17Th Knuth Prize: Call for Nominations
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Reproducibility and Pseudo-Determinism in Log-Space
Reproducibility and Pseudo-determinism in Log-Space by Ofer Grossman S.B., Massachusetts Institute of Technology (2017) Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering and Computer Science at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 2020 c Massachusetts Institute of Technology 2020. All rights reserved. Author...................................................................... Department of Electrical Engineering and Computer Science May 15, 2020 Certified by.................................................................. Shafi Goldwasser RSA Professor of Electrical Engineering and Computer Science Thesis Supervisor Accepted by................................................................. Leslie A. Kolodziejski Professor of Electrical Engineering and Computer Science Chair, Department Committee on Graduate Students 2 Reproducibility and Pseudo-determinism in Log-Space by Ofer Grossman Submitted to the Department of Electrical Engineering and Computer Science on May 15, 2020, in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering and Computer Science Abstract Acuriouspropertyofrandomizedlog-spacesearchalgorithmsisthattheiroutputsareoften longer than their workspace. This leads to the question: how can we reproduce the results of a randomized log space computation without storing the output or randomness verbatim? Running the algorithm again with new -
Going Beyond Dual Execution: MPC for Functions with Efficient Verification
Going Beyond Dual Execution: MPC for Functions with Efficient Verification Carmit Hazay abhi shelat ∗ Bar-Ilan University Northeastern Universityy Muthuramakrishnan Venkitasubramaniamz University of Rochester Abstract The dual execution paradigm of Mohassel and Franklin (PKC’06) and Huang, Katz and Evans (IEEE ’12) shows how to achieve the notion of 1-bit leakage security at roughly twice the cost of semi-honest security for the special case of two-party secure computation. To date, there are no multi-party compu- tation (MPC) protocols that offer such a strong trade-off between security and semi-honest performance. Our main result is to address this shortcoming by designing 1-bit leakage protocols for the multi- party setting, albeit for a special class of functions. We say that function f (x, y) is efficiently verifiable by g if the running time of g is always smaller than f and g(x, y, z) = 1 if and only if f (x, y) = z. In the two-party setting, we first improve dual execution by observing that the “second execution” can be an evaluation of g instead of f , and that by definition, the evaluation of g is asymptotically more efficient. Our main MPC result is to construct a 1-bit leakage protocol for such functions from any passive protocol for f that is secure up to additive errors and any active protocol for g. An important result by Genkin et al. (STOC ’14) shows how the classic protocols by Goldreich et al. (STOC ’87) and Ben-Or et al. (STOC ’88) naturally support this property, which allows to instantiate our compiler with two-party and multi-party protocols. -
Fault-Tolerant Distributed Computing in Full-Information Networks
Fault-Tolerant Distributed Computing in Full-Information Networks Shafi Goldwasser∗ Elan Pavlov Vinod Vaikuntanathan∗ CSAIL, MIT MIT CSAIL, MIT Cambridge MA, USA Cambridge MA, USA Cambridge MA, USA December 15, 2006 Abstract In this paper, we use random-selection protocols in the full-information model to solve classical problems in distributed computing. Our main results are the following: • An O(log n)-round randomized Byzantine Agreement (BA) protocol in a synchronous full-information n network tolerating t < 3+ faulty players (for any constant > 0). As such, our protocol is asymp- totically optimal in terms of fault-tolerance. • An O(1)-round randomized BA protocol in a synchronous full-information network tolerating t = n O( (log n)1.58 ) faulty players. • A compiler that converts any randomized protocol Πin designed to tolerate t fail-stop faults, where the n source of randomness of Πin is an SV-source, into a protocol Πout that tolerates min(t, 3 ) Byzantine ∗ faults. If the round-complexity of Πin is r, that of Πout is O(r log n). Central to our results is the development of a new tool, “audited protocols”. Informally “auditing” is a transformation that converts any protocol that assumes built-in broadcast channels into one that achieves a slightly weaker guarantee, without assuming broadcast channels. We regard this as a tool of independent interest, which could potentially find applications in the design of simple and modular randomized distributed algorithms. ∗Supported by NSF grants CNS-0430450 and CCF0514167. 1 1 Introduction The problem of how n players, some of who may be faulty, can make a common random selection in a set, has received much attention. -
Computational Complexity Computational Complexity
In 1965, the year Juris Hartmanis became Chair Computational of the new CS Department at Cornell, he and his KLEENE HIERARCHY colleague Richard Stearns published the paper On : complexity the computational complexity of algorithms in the Transactions of the American Mathematical Society. RE CO-RE RECURSIVE The paper introduced a new fi eld and gave it its name. Immediately recognized as a fundamental advance, it attracted the best talent to the fi eld. This diagram Theoretical computer science was immediately EXPSPACE shows how the broadened from automata theory, formal languages, NEXPTIME fi eld believes and algorithms to include computational complexity. EXPTIME complexity classes look. It As Richard Karp said in his Turing Award lecture, PSPACE = IP : is known that P “All of us who read their paper could not fail P-HIERARCHY to realize that we now had a satisfactory formal : is different from ExpTime, but framework for pursuing the questions that Edmonds NP CO-NP had raised earlier in an intuitive fashion —questions P there is no proof about whether, for instance, the traveling salesman NLOG SPACE that NP ≠ P and problem is solvable in polynomial time.” LOG SPACE PSPACE ≠ P. Hartmanis and Stearns showed that computational equivalences and separations among complexity problems have an inherent complexity, which can be classes, fundamental and hard open problems, quantifi ed in terms of the number of steps needed on and unexpected connections to distant fi elds of a simple model of a computer, the multi-tape Turing study. An early example of the surprises that lurk machine. In a subsequent paper with Philip Lewis, in the structure of complexity classes is the Gap they proved analogous results for the number of Theorem, proved by Hartmanis’s student Allan tape cells used. -
How Easy Is Local Search?
JOURNAL OF COMPUTER AND SYSTEM SCIENCES 37, 79-100 (1988) How Easy Is Local Search? DAVID S. JOHNSON AT & T Bell Laboratories, Murray Hill, New Jersey 07974 CHRISTOS H. PAPADIMITRIOU Stanford University, Stanford, California and National Technical University of Athens, Athens, Greece AND MIHALIS YANNAKAKIS AT & T Bell Maboratories, Murray Hill, New Jersey 07974 Received December 5, 1986; revised June 5, 1987 We investigate the complexity of finding locally optimal solutions to NP-hard com- binatorial optimization problems. Local optimality arises in the context of local search algorithms, which try to find improved solutions by considering perturbations of the current solution (“neighbors” of that solution). If no neighboring solution is better than the current solution, it is locally optimal. Finding locally optimal solutions is presumably easier than finding optimal solutions. Nevertheless, many popular local search algorithms are based on neighborhood structures for which locally optimal solutions are not known to be computable in polynomial time, either by using the local search algorithms themselves or by taking some indirect route. We define a natural class PLS consisting essentially of those local search problems for which local optimality can be verified in polynomial time, and show that there are complete problems for this class. In particular, finding a partition of a graph that is locally optimal with respect to the well-known Kernighan-Lin algorithm for graph partitioning is PLS-complete, and hence can be accomplished in polynomial time only if local optima can be found in polynomial time for all local search problems in PLS. 0 1988 Academic Press, Inc. 1. -
Conformance Testing David Lee and Mihalis Yannakakis Bell
Conformance Testing David Lee and Mihalis Yannakakis Bell Laboratories, Lucent Technologies 600 Mountain Avenue, RM 2C-423 Murray Hill, NJ 07974 - 2 - System reliability can not be overemphasized in software engineering as large and complex systems are being built to fulfill complicated tasks. Consequently, testing is an indispensable part of system design and implementation; yet it has proved to be a formidable task for complex systems. Testing software contains very wide fields with an extensive literature. See the articles in this volume. We discuss testing of software systems that can be modeled by finite state machines or their extensions to ensure that the implementation conforms to the design. A finite state machine contains a finite number of states and produces outputs on state transitions after receiving inputs. Finite state machines are widely used to model software systems such as communication protocols. In a testing problem we have a specification machine, which is a design of a system, and an implementation machine, which is a ‘‘black box’’ for which we can only observe its I/O behavior. The task is to test whether the implementation conforms to the specification. This is called the conformance testing or fault detection problem. A test sequence that solves this problem is called a checking sequence. Testing finite state machines has been studied for a very long time starting with Moore’s seminal 1956 paper on ‘‘gedanken-experiments’’ (31), which introduced the basic framework for testing problems. Among other fundamental problems, Moore posed the conformance testing problem, proposed an approach, and asked for a better solution. -
Xi Chen: Curriculum Vitae
Xi Chen Associate Professor Phone: 1-212-939-7136 Department of Computer Science Email: [email protected] Columbia University Homepage: http://www.cs.columbia.edu/∼xichen New York, NY 10027 Date of Preparation: March 12, 2016 Research Interests Theoretical Computer Science, including Algorithmic Game Theory and Economics, Complexity Theory, Graph Isomorphism Testing, and Property Testing. Academic Training B.S. Physics / Mathematics, Tsinghua University, Sep 1999 { Jul 2003 Ph.D. Computer Science, Tsinghua University, Sep 2003 { Jul 2007 Advisor: Professor Bo Zhang, Tsinghua University Thesis Title: The Complexity of Two-Player Nash Equilibria Academic Positions Associate Professor (with tenure), Columbia University, Mar 2016 { Now Associate Professor (without tenure), Columbia University, Jul 2015 { Mar 2016 Assistant Professor, Columbia University, Jan 2011 { Jun 2015 Postdoctoral Researcher, Columbia University, Aug 2010 { Dec 2010 Postdoctoral Researcher, University of Southern California, Aug 2009 { Aug 2010 Postdoctoral Researcher, Princeton University, Aug 2008 { Aug 2009 Postdoctoral Researcher, Institute for Advanced Study, Sep 2007 { Aug 2008 Honors and Awards SIAM Outstanding Paper Award, 2016 EATCS Presburger Award, 2015 Alfred P. Sloan Research Fellowship, 2012 NSF CAREER Award, 2012 Best Paper Award The 4th International Frontiers of Algorithmics Workshop, 2010 Best Paper Award The 20th International Symposium on Algorithms and Computation, 2009 Xi Chen 2 Silver Prize, New World Mathematics Award (Ph.D. Thesis) The 4th International Congress of Chinese Mathematicians, 2007 Best Paper Award The 47th Annual IEEE Symposium on Foundations of Computer Science, 2006 Grants Current, Natural Science Foundation, Title: On the Complexity of Optimal Pricing and Mechanism Design, Period: Aug 2014 { Jul 2017, Amount: $449,985. -
László Lovász Avi Wigderson De L’Université Eötvös Loránd À De L’Institute for Advanced Study De Budapest, En Hongrie Et À Princeton, Aux États-Unis
2021 L’Académie des sciences et des lettres de Norvège a décidé de décerner le prix Abel 2021 à László Lovász Avi Wigderson de l’université Eötvös Loránd à de l’Institute for Advanced Study de Budapest, en Hongrie et à Princeton, aux États-Unis, « pour leurs contributions fondamentales à l’informatique théorique et aux mathématiques discrètes, et pour leur rôle de premier plan dans leur transformation en domaines centraux des mathématiques contemporaines ». L’informatique théorique est l’étude de la puissance croissante sur plusieurs autres sciences, ce et des limites du calcul. Elle trouve son origine qui permet de faire de nouvelles découvertes dans les travaux fondateurs de Kurt Gödel, Alonzo en « chaussant des lunettes d’informaticien ». Church, Alan Turing et John von Neumann, qui ont Les structures discrètes telles que les graphes, conduit au développement de véritables ordinateurs les chaînes de caractères et les permutations physiques. L’informatique théorique comprend deux sont au cœur de l’informatique théorique, et les sous-disciplines complémentaires : l’algorithmique mathématiques discrètes et l’informatique théorique qui développe des méthodes efficaces pour une ont naturellement été des domaines étroitement multitude de problèmes de calcul ; et la complexité, liés. Certes, ces deux domaines ont énormément qui montre les limites inhérentes à l’efficacité des bénéficié des champs de recherche plus traditionnels algorithmes. La notion d’algorithmes en temps des mathématiques, mais on constate également polynomial mise en avant dans les années 1960 par une influence croissante dans le sens inverse. Alan Cobham, Jack Edmonds et d’autres, ainsi que Les applications, concepts et techniques de la célèbre conjecture P≠NP de Stephen Cook, Leonid l’informatique théorique ont généré de nouveaux Levin et Richard Karp ont eu un fort impact sur le défis, ouvert de nouvelles directions de recherche domaine et sur les travaux de Lovász et Wigderson. -
Relations and Equivalences Between Circuit Lower Bounds and Karp-Lipton Theorems*
Electronic Colloquium on Computational Complexity, Report No. 75 (2019) Relations and Equivalences Between Circuit Lower Bounds and Karp-Lipton Theorems* Lijie Chen Dylan M. McKay Cody D. Murray† R. Ryan Williams MIT MIT MIT Abstract A frontier open problem in circuit complexity is to prove PNP 6⊂ SIZE[nk] for all k; this is a neces- NP sary intermediate step towards NP 6⊂ P=poly. Previously, for several classes containing P , including NP NP NP , ZPP , and S2P, such lower bounds have been proved via Karp-Lipton-style Theorems: to prove k C 6⊂ SIZE[n ] for all k, we show that C ⊂ P=poly implies a “collapse” D = C for some larger class D, where we already know D 6⊂ SIZE[nk] for all k. It seems obvious that one could take a different approach to prove circuit lower bounds for PNP that does not require proving any Karp-Lipton-style theorems along the way. We show this intuition is wrong: (weak) Karp-Lipton-style theorems for PNP are equivalent to fixed-polynomial size circuit lower NP NP k NP bounds for P . That is, P 6⊂ SIZE[n ] for all k if and only if (NP ⊂ P=poly implies PH ⊂ i.o.-P=n ). Next, we present new consequences of the assumption NP ⊂ P=poly, towards proving similar re- sults for NP circuit lower bounds. We show that under the assumption, fixed-polynomial circuit lower bounds for NP, nondeterministic polynomial-time derandomizations, and various fixed-polynomial time simulations of NP are all equivalent. Applying this equivalence, we show that circuit lower bounds for NP imply better Karp-Lipton collapses. -
The Flajolet-Martin Sketch Itself Preserves Differential Privacy: Private Counting with Minimal Space
The Flajolet-Martin Sketch Itself Preserves Differential Privacy: Private Counting with Minimal Space Adam Smith Shuang Song Abhradeep Thakurta Boston University Google Research, Brain Team Google Research, Brain Team [email protected] [email protected] [email protected] Abstract We revisit the problem of counting the number of distinct elements F0(D) in a data stream D, over a domain [u]. We propose an ("; δ)-differentially private algorithm that approximates F0(D) within a factor of (1 ± γ), and with additive error of p O( ln(1/δ)="), using space O(ln(ln(u)/γ)/γ2). We improve on the prior work at least quadratically and up to exponentially, in terms of both space and additive p error. Our additive error guarantee is optimal up to a factor of O( ln(1/δ)), n ln(u) 1 o and the space bound is optimal up to a factor of O min ln γ ; γ2 . We assume the existence of an ideal uniform random hash function, and ignore the space required to store it. We later relax this requirement by assuming pseudo- random functions and appealing to a computational variant of differential privacy, SIM-CDP. Our algorithm is built on top of the celebrated Flajolet-Martin (FM) sketch. We show that FM-sketch is differentially private as is, as long as there are p ≈ ln(1/δ)=(εγ) distinct elements in the data set. Along the way, we prove a structural result showing that the maximum of k i.i.d. random variables is statisti- cally close (in the sense of "-differential privacy) to the maximum of (k + 1) i.i.d. -
The Computational Complexity of Nash Equilibria in Concisely Represented Games∗
Electronic Colloquium on Computational Complexity, Report No. 52 (2005) The Computational Complexity of Nash Equilibria in Concisely Represented Games∗ Grant R. Schoenebeck y Salil P. Vadhanz May 4, 2005 Abstract Games may be represented in many different ways, and different representations of games affect the complexity of problems associated with games, such as finding a Nash equilibrium. The traditional method of representing a game is to explicitly list all the payoffs, but this incurs an exponential blowup as the number of agents grows. We study two models of concisely represented games: circuit games, where the payoffs are computed by a given boolean circuit, and graph games, where each agent's payoff is a function of only the strategies played by its neighbors in a given graph. For these two models, we study the complexity of four questions: determining if a given strategy is a Nash equilibrium, finding a Nash equilibrium, determining if there exists a pure Nash equilibrium, and determining if there exists a Nash equilibrium in which the payoffs to a player meet some given guarantees. In many cases, we obtain tight results, showing that the problems are complete for various complexity classes. 1 Introduction In recent years, there has been a surge of interest at the interface between computer science and game theory. On one hand, game theory and its notions of equilibria provide a rich framework for modelling the behavior of selfish agents in the kinds of distributed or networked environments that often arise in computer science, and offer mechanisms to achieve efficient and desirable global outcomes in spite of the selfish behavior. -
A Decade of Lattice Cryptography
Full text available at: http://dx.doi.org/10.1561/0400000074 A Decade of Lattice Cryptography Chris Peikert Computer Science and Engineering University of Michigan, United States Boston — Delft Full text available at: http://dx.doi.org/10.1561/0400000074 Foundations and Trends R in Theoretical Computer Science Published, sold and distributed by: now Publishers Inc. PO Box 1024 Hanover, MA 02339 United States Tel. +1-781-985-4510 www.nowpublishers.com [email protected] Outside North America: now Publishers Inc. PO Box 179 2600 AD Delft The Netherlands Tel. +31-6-51115274 The preferred citation for this publication is C. Peikert. A Decade of Lattice Cryptography. Foundations and Trends R in Theoretical Computer Science, vol. 10, no. 4, pp. 283–424, 2014. R This Foundations and Trends issue was typeset in LATEX using a class file designed by Neal Parikh. Printed on acid-free paper. ISBN: 978-1-68083-113-9 c 2016 C. Peikert All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, mechanical, photocopying, recording or otherwise, without prior written permission of the publishers. Photocopying. In the USA: This journal is registered at the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923. Authorization to photocopy items for in- ternal or personal use, or the internal or personal use of specific clients, is granted by now Publishers Inc for users registered with the Copyright Clearance Center (CCC). The ‘services’ for users can be found on the internet at: www.copyright.com For those organizations that have been granted a photocopy license, a separate system of payment has been arranged.