.2025.115080","DOIUrl":"10.1016/j.tcs.2025.115080","url":null,"abstract":"<div><div>A <em>Conflict-Free Open Neighborhood coloring</em>, abbreviated CFON<sup>⁎</sup> coloring, of a graph <span><math><mi>G</mi><mo>=</mo><mo>(</mo><mi>V</mi><mo>,</mo><mi>E</mi><mo>)</mo></math></span> using <em>k</em> colors is an assignment of colors from a set of <em>k</em> colors to a subset of vertices of <em>V</em> such that every vertex sees some color exactly once in its open neighborhood. The minimum <em>k</em> for which <em>G</em> has a CFON<sup>⁎</sup> coloring using <em>k</em> colors is called the <em>CFON</em><sup>⁎</sup> <em>chromatic number</em> of <em>G</em>, denoted by <span><math><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>O</mi><mi>N</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. The analogous notion for closed neighborhood is called CFCN<sup>⁎</sup> coloring and the analogous parameter is denoted by <span><math><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>C</mi><mi>N</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. The problem of deciding whether a given graph admits a CFON<sup>⁎</sup> (or CFCN<sup>⁎</sup>) coloring that uses <em>k</em> colors is <span>NP</span>-complete. Below, we describe briefly the main results of this paper.<ul><li><span>•</span><span><div>We show that it is <span>NP</span>-hard to determine the CFCN<sup>⁎</sup> chromatic number of chordal graphs. We also show the existence of a family of chordal graphs <em>G</em> that requires <span><math><mi>Ω</mi><mo>(</mo><msqrt><mrow><mi>ω</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></msqrt><mo>)</mo></math></span> colors to CFCN<sup>⁎</sup> color <em>G</em>, where <span><math><mi>ω</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> represents the size of a maximum clique in <em>G</em>.</div></span></li><li><span>•</span><span><div>We give a polynomial time algorithm to compute <span><math><msubsup><mrow><mi>χ</mi></mrow><mrow><mi>O</mi><mi>N</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mi>G</mi><mo>)</mo></math></span> for interval graphs <em>G</em>. This answers in positive the open question posed by Reddy [Theoretical Comp. Science, 2018] to determine whether CFON<sup>⁎</sup> chromatic number can be computed in polynomial time for interval graphs.</div></span></li><li><span>•</span><span><div>We explore biconvex graphs, a subclass of bipartite graphs, and give a polynomial time algorithm to compute their CFON<sup>⁎</sup> chromatic number.</div></span></li></ul></div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1031 ","pages":"Article 115080"},"PeriodicalIF":0.9,"publicationDate":"2025-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143265812","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}
Tapas Das , Florent Foucaud , Clara Marcille , P.D. Pavan , Sagnik Sen
{"title":"Monitoring arc-geodetic sets of oriented graphs","authors":"Tapas Das , Florent Foucaud , Clara Marcille , P.D. Pavan , Sagnik Sen","doi":"10.1016/j.tcs.2025.115079","DOIUrl":"10.1016/j.tcs.2025.115079","url":null,"abstract":"<div><div>Monitoring edge-geodetic sets in a graph are subsets of vertices such that every edge of the graph must lie on all the shortest paths between two vertices of the monitoring set. These objects were introduced in a work by Foucaud, Krishna and Ramasubramony Sulochana with relation to several prior notions in the area of network monitoring like distance edge-monitoring.</div><div>In this work, we explore the extension of those notions unto oriented graphs, modelling oriented networks, and call these objects monitoring arc-geodetic sets. We also define the lower and upper monitoring arc-geodetic number of an undirected graph as the minimum and maximum of the monitoring arc-geodetic number of all orientations of the graph. We determine the monitoring arc-geodetic number of fundamental graph classes such as bipartite graphs, trees, cycles, etc. Then, we characterize the graphs for which every monitoring arc-geodetic set is the entire set of vertices, and also characterize the solutions for tournaments. We also cover some complexity aspects by studying two algorithmic problems. We show that the problem of determining if an undirected graph has an orientation with the minimal monitoring arc-geodetic set being the entire set of vertices, is NP-hard. We also show that the problem of finding a monitoring arc-geodetic set of size at most <em>k</em> is NP-complete when restricted to oriented graphs with maximum degree 4.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1031 ","pages":"Article 115079"},"PeriodicalIF":0.9,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143265848","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":"Asynchronous fully-decentralized SGD in the cluster-based model","authors":"Hagit Attiya , Noa Schiller","doi":"10.1016/j.tcs.2025.115073","DOIUrl":"10.1016/j.tcs.2025.115073","url":null,"abstract":"<div><div>This paper presents fault-tolerant asynchronous <em>Stochastic Gradient Descent</em> (<em>SGD</em>) algorithms. SGD is widely used for approximating the minimum of a cost function <em>Q</em>, a core part of optimization and learning algorithms. Our algorithms are designed for the <em>cluster-based</em> model, which combines message-passing and shared-memory communication layers. Processes may fail by <em>crashing</em>, and the algorithm inside each cluster is <em>wait-free</em>, using only reads and writes.</div><div>For a <em>strongly convex Q</em>, our algorithm <em>can withstand partitions of the system</em>. It provides convergence rate that is the maximal distributed acceleration over the optimal convergence rate of <em>sequential</em> SGD.</div><div>For arbitrary smooth functions, the convergence rate has an additional term that depends on the maximal difference between the parameters at the same iteration. (This holds under standard assumptions on <em>Q</em>.) In this case, the algorithm obtains the same convergence rate as sequential SGD, up to a logarithmic factor. This is achieved by using, at each iteration, a <em>multidimensional approximate agreement</em> algorithm, tailored for the cluster-based model.</div><div>The general algorithm communicates with nonfaulty processes belonging to clusters that include a majority of all processes. We prove that this condition is necessary when optimizing some non-convex functions.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1031 ","pages":"Article 115073"},"PeriodicalIF":0.9,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143265843","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}
Lulu Yang , Shuming Zhou , Qifan Zhang , Guanqin Lian
{"title":"The (conditional) matroidal connectivity of varietal hypercube","authors":"Lulu Yang , Shuming Zhou , Qifan Zhang , Guanqin Lian","doi":"10.1016/j.tcs.2025.115076","DOIUrl":"10.1016/j.tcs.2025.115076","url":null,"abstract":"<div><div>As multiprocessor systems continue to grow in scale, their underlying interconnection networks face increasingly challenging issues to characterize reliability and fault tolerance. Matroidal connectivity and conditional matroidal connectivity are two novel metrics that enhance network reliability by dividing the edge set into several parts and flexibly adjusting the number of faulty edges in each dimension to meet practical requirements. The <em>n</em>-dimensional varietal hypercube <span><math><mi>V</mi><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> is vertex-transitive and edge-transitive, and it is a variant of the traditional hypercube. In this paper, we first determine the matroidal connectivity and conditional matroidal connectivity of <span><math><mi>V</mi><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. Then we conduct a comparative analysis of <span><math><mi>V</mi><msub><mrow><mi>Q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>'s matroidal connectivity with some kinds of conditional connectivities, namely <em>g</em>-extra edge connectivity, <em>g</em>-component edge connectivity, and <em>g</em>-super edge connectivity. Our results show that matroidal connectivity outperforms the conditional edge connectivities above, underscoring its efficiency in bolstering the fault tolerance of interconnection networks under specific conditions.</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1030 ","pages":"Article 115076"},"PeriodicalIF":0.9,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143305540","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}
Henrique Hepp , Murilo V.G. da Silva , Leandro M. Zatesko
{"title":"Oracle separations for non-adaptive collapse-free quantum computing","authors":"Henrique Hepp , Murilo V.G. da Silva , Leandro M. Zatesko","doi":"10.1016/j.tcs.2025.115078","DOIUrl":"10.1016/j.tcs.2025.115078","url":null,"abstract":"<div><div>Aaronson et al. (2016) introduced the quantum complexity class <span><math><mi>naCQP</mi></math></span> (<em>non-adaptive Collapse-free Quantum Polynomial time</em>), also known as <span><math><mi>PDQP</mi></math></span> (<em>Product Dynamical Quantum Polynomial time</em>), aiming to define a class larger than <span><math><mi>BQP</mi></math></span> (<em>Bounded-error Quantum Polynomial time</em>), but not large enough to include <span><math><mi>NP</mi></math></span>-complete problems. Aaronson et al. showed that <span><math><mi>SZK</mi></math></span> (<em>Statistical Zero Knowledge</em>) is contained in <span><math><mi>naCQP</mi></math></span> and that there is an oracle <em>A</em> for which <span><math><msup><mrow><mi>NP</mi></mrow><mrow><mi>A</mi></mrow></msup><mo>⊈</mo><msup><mrow><mi>naCQP</mi></mrow><mrow><mi>A</mi></mrow></msup></math></span>. We prove that: there is an oracle <em>A</em> for which <span><math><msup><mrow><mi>P</mi></mrow><mrow><mi>A</mi></mrow></msup><mo>=</mo><msup><mrow><mi>BQP</mi></mrow><mrow><mi>A</mi></mrow></msup><mo>=</mo><msup><mrow><mi>SZK</mi></mrow><mrow><mi>A</mi></mrow></msup><mo>=</mo><msup><mrow><mi>naCQP</mi></mrow><mrow><mi>A</mi></mrow></msup><mo>≠</mo><msup><mrow><mo>(</mo><mi>UP</mi><mo>∩</mo><mi>coUP</mi><mo>)</mo></mrow><mrow><mi>A</mi></mrow></msup><mo>=</mo><msup><mrow><mi>EXP</mi></mrow><mrow><mi>A</mi></mrow></msup></math></span>, where <span><math><mi>UP</mi></math></span> (<em>Unambiguous Polynomial time</em>) is an important subclass of <span><math><mi>NP</mi></math></span>; relative to an oracle <em>A</em> chosen uniformly at random, it holds <span><math><msup><mrow><mo>(</mo><mi>UP</mi><mo>∩</mo><mi>coUP</mi><mo>)</mo></mrow><mrow><mi>A</mi></mrow></msup><mo>⊈</mo><msup><mrow><mi>naCQP</mi></mrow><mrow><mi>A</mi></mrow></msup></math></span> with probability 1. Our results are a strengthening of the results by Bennett et al. (1997), Fortnow and Rogers (1999), Tamon and Yamakami (2001), and Aaronson et al. (2016).</div></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":"1030 ","pages":"Article 115078"},"PeriodicalIF":0.9,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143305538","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}
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