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 : 2022-11-18DOI: https://dl.acm.org/doi/10.1145/3563772
Gabriele Farina, Andrea Celli, Alberto Marchesi, Nicola Gatti
{"title":"Simple Uncoupled No-regret Learning Dynamics for Extensive-form Correlated Equilibrium","authors":"Gabriele Farina, Andrea Celli, Alberto Marchesi, Nicola Gatti","doi":"https://dl.acm.org/doi/10.1145/3563772","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3563772","url":null,"abstract":"<p>The existence of simple uncoupled no-regret learning dynamics that converge to correlated equilibria in normal-form games is a celebrated result in the theory of multi-agent systems. Specifically, it has been known for more than 20 years that when all players seek to minimize their <i>internal</i> regret in a repeated normal-form game, the empirical frequency of play converges to a normal-form correlated equilibrium. Extensive-form (that is, tree-form) games generalize normal-form games by modeling both sequential and simultaneous moves, as well as imperfect information. Because of the sequential nature and presence of private information in the game, correlation in extensive-form games possesses significantly different properties than in normal-form games, many of which are still open research directions. Extensive-form correlated equilibrium (EFCE) has been proposed as the natural extensive-form counterpart to the classical notion of correlated equilibrium in normal-form games. Compared to the latter, the constraints that define the set of EFCEs are significantly more complex, as the correlation device (a.k.a. mediator) must take into account the evolution of beliefs of each player as they make observations throughout the game. Due to that significant added complexity, the existence of uncoupled learning dynamics leading to an EFCE has remained a challenging open research question for a long time. In this article, we settle that question by giving the first uncoupled no-regret dynamics that converge to the set of EFCEs in <i>n</i>-player general-sum extensive-form games with perfect recall. We show that each iterate can be computed in time polynomial in the size of the game tree, and that, when all players play repeatedly according to our learning dynamics, the empirical frequency of play after <i>T</i> game repetitions is proven to be a ( O(1/sqrt {T}) )-approximate EFCE with high probability, and an EFCE almost surely in the limit.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"22 5","pages":""},"PeriodicalIF":2.5,"publicationDate":"2022-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525699","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/10.1145/3556971
Matthew Fahrbach, Zhiyi Huang, Runzhou Tao, Morteza Zadimoghaddam
{"title":"Edge-Weighted Online Bipartite Matching","authors":"Matthew Fahrbach, Zhiyi Huang, Runzhou Tao, Morteza Zadimoghaddam","doi":"https://dl.acm.org/doi/10.1145/3556971","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3556971","url":null,"abstract":"<p>Online bipartite matching is one of the most fundamental problems in the online algorithms literature. Karp, Vazirani, and Vazirani (STOC 1990) gave an elegant algorithm for unweighted bipartite matching that achieves an optimal competitive ratio of 1-1/e . Aggarwal et al. (SODA 2011) later generalized their algorithm and analysis to the vertex-weighted case. Little is known, however, about the most general edge-weighted problem aside from the trivial 1/2-competitive greedy algorithm. In this article, we present the first online algorithm that breaks the long-standing 1/2 barrier and achieves a competitive ratio of at least 0.5086. In light of the hardness result of Kapralov, Post, and Vondrák (SODA 2013), which restricts beating a 1/2 competitive ratio for the more general monotone submodular welfare maximization problem, our result can be seen as strong evidence that edge-weighted bipartite matching is strictly easier than submodular welfare maximization in an online setting.</p><p>The main ingredient in our online matching algorithm is a novel subroutine called <i>online correlated selection</i> (OCS), which takes a sequence of pairs of vertices as input and selects one vertex from each pair. Instead of using a fresh random bit to choose a vertex from each pair, the OCS negatively correlates decisions across different pairs and provides a quantitative measure on the level of correlation. We believe our OCS technique is of independent interest and will find further applications in other online optimization problems.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"4 2","pages":""},"PeriodicalIF":2.5,"publicationDate":"2022-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525677","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}
Martin Grohe, Benjamin Lucien Kaminski, J. Katoen, P. Lindner
{"title":"Generative Datalog with Continuous Distributions","authors":"Martin Grohe, Benjamin Lucien Kaminski, J. Katoen, P. Lindner","doi":"10.1145/3559102","DOIUrl":"https://doi.org/10.1145/3559102","url":null,"abstract":"Arguing for the need to combine declarative and probabilistic programming, Bárány et al. (TODS 2017) recently introduced a probabilistic extension of Datalog as a “purely declarative probabilistic programming language.” We revisit this language and propose a more principled approach towards defining its semantics based on stochastic kernels and Markov processes—standard notions from probability theory. This allows us to extend the semantics to continuous probability distributions, thereby settling an open problem posed by Bárány et al. We show that our semantics is fairly robust, allowing both parallel execution and arbitrary chase orders when evaluating a program. We cast our semantics in the framework of infinite probabilistic databases (Grohe and Lindner, LMCS 2022) and show that the semantics remains meaningful even when the input of a probabilistic Datalog program is an arbitrary probabilistic database.","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"22 1","pages":"1 - 52"},"PeriodicalIF":2.5,"publicationDate":"2022-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80064994","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}