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Test of Quantumness with Small-Depth Quantum Circuits 小深度量子电路的量子性测试
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-05-12 DOI: 10.4230/LIPIcs.MFCS.2021.59
Shuichi Hirahara, Franccois Le Gall
{"title":"Test of Quantumness with Small-Depth Quantum Circuits","authors":"Shuichi Hirahara, Franccois Le Gall","doi":"10.4230/LIPIcs.MFCS.2021.59","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.59","url":null,"abstract":"Recently Brakerski, Christiano, Mahadev, Vazirani and Vidick (FOCS 2018) have shown how to construct a test of quantumness based on the learning with errors (LWE) assumption: a test that can be solved efficiently by a quantum computer but cannot be solved by a classical polynomial-time computer under the LWE assumption. This test has lead to several cryptographic applications. In particular, it has been applied to producing certifiable randomness from a single untrusted quantum device, self-testing a single quantum device and device-independent quantum key distribution. In this paper, we show that this test of quantumness, and essentially all the above applications, can actually be implemented by a very weak class of quantum circuits: constant-depth quantum circuits combined with logarithmic-depth classical computation. This reveals novel complexity-theoretic properties of this fundamental test of quantumness and gives new concrete evidence of the superiority of small-depth quantum circuits over classical computation.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122576735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
Reconfiguring Independent Sets on Interval Graphs 重新配置区间图上的独立集
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-05-07 DOI: 10.4230/LIPIcs.MFCS.2021.23
Marcin Bria'nski, S. Felsner, Jkedrzej Hodor, Piotr Micek
{"title":"Reconfiguring Independent Sets on Interval Graphs","authors":"Marcin Bria'nski, S. Felsner, Jkedrzej Hodor, Piotr Micek","doi":"10.4230/LIPIcs.MFCS.2021.23","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.23","url":null,"abstract":"We study reconfiguration of independent sets in interval graphs under the token sliding rule. We show that if two independent sets of size k are reconfigurable in an n-vertex interval graph, then there is a reconfiguration sequence of length O(k · n). We also provide a construction in which the shortest reconfiguration sequence is of length Ω(k · n). As a counterpart to these results, we also establish that Independent Set Reconfiguration is PSPACE-hard on incomparability graphs, of which interval graphs are a special case.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"201 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115711317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
A Bit of Nondeterminism Makes Pushdown Automata Expressive and Succinct 一点不确定性使下推自动机具有表现力和简洁性
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-05-06 DOI: 10.4230/LIPIcs.MFCS.2021.53
Shibashis Guha, Ismaël Jecker, K. Lehtinen, Martin Zimmermann
{"title":"A Bit of Nondeterminism Makes Pushdown Automata Expressive and Succinct","authors":"Shibashis Guha, Ismaël Jecker, K. Lehtinen, Martin Zimmermann","doi":"10.4230/LIPIcs.MFCS.2021.53","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.53","url":null,"abstract":"We study the expressiveness and succinctness of history-deterministic pushdown automata (HD-PDA) over finite words, that is, pushdown automata whose nondeterminism can be resolved based on the run constructed so far, but independently of the remainder of the input word. These are also known as good-for-games pushdown automata. We prove that HD-PDA recognise more languages than deterministic PDA (DPDA) but not all context-free languages (CFL). This class is orthogonal to unambiguous CFL. We further show that HD-PDA can be exponentially more succinct than DPDA, while PDA can be double-exponentially more succinct than HD-PDA. We also study HDness in visibly pushdown automata (VPA), which enjoy better closure properties than PDA, and for which we show that deciding HDness is ExpTime-complete. HD-VPA can be exponentially more succinct than deterministic VPA, while VPA can be exponentially more succinct than HD-VPA. Both of these lower bounds are tight. We then compare HD-PDA with PDA for which composition with games is well-behaved, i.e. good-for-games automata. We show that these two notions coincide, but only if we consider potentially infinitely branching games. Finally, we study the complexity of resolving nondeterminism in HD-PDA. Every HDPDA has a positional resolver, a function that resolves nondeterminism and that is only dependant on the current configuration. Pushdown transducers are sufficient to implement the resolvers of HD-VPA, but not those of HD-PDA. HD-PDA with finite-state resolvers are determinisable.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126892776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
Dots & Boxes is PSPACE-complete Dots & Boxes是pspace完成的
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-05-06 DOI: 10.4230/LIPIcs.MFCS.2021.25
K. Buchin, Mart Hagedoorn, I. Kostitsyna, Max van Mulken
{"title":"Dots & Boxes is PSPACE-complete","authors":"K. Buchin, Mart Hagedoorn, I. Kostitsyna, Max van Mulken","doi":"10.4230/LIPIcs.MFCS.2021.25","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.25","url":null,"abstract":"Exactly 20 years ago at MFCS, Demaine posed the open problem whether the game of Dots&Boxes is PSPACE-complete. Dots&Boxes has been studied extensively, with for instance a chapter in Berlekamp et al.\"Winning Ways for Your Mathematical Plays\", a whole book on the game\"The Dots and Boxes Game: Sophisticated Child's Play\"by Berlekamp, and numerous articles in the\"Games of No Chance\"series. While known to be NP-hard, the question of its complexity remained open. We resolve this question, proving that the game is PSPACE-complete by a reduction from a game played on propositional formulas.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114240554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Online Domination: The Value of Getting to Know All your Neighbors 网络支配:了解你所有邻居的价值
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-05-01 DOI: 10.4230/LIPIcs.MFCS.2021.57
Hovhannes A. Harutyunyan, D. Pankratov, Jesse Racicot
{"title":"Online Domination: The Value of Getting to Know All your Neighbors","authors":"Hovhannes A. Harutyunyan, D. Pankratov, Jesse Racicot","doi":"10.4230/LIPIcs.MFCS.2021.57","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.57","url":null,"abstract":"We study the dominating set problem in an online setting. An algorithm is required to guarantee competitiveness against an adversary that reveals the input graph one node at a time. When a node is revealed, the algorithm learns about the entire neighborhood of the node (including those nodes that have not yet been revealed). Furthermore, the adversary is required to keep the revealed portion of the graph connected at all times. We present an algorithm that achieves 2-competitiveness on trees and prove that this competitive ratio cannot be improved by any other algorithm. We also present algorithms that achieve 2.5-competitiveness on cactus graphs, $(t-1)$-competitiveness on $K_{1,t}$-free graphs, and $Theta(sqrt{Delta})$ for maximum degree $Delta$ graphs. We show that all of those competitive ratios are tight. Then, we study several more general classes of graphs, such as threshold, bipartite planar, and series-parallel graphs, and show that they do not admit competitive algorithms (that is, when competitive ratio is independent of the input size). Previously, the dominating set problem was considered in a slightly different input model, where a vertex is revealed alongside its restricted neighborhood: those neighbors that are among already revealed vertices. Thus, conceptually, our results quantify the value of knowing the entire neighborhood at the time a vertex is revealed as compared to the restricted neighborhood. For instance, it was known in the restricted neighborhood model that 3-competitiveness is optimal for trees, whereas knowing the neighbors allows us to improve it to 2-competitiveness.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130463627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Graph Traversals as Universal Constructions 图遍历作为通用结构
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-04-30 DOI: 10.4230/LIPIcs.MFCS.2021.17
Siddharth Bhaskar, R. Kaarsgaard
{"title":"Graph Traversals as Universal Constructions","authors":"Siddharth Bhaskar, R. Kaarsgaard","doi":"10.4230/LIPIcs.MFCS.2021.17","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.17","url":null,"abstract":"We exploit a decomposition of graph traversals to give a novel characterization of depth-first and breadth-first traversals as universal constructions. Specifically, we introduce functors from two different categories of edge-ordered directed graphs into two different categories of transitively closed edge-ordered graphs; one defines the lexicographic depth-first traversal and the other the lexicographic breadth-first traversal. We show that each functor factors as a composition of universal constructions, and that the usual presentation of traversals as linear orders on vertices can be recovered with the addition of an inclusion functor. Finally, we raise the question of to what extent we can recover search algorithms from the categorical description of the traversal they compute.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129502409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Parameterized (Modular) Counting and Cayley Graph Expanders 参数化(模块化)计数和Cayley图展开器
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-04-29 DOI: 10.4230/LIPIcs.MFCS.2021.84
N. Peyerimhoff, M. Roth, Johannes Schmitt, J. Stix, A. Vdovina
{"title":"Parameterized (Modular) Counting and Cayley Graph Expanders","authors":"N. Peyerimhoff, M. Roth, Johannes Schmitt, J. Stix, A. Vdovina","doi":"10.4230/LIPIcs.MFCS.2021.84","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.84","url":null,"abstract":"We study the problem $#mathrm{EdgeSub}(Phi)$ of counting $k$-edge subgraphs satisfying a given graph property $Phi$ in a large host graph $G$. Building upon the breakthrough result of Curticapean, Dell and Marx (STOC 17), we express the number of such subgraphs as a finite linear combination of graph homomorphism counts and derive the complexity of computing this number by studying its coefficients. Our approach relies on novel constructions of low-degree Cayley graph expanders of $p$-groups, which might be of independent interest. The properties of those expanders allow us to analyse the coefficients in the aforementioned linear combinations over the field $mathbb{F}_p$ which gives us significantly more control over the cancellation behaviour of the coefficients. Our main result is an exhaustive and fine-grained complexity classification of $#mathrm{EdgeSub}(Phi)$ for minor-closed properties $Phi$, closing the missing gap in previous work by Roth, Schmitt and Wellnitz (ICALP 21). Additionally, we observe that our methods also apply to modular counting. Among others, we investigate the problems of modular counting of paths, cycles, forests and matroid bases. In the course of our investigations we also provide an exhaustive parameterized complexity classification for the problem of counting graph homomorphisms modulo a prime $p$.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"200 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115016760","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
A Timecop's Chase Around the Table 时间警察在桌子周围的追逐
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-04-17 DOI: 10.4230/LIPIcs.MFCS.2021.77
Nils Morawietz, Petra Wolf
{"title":"A Timecop's Chase Around the Table","authors":"Nils Morawietz, Petra Wolf","doi":"10.4230/LIPIcs.MFCS.2021.77","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.77","url":null,"abstract":"We consider the cops and robber game variant consisting of one cop and one robber on time-varying graphs (TVG). The considered TVGs are edge periodic graphs, i.e., for each edge, a binary string se determines in which time step the edge is present, namely the edge e is present in time step t if and only if the string se contains a 1 at position t mod |se|. This periodicity allows for a compact representation of the infinite TVG. We proof that even for very simple underlying graphs, i.e., directed and undirected cycles the problem whether a cop-winning strategy exists is NP-hard and W[1]-hard parameterized by the number of vertices. Our second main result are matching lower bounds for the ration between the length of the underlying cycle and the least common multiple (lcm) of the lengths of binary strings describing edge-periodicies over which the graph is robber-winning. Our third main result improves the previously known EXPTIME upper bound for PERIODIC COP & ROBBER on general edge periodic graphs to PSPACE-membership.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128559250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A note on the join of varieties of monoids with LI 一元群与LI的联结的一个注记
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-03-29 DOI: 10.4230/LIPIcs.MFCS.2021.51
Nathan Grosshans
{"title":"A note on the join of varieties of monoids with LI","authors":"Nathan Grosshans","doi":"10.4230/LIPIcs.MFCS.2021.51","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.51","url":null,"abstract":"In this note, we give a characterisation in terms of identities of the join of $mathbf{V}$ with the variety of finite locally trivial semigroups $mathbf{LI}$ for several well-known varieties of finite monoids $mathbf{V}$ by using classical algebraic-automata-theoretic techniques. To achieve this, we use the new notion of essentially-$mathbf{V}$ stamps defined by Grosshans, McKenzie and Segoufin and show that it actually coincides with the join of $mathbf{V}$ and $mathbf{LI}$ precisely when some natural condition on the variety of languages corresponding to $mathbf{V}$ is verified.This work is a kind of rediscovery of the work of J. C. Costa around 20 years ago from a rather different angle, since Costa's work relies on the use of advanced developments in profinite topology, whereas what is presented here essentially uses an algebraic, language-based approach.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"222 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115963759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Ordered fragments of first-order logic 一阶逻辑的有序片段
International Symposium on Mathematical Foundations of Computer Science Pub Date : 2021-03-14 DOI: 10.4230/LIPIcs.MFCS.2021.62
Reijo Jaakkola
{"title":"Ordered fragments of first-order logic","authors":"Reijo Jaakkola","doi":"10.4230/LIPIcs.MFCS.2021.62","DOIUrl":"https://doi.org/10.4230/LIPIcs.MFCS.2021.62","url":null,"abstract":"Using a recently introduced algebraic framework for the classification of fragments of first-order logic, we study the complexity of the satisfiability problem for several ordered fragments of first-order logic, which are obtained from the ordered logic and the fluted logic by modifying some of their syntactical restrictions.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126654385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
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