Journal of the ACMPub Date : 2022-12-19DOI: https://dl.acm.org/doi/10.1145/3566051
Manuel Bodirsky, Jakub Rydval
{"title":"On the Descriptive Complexity of Temporal Constraint Satisfaction Problems","authors":"Manuel Bodirsky, Jakub Rydval","doi":"https://dl.acm.org/doi/10.1145/3566051","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3566051","url":null,"abstract":"<p>Finite-domain constraint satisfaction problems are either solvable by Datalog or not even expressible in fixed-point logic with counting. The border between the two regimes can be described by a universal-algebraic minor condition. For infinite-domain constraint satisfaction problems (CSPs), the situation is more complicated even if the template structure of the CSP is model-theoretically tame. We prove that there is no Maltsev condition that characterizes Datalog already for the CSPs of first-order reducts of (ℚ;<); such CSPs are called <i>temporal CSPs</i> and are of fundamental importance in infinite-domain constraint satisfaction. Our main result is a complete classification of temporal CSPs that can be expressed in one of the following logical formalisms: Datalog, fixed-point logic (with or without counting), or fixed-point logic with the mod-2 rank operator. The classification shows that many of the equivalent conditions in the finite fail to capture expressibility in Datalog or fixed-point logic already for temporal CSPs.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"42 9-10","pages":""},"PeriodicalIF":2.5,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Journal of the ACMPub Date : 2022-12-19DOI: https://dl.acm.org/doi/10.1145/3565019
James B. Orlin, László Végh
{"title":"Directed Shortest Paths via Approximate Cost Balancing","authors":"James B. Orlin, László Végh","doi":"https://dl.acm.org/doi/10.1145/3565019","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3565019","url":null,"abstract":"<p>We present an <i>O(nm)</i> algorithm for all-pairs shortest paths computations in a directed graph with <i>n</i> nodes, <i>m</i> arcs, and nonnegative integer arc costs. This matches the complexity bound attained by Thorup [31] for the all-pairs problems in undirected graphs. The main insight is that shortest paths problems with approximately balanced directed cost functions can be solved similarly to the undirected case. The algorithm finds an approximately balanced reduced cost function in an <i>O(m</i>√ <i>n</i> log <i>n</i>) preprocessing step. Using these reduced costs, every shortest path query can be solved in <i>O(m)</i> time using an adaptation of Thorup’s component hierarchy method. The balancing result can also be applied to the ℓ<sub>∞</sub>-matrix balancing problem.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"23 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Journal of the ACMPub Date : 2022-12-19DOI: https://dl.acm.org/doi/10.1145/3559103
Joachim Kock
{"title":"Whole-grain Petri Nets and Processes","authors":"Joachim Kock","doi":"https://dl.acm.org/doi/10.1145/3559103","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3559103","url":null,"abstract":"<p>We present a formalism for Petri nets based on polynomial-style finite-set configurations and etale maps. The formalism supports both a geometric semantics in the style of Goltz and Reisig (processes are etale maps from graphs) and an algebraic semantics in the style of Meseguer and Montanari, in terms of free coloured props, and allows the following unification: for <monospace>P</monospace> a Petri net, the Segal space of <monospace>P</monospace>-processes is shown to be the free coloured prop-in-groupoids on <monospace>P</monospace>. There is also an unfolding semantics à la Winskel, which bypasses the classical symmetry problems: with the new formalism, every Petri net admits a universal unfolding, which in turn has associated an event structure and a Scott domain. Since everything is encoded with explicit sets, Petri nets and their processes have elements. In particular, individual-token semantics is native. (Collective-token semantics emerges from rather drastic quotient constructions à la Best–Devillers, involving taking π<sub>0</sub> of the groupoids of states.)</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"AES-2 3","pages":""},"PeriodicalIF":2.5,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Journal of the ACMPub Date : 2022-12-19DOI: https://dl.acm.org/doi/10.1145/3566049
Gilad Asharov, Ilan Komargodski, Wei-Kai Lin, Kartik Nayak, Enoch Peserico, Elaine Shi
{"title":"OptORAMa: Optimal Oblivious RAM","authors":"Gilad Asharov, Ilan Komargodski, Wei-Kai Lin, Kartik Nayak, Enoch Peserico, Elaine Shi","doi":"https://dl.acm.org/doi/10.1145/3566049","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3566049","url":null,"abstract":"<p>Oblivious RAM (ORAM), first introduced in the ground-breaking work of Goldreich and Ostrovsky (STOC ’87 and J. ACM ’96) is a technique for provably obfuscating programs’ access patterns, such that the access patterns leak no information about the programs’ secret inputs. To compile a general program to an oblivious counterpart, it is well-known that Ω (log <i>N</i>) amortized blowup in memory accesses is necessary, where <i>N</i> is the size of the logical memory. This was shown in Goldreich and Ostrovksy’s original ORAM work for statistical security and in a somewhat restricted model (the so-called <i>balls-and-bins</i> model), and recently by Larsen and Nielsen (CRYPTO ’18) for computational security.</p><p>A long-standing open question is whether there exists an <i>optimal</i> ORAM construction that matches the aforementioned logarithmic lower bounds (without making large memory word assumptions, and assuming a constant number of CPU registers). In this article, we resolve this problem and present the first secure ORAM with <i>O</i>(log <i>N</i>) amortized blowup, assuming one-way functions. Our result is inspired by and non-trivially improves on the recent beautiful work of Patel et al. (FOCS ’18) who gave a construction with <i>O</i>(log <i>N</i>⋅ log log <i>N</i>) amortized blowup, assuming one-way functions. </p><p>One of our building blocks of independent interest is a linear-time deterministic oblivious algorithm for tight compaction: Given an array of <i>n</i> elements where some elements are marked, we permute the elements in the array so that all marked elements end up in the front of the array. Our <i>O</i>(<i>n</i>) algorithm improves the previously best-known deterministic or randomized algorithms whose running time is <i>O</i>(<i>n</i> ⋅ log <i>n</i>) or <i>O</i>(<i>n</i> ⋅ log log <i>n</i>), respectively.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"22 4","pages":""},"PeriodicalIF":2.5,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Journal of the ACMPub Date : 2022-11-24DOI: https://dl.acm.org/doi/10.1145/3561047
Guy Blanc, Jane Lange, Mingda Qiao, Li-Yang Tan
{"title":"Properly Learning Decision Trees in almost Polynomial Time","authors":"Guy Blanc, Jane Lange, Mingda Qiao, Li-Yang Tan","doi":"https://dl.acm.org/doi/10.1145/3561047","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3561047","url":null,"abstract":"<p>We give an <i>n</i><sup><i>O</i>(log log <i>n</i>)</sup>-time membership query algorithm for properly and agnostically learning decision trees under the uniform distribution over { ± 1}<sup><i>n</i></sup>. Even in the realizable setting, the previous fastest runtime was <i>n</i><sup><i>O</i>(log <i>n</i>)</sup>, a consequence of a classic algorithm of Ehrenfeucht and Haussler.</p><p>Our algorithm shares similarities with practical heuristics for learning decision trees, which we augment with additional ideas to circumvent known lower bounds against these heuristics. To analyze our algorithm, we prove a new structural result for decision trees that strengthens a theorem of O’Donnell, Saks, Schramm, and Servedio. While the OSSS theorem says that every decision tree has an influential variable, we show how every decision tree can be “pruned” so that <i>every</i> variable in the resulting tree is influential.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"52 10","pages":""},"PeriodicalIF":2.5,"publicationDate":"2022-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Journal of the ACMPub Date : 2022-11-24DOI: https://dl.acm.org/doi/10.1145/3556972
Avinatan Hassidim, Haim Kaplan, Yishay Mansour, Yossi Matias, Uri Stemmer
{"title":"Adversarially Robust Streaming Algorithms via Differential Privacy","authors":"Avinatan Hassidim, Haim Kaplan, Yishay Mansour, Yossi Matias, Uri Stemmer","doi":"https://dl.acm.org/doi/10.1145/3556972","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3556972","url":null,"abstract":"<p>A streaming algorithm is said to be <i>adversarially robust</i> if its accuracy guarantees are maintained even when the data stream is chosen maliciously, by an <i>adaptive adversary</i>. We establish a connection between adversarial robustness of streaming algorithms and the notion of <i>differential privacy</i>. This connection allows us to design new adversarially robust streaming algorithms that outperform the current state-of-the-art constructions for many interesting regimes of parameters.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"3 4","pages":""},"PeriodicalIF":2.5,"publicationDate":"2022-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"On the Need for Large Quantum Depth","authors":"Nai-Hui Chia, Kai-Min Chung, C. Lai","doi":"10.1145/3570637","DOIUrl":"https://doi.org/10.1145/3570637","url":null,"abstract":"Near-term quantum computers are likely to have small depths due to short coherence time and noisy gates. A natural approach to leverage these quantum computers is interleaving them with classical computers. Understanding the capabilities and limits of this hybrid approach is an essential topic in quantum computation. Most notably, the quantum Fourier transform can be implemented by a hybrid of logarithmic-depth quantum circuits and a classical polynomial-time algorithm. Therefore, it seems possible that quantum polylogarithmic depth is as powerful as quantum polynomial depth in the presence of classical computation. Indeed, Jozsa conjectured that “Any quantum polynomial-time algorithm can be implemented with only O(log n) quantum depth interspersed with polynomial-time classical computations.” This can be formalized as asserting the equivalence of BQP and “BQNCBPP.” However, Aaronson conjectured that “there exists an oracle separation between BQP and BPPBQNC.” BQNCBPP and BPPBQNC are two natural and seemingly incomparable ways of hybrid classical-quantum computation. In this work, we manage to prove Aaronson’s conjecture and in the meantime prove that Jozsa’s conjecture, relative to an oracle, is false. In fact, we prove a stronger statement that for any depth parameter d, there exists an oracle that separates quantum depth d and 2d+1 in the presence of classical computation. Thus, our results show that relative to oracles, doubling the quantum circuit depth does make the hybrid model more powerful, and this cannot be traded by classical computation.","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"282 1","pages":"1 - 38"},"PeriodicalIF":2.5,"publicationDate":"2022-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75401752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Journal of the ACMPub Date : 2022-11-17DOI: https://dl.acm.org/doi/10.1145/3557045
Nicole Immorlica, Karthik Sankararaman, Robert Schapire, Aleksandrs Slivkins
{"title":"Adversarial Bandits with Knapsacks","authors":"Nicole Immorlica, Karthik Sankararaman, Robert Schapire, Aleksandrs Slivkins","doi":"https://dl.acm.org/doi/10.1145/3557045","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3557045","url":null,"abstract":"<p>We consider <b><i>Bandits with Knapsacks</i></b> (henceforth, <i><b>BwK</b></i>), a general model for multi-armed bandits under supply/budget constraints. In particular, a bandit algorithm needs to solve a well-known <i>knapsack problem</i>: find an optimal packing of items into a limited-size knapsack. The BwK problem is a common generalization of numerous motivating examples, which range from dynamic pricing to repeated auctions to dynamic ad allocation to network routing and scheduling. While the prior work on BwK focused on the stochastic version, we pioneer the other extreme in which the outcomes can be chosen adversarially. This is a considerably harder problem, compared to both the stochastic version and the “classic” adversarial bandits, in that regret minimization is no longer feasible. Instead, the objective is to minimize the <i>competitive ratio</i>: the ratio of the benchmark reward to algorithm’s reward.</p><p>We design an algorithm with competitive ratio <i>O</i>(log <i>T</i>) relative to the best fixed distribution over actions, where <i>T</i> is the time horizon; we also prove a matching lower bound. The key conceptual contribution is a new perspective on the stochastic version of the problem. We suggest a new algorithm for the stochastic version, which builds on the framework of regret minimization in repeated games and admits a substantially simpler analysis compared to prior work. We then analyze this algorithm for the adversarial version, and use it as a subroutine to solve the latter.</p><p>Our algorithm is the first “black-box reduction” from bandits to BwK: it takes an arbitrary bandit algorithm and uses it as a subroutine. We use this reduction to derive several extensions.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"15 2","pages":""},"PeriodicalIF":2.5,"publicationDate":"2022-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Journal of the ACMPub Date : 2022-11-17DOI: https://dl.acm.org/doi/10.1145/3555307
Dean Doron, Dana Moshkovitz, Justin Oh, David Zuckerman
{"title":"Nearly Optimal Pseudorandomness from Hardness","authors":"Dean Doron, Dana Moshkovitz, Justin Oh, David Zuckerman","doi":"https://dl.acm.org/doi/10.1145/3555307","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3555307","url":null,"abstract":"<p>Existing proofs that deduce BPP = P from circuit lower bounds convert randomized algorithms into deterministic algorithms with a large polynomial slowdown. We convert randomized algorithms into deterministic ones with <i>little slowdown</i>. Specifically, assuming exponential lower bounds against randomized NP ∩ coNP circuits, formally known as randomized SVN circuits, we convert any randomized algorithm over inputs of length <i>n</i> running in time <i>t</i> ≥ <i>n</i> into a deterministic one running in time <i>t</i><sup>2+α</sup> for an arbitrarily small constant α > 0. Such a slowdown is nearly optimal for <i>t</i> close to <i>n</i>, since under standard complexity-theoretic assumptions, there are problems with an inherent quadratic derandomization slowdown. We also convert any randomized algorithm that <i>errs rarely</i> into a deterministic algorithm having a similar running time (with pre-processing). The latter derandomization result holds under weaker assumptions, of exponential lower bounds against deterministic SVN circuits.</p><p>Our results follow from a new, nearly optimal, explicit pseudorandom generator fooling circuits of size <i>s</i> with seed length (1+α)log <i>s</i>, under the assumption that there exists a function <i>f</i> ∈ E that requires randomized SVN circuits of size at least 2<sup>(1-α′)</sup><i>n</i>, where α = <i>O</i>(α)′. The construction uses, among other ideas, a new connection between pseudoentropy generators and locally list recoverable codes.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"12 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2022-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nai-Hui Chia, A. Gilyén, Tongyang Li, Han-Hsuan Lin, Ewin Tang, C. Wang
{"title":"Sampling-based Sublinear Low-rank Matrix Arithmetic Framework for Dequantizing Quantum Machine Learning","authors":"Nai-Hui Chia, A. Gilyén, Tongyang Li, Han-Hsuan Lin, Ewin Tang, C. Wang","doi":"10.1145/3549524","DOIUrl":"https://doi.org/10.1145/3549524","url":null,"abstract":"We present an algorithmic framework for quantum-inspired classical algorithms on close-to-low-rank matrices, generalizing the series of results started by Tang’s breakthrough quantum-inspired algorithm for recommendation systems [STOC’19]. Motivated by quantum linear algebra algorithms and the quantum singular value transformation (SVT) framework of Gilyén et al. [STOC’19], we develop classical algorithms for SVT that run in time independent of input dimension, under suitable quantum-inspired sampling assumptions. Our results give compelling evidence that in the corresponding QRAM data structure input model, quantum SVT does not yield exponential quantum speedups. Since the quantum SVT framework generalizes essentially all known techniques for quantum linear algebra, our results, combined with sampling lemmas from previous work, suffice to generalize all prior results about dequantizing quantum machine learning algorithms. In particular, our classical SVT framework recovers and often improves the dequantization results on recommendation systems, principal component analysis, supervised clustering, support vector machines, low-rank regression, and semidefinite program solving. We also give additional dequantization results on low-rank Hamiltonian simulation and discriminant analysis. Our improvements come from identifying the key feature of the quantum-inspired input model that is at the core of all prior quantum-inspired results: ℓ2-norm sampling can approximate matrix products in time independent of their dimension. We reduce all our main results to this fact, making our exposition concise, self-contained, and intuitive.","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"75 1","pages":"1 - 72"},"PeriodicalIF":2.5,"publicationDate":"2022-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82026044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
