Combinatorial Topology and Distributed Computing Copyright 2010 Herlihy, Kozlov, and Rajsbaum All Rights Reserved
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Arxiv:2104.04742V2 [Quant-Ph] 13 Apr 2021 Keywords: Quantum Cryptography, Remote State Preparation, Zero-Knowledge, Learning with Errors Table of Contents
Non-Destructive Zero-Knowledge Proofs on Quantum States, and Multi-Party Generation of Authorized Hidden GHZ States Léo Colisson 1, Frédéric Grosshans 1, Elham Kashefi1,2 1 Laboratoire d’Informatique de Paris 6 (LIP6), Sorbonne Université, 4 Place Jussieu, 75252 Paris CEDEX 05, France {leo.colisson, frederic.grosshans}@lip6.fr 2 School of Informatics, University of Edinburgh, 10 Crichton Street, Edinburgh EH8 9AB, UK Abstract. Due to the special no-cloning principle, quantum states appear to be very useful in cryptography. But this very same property also has drawbacks: when receiving a quantum state, it is nearly impossible for the receiver to efficiently check non-trivial properties on that state without destroying it. This allows a malicious sender to send maliciously crafted states without being detected. The natural (destructive) method for testing a quantum state is the “cut-and-choose” method. However, this method has many drawbacks: the security is only linear, and the class of states and properties that can be tested is quite restricted. In this work, we propose a different approach, and we initiate the study of Non-Destructive Zero-Knowledge Proofs on Quantum States. Our method binds a quantum state to a classical encryption of that quantum state. That way, the receiver can obtain guarantees on the quantum state by asking to the sender to prove properties directly on the classical encryption. This method is therefore non-destructive, and it is possible to verify a very large class of properties. For instance, we can force the sender to send different categories of states depending on whether they know a classical password or not. -
On the Randomness Complexity of Interactive Proofs and Statistical Zero-Knowledge Proofs*
On the Randomness Complexity of Interactive Proofs and Statistical Zero-Knowledge Proofs* Benny Applebaum† Eyal Golombek* Abstract We study the randomness complexity of interactive proofs and zero-knowledge proofs. In particular, we ask whether it is possible to reduce the randomness complexity, R, of the verifier to be comparable with the number of bits, CV , that the verifier sends during the interaction. We show that such randomness sparsification is possible in several settings. Specifically, unconditional sparsification can be obtained in the non-uniform setting (where the verifier is modelled as a circuit), and in the uniform setting where the parties have access to a (reusable) common-random-string (CRS). We further show that constant-round uniform protocols can be sparsified without a CRS under a plausible worst-case complexity-theoretic assumption that was used previously in the context of derandomization. All the above sparsification results preserve statistical-zero knowledge provided that this property holds against a cheating verifier. We further show that randomness sparsification can be applied to honest-verifier statistical zero-knowledge (HVSZK) proofs at the expense of increasing the communica- tion from the prover by R−F bits, or, in the case of honest-verifier perfect zero-knowledge (HVPZK) by slowing down the simulation by a factor of 2R−F . Here F is a new measure of accessible bit complexity of an HVZK proof system that ranges from 0 to R, where a maximal grade of R is achieved when zero- knowledge holds against a “semi-malicious” verifier that maliciously selects its random tape and then plays honestly. -
Dagrep-V007-I011-Complete.Pdf
Volume 7, Issue 11, November 2017 New Challenges in Parallelism (Dagstuhl Seminar 17451) Annette Bieniusa, Hans-J. Boehm, Maurice Herlihy, and Erez Petrank ........... 1 Algorithmic Cheminformatics (Dagstuhl Seminar 17452) Jakob L. Andersen, Christoph Flamm, Daniel Merkle, and Peter F. Stadler . 28 Connecting Visualization and Data Management Research (Dagstuhl Seminar 17461) Remco Chang, Jean-Daniel Fekete, Juliana Freire, and Carlos E. Scheidegger . 46 A Shared Challenge in Behavioural Specification (Dagstuhl Seminar 17462) Klaus Havelund, Martin Leucker, Giles Reger, and Volker Stolz . 59 Artificial and Computational Intelligence in Games: AI-Driven Game Design (Dagstuhl Seminar 17471) Pieter Spronck, Elisabeth André, Michael Cook, and Mike Preuß . 86 Addressing the Computational Challenges of Personalized Medicine (Dagstuhl Seminar 17472) Niko Beerenwinkel, Holger Fröhlich, and Susan A. Murphy . 130 Reliable Computation and Complexity on the Reals (Dagstuhl Seminar 17481) Norbert T. Müller, Siegfried M. Rump, Klaus Weihrauch, and Martin Ziegler . 142 DagstuhlReports,Vol. 7,Issue11 ISSN2192-5283 ISSN 2192-5283 Published online and open access by Aims and Scope Schloss Dagstuhl – Leibniz-Zentrum für Informatik The periodical Dagstuhl Reports documents the GmbH, Dagstuhl Publishing, Saarbrücken/Wadern, program and the results of Dagstuhl Seminars and Germany. Online available at Dagstuhl Perspectives Workshops. http://www.dagstuhl.de/dagpub/2192-5283 In principal, for each Dagstuhl Seminar or Dagstuhl Perspectives Workshop a report is published that Publication date contains the following: March, 2018 an executive summary of the seminar program and the fundamental results, Bibliographic information published by the Deutsche an overview of the talks given during the seminar Nationalbibliothek (summarized as talk abstracts), and The Deutsche Nationalbibliothek lists this publica- summaries from working groups (if applicable). -
Topology in Distributed Computing
Die approbierte Originalversion dieser Diplom-/Masterarbeit ist an der Hauptbibliothek der Technischen Universität Wien aufgestellt (http://www.ub.tuwien.ac.at). The approved original version of this diploma or master thesis is available at the main library of the Vienna University of Technology (http://www.ub.tuwien.ac.at/englweb/). Topology in Distributed Computing DIPLOMARBEIT zur Erlangung des akademischen Grades Diplom-Ingenieur im Rahmen des Studiums Technische Informatik ausgeführt von Thomas Nowak Matrikelnummer 0425201 an der Fakultät für Informatik der Technischen Universität Wien Betreuer: Univ.Prof. Dr. Ulrich Schmid Wien, 18.03.2010 _______________________ ______________________ (Unterschrift Verfasser) (Unterschrift Betreuer) Technische Universität Wien A-1040 Wien Karlsplatz 13 Tel. +43/(0)1/58801-0 http://www.tuwien.ac.at Erklärung Thomas Nowak Rechte Wienzeile 73/23 1050 Wien Hiermit erkläre ich, dass ich diese Arbeit selbstständig verfasst habe, dass ich die verwendeten Quellen und Hilfsmittel vollständig angegeben habe und dass ich die Stellen der Arbeit – einschließlich Tabellen, Karten und Abbildungen –, die anderen Werken oder dem Internet im Wortlaut oder dem Sinn nach entnommen sind, auf jeden Fall unter Angabe der Quelle als Entlehnung kenntlich gemacht habe. Wien, 18.03.2010 ______________________ (Unterschrift) Abstract Topology is the general mathematical theory of convergence. Distributed com- puting is the formal investigation of communicating concurrent processes. We explore applications of topology to distributed computing in two directions: (1) Point-set topology and (2) algebraic topology. We use the former to study the topological structure of infinite execution trees. This enables us to unify a number of impossibility proofs, in particular, the impossibility of distributed consensus — the task of all processes in a system agreeing on a single value — in various (close to) asynchronous systems with crash failures. -
FOCS 2005 Program SUNDAY October 23, 2005
FOCS 2005 Program SUNDAY October 23, 2005 Talks in Grand Ballroom, 17th floor Session 1: 8:50am – 10:10am Chair: Eva´ Tardos 8:50 Agnostically Learning Halfspaces Adam Kalai, Adam Klivans, Yishay Mansour and Rocco Servedio 9:10 Noise stability of functions with low influences: invari- ance and optimality The 46th Annual IEEE Symposium on Elchanan Mossel, Ryan O’Donnell and Krzysztof Foundations of Computer Science Oleszkiewicz October 22-25, 2005 Omni William Penn Hotel, 9:30 Every decision tree has an influential variable Pittsburgh, PA Ryan O’Donnell, Michael Saks, Oded Schramm and Rocco Servedio Sponsored by the IEEE Computer Society Technical Committee on Mathematical Foundations of Computing 9:50 Lower Bounds for the Noisy Broadcast Problem In cooperation with ACM SIGACT Navin Goyal, Guy Kindler and Michael Saks Break 10:10am – 10:30am FOCS ’05 gratefully acknowledges financial support from Microsoft Research, Yahoo! Research, and the CMU Aladdin center Session 2: 10:30am – 12:10pm Chair: Satish Rao SATURDAY October 22, 2005 10:30 The Unique Games Conjecture, Integrality Gap for Cut Problems and Embeddability of Negative Type Metrics Tutorials held at CMU University Center into `1 [Best paper award] Reception at Omni William Penn Hotel, Monongahela Room, Subhash Khot and Nisheeth Vishnoi 17th floor 10:50 The Closest Substring problem with small distances Tutorial 1: 1:30pm – 3:30pm Daniel Marx (McConomy Auditorium) Chair: Irit Dinur 11:10 Fitting tree metrics: Hierarchical clustering and Phy- logeny Subhash Khot Nir Ailon and Moses Charikar On the Unique Games Conjecture 11:30 Metric Embeddings with Relaxed Guarantees Break 3:30pm – 4:00pm Ittai Abraham, Yair Bartal, T-H. -
Interactive Proofs
Interactive proofs April 12, 2014 [72] L´aszl´oBabai. Trading group theory for randomness. In Proc. 17th STOC, pages 421{429. ACM Press, 1985. doi:10.1145/22145.22192. [89] L´aszl´oBabai and Shlomo Moran. Arthur-Merlin games: A randomized proof system and a hierarchy of complexity classes. J. Comput. System Sci., 36(2):254{276, 1988. doi:10.1016/0022-0000(88)90028-1. [99] L´aszl´oBabai, Lance Fortnow, and Carsten Lund. Nondeterministic ex- ponential time has two-prover interactive protocols. In Proc. 31st FOCS, pages 16{25. IEEE Comp. Soc. Press, 1990. doi:10.1109/FSCS.1990.89520. See item 1991.108. [108] L´aszl´oBabai, Lance Fortnow, and Carsten Lund. Nondeterministic expo- nential time has two-prover interactive protocols. Comput. Complexity, 1 (1):3{40, 1991. doi:10.1007/BF01200056. Full version of 1990.99. [136] Sanjeev Arora, L´aszl´oBabai, Jacques Stern, and Z. (Elizabeth) Sweedyk. The hardness of approximate optima in lattices, codes, and systems of linear equations. In Proc. 34th FOCS, pages 724{733, Palo Alto CA, 1993. IEEE Comp. Soc. Press. doi:10.1109/SFCS.1993.366815. Conference version of item 1997:160. [160] Sanjeev Arora, L´aszl´oBabai, Jacques Stern, and Z. (Elizabeth) Sweedyk. The hardness of approximate optima in lattices, codes, and systems of linear equations. J. Comput. System Sci., 54(2):317{331, 1997. doi:10.1006/jcss.1997.1472. Full version of 1993.136. [111] L´aszl´oBabai, Lance Fortnow, Noam Nisan, and Avi Wigderson. BPP has subexponential time simulations unless EXPTIME has publishable proofs. In Proc. -
Why Extension-Based Proofs Fail
Why Extension-Based Proofs Fail Dan Alistarh James Aspnes Faith Ellen IST Austria Yale University of Toronto [email protected] [email protected] [email protected] Rati Gelashvili Leqi Zhu University of Toronto University of Michigan [email protected] [email protected] August 2, 2020 Abstract We introduce extension-based proofs, a class of impossibility proofs that includes valency arguments. They are modelled as an interaction between a prover and a protocol. Using proofs based on combinatorial topology, it has been shown that it is impossible to deterministically solve k-set agreement among n > k 2 processes in a wait-free manner in certain asynchronous models. However, it was unknown whether≥ proofs based on simpler techniques were possible. We show that this impossibility result cannot be obtained for one of these models by an extension- based proof and, hence, extension-based proofs are limited in power. 1 Introduction One of the most well-known results in the theory of distributed computing, due to Fischer, Lynch, and Paterson [FLP85], is that there is no deterministic, wait-free protocol solving consensus among n 2 processes in an asynchronous message passing system, even if at most one process may ≥ crash. Their result has been extended to asynchronous shared memory systems where processes communicate by reading from and writing to shared registers [Abr88, CIL87, Her91, LAA87]. Moses and Rajsbaum [MR02] gave a unified framework for proving the impossibility of consensus in a number of different systems. Chaudhuri [Cha93] conjectured that the impossibility of consensus could be generalized to the k-set agreement problem. -
Chicago Journal of Theoretical Computer Science the MIT Press
Chicago Journal of Theoretical Computer Science The MIT Press Volume 1997, Article 1 12 March 1997 ISSN 1073–0486. MIT Press Journals, 55 Hayward St., Cambridge, MA 02142 USA; (617)253-2889; [email protected], [email protected]. Published one article at a time in LATEX source form on the Internet. Pag- ination varies from copy to copy. For more information and other articles see: http://www-mitpress.mit.edu/jrnls-catalog/chicago.html • http://www.cs.uchicago.edu/publications/cjtcs/ • ftp://mitpress.mit.edu/pub/CJTCS • ftp://cs.uchicago.edu/pub/publications/cjtcs • Feige and Kilian Limited vs. Polynomial Nondeterminism (Info) The Chicago Journal of Theoretical Computer Science is abstracted or in- R R R dexed in Research Alert, SciSearch, Current Contents /Engineering Com- R puting & Technology, and CompuMath Citation Index. c 1997 The Massachusetts Institute of Technology. Subscribers are licensed to use journal articles in a variety of ways, limited only as required to insure fair attribution to authors and the journal, and to prohibit use in a competing commercial product. See the journal’s World Wide Web site for further details. Address inquiries to the Subsidiary Rights Manager, MIT Press Journals; (617)253-2864; [email protected]. The Chicago Journal of Theoretical Computer Science is a peer-reviewed scholarly journal in theoretical computer science. The journal is committed to providing a forum for significant results on theoretical aspects of all topics in computer science. Editor in chief: Janos Simon Consulting -
On the Asynchronous Computability Theorem
On the Asynchronous Computability Theorem Rachid Guerraoui Petr Kouznetsov Bastian Pochon Distributed Programming Laboratory EPFL GETCO 2004 2/23 Characterization T 1 of wait-free computable decision tasks [Herlihy and Shavit, 1993, 1994] • representing decision tasks through simplicial complexes and simplicial maps • a task is solvable iff the corresponding complexes satisfy a topological property T 1 • long-standing impossibility results: set agreement [BG93, SZ93] and (n, 2n)-renaming GETCO 2004 3/23 [Borowsky and Gafni, 1997]: a “stronger” geometric property T 2 • a “simpler” algorithmic proof of T 2 • the equivalence of the properties: T 1 = T 2 (through proving a geometric result with a distributed algorithm) Why “stronger” and “simpler” ? What is the distributed algorithm? GETCO 2004 4/23 Decision task T = (I, O, ∆) [HS93] • I — chromatic input complex (a set of possible input simplexes) • O — chromatic output complex (a set of possible output simplexes) • ∆ ⊆ I × O — task specification (a color-preserving map that carries every input simplex to a set of output simplexes) GETCO 2004 5/23 Wait-free protocols Every process starts with an input value, executes a number of writes and reads of the shared memory, and finishes with an output value (applies a decision map to its final state). A protocol solves a task T = (I, O, ∆) if it satisfies the task specification: for any input simplex S ∈ I, any resulting output simplex O ∈ ∆(S). A protocol wait-free if every process finishes in a bounded number of its own steps, no matter how other processes behave. GETCO 2004 6/23 Herlihy and Shavit’s criterion [HS94] Theorem 1. -
Is It Easier to Prove Theorems That Are Guaranteed to Be True?
Is it Easier to Prove Theorems that are Guaranteed to be True? Rafael Pass∗ Muthuramakrishnan Venkitasubramaniamy Cornell Tech University of Rochester [email protected] [email protected] April 15, 2020 Abstract Consider the following two fundamental open problems in complexity theory: • Does a hard-on-average language in NP imply the existence of one-way functions? • Does a hard-on-average language in NP imply a hard-on-average problem in TFNP (i.e., the class of total NP search problem)? Our main result is that the answer to (at least) one of these questions is yes. Both one-way functions and problems in TFNP can be interpreted as promise-true distri- butional NP search problems|namely, distributional search problems where the sampler only samples true statements. As a direct corollary of the above result, we thus get that the existence of a hard-on-average distributional NP search problem implies a hard-on-average promise-true distributional NP search problem. In other words, It is no easier to find witnesses (a.k.a. proofs) for efficiently-sampled statements (theorems) that are guaranteed to be true. This result follows from a more general study of interactive puzzles|a generalization of average-case hardness in NP|and in particular, a novel round-collapse theorem for computationally- sound protocols, analogous to Babai-Moran's celebrated round-collapse theorem for information- theoretically sound protocols. As another consequence of this treatment, we show that the existence of O(1)-round public-coin non-trivial arguments (i.e., argument systems that are not proofs) imply the existence of a hard-on-average problem in NP=poly. -
On the Space Complexity of Colourless Tasks by Leqi Zhu A
On the Space Complexity of Colourless Tasks by Leqi Zhu A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Computer Science University of Toronto c Copyright 2019 by Leqi Zhu Abstract On the Space Complexity of Colourless Tasks Leqi Zhu Doctor of Philosophy Graduate Department of Computer Science University of Toronto 2019 In this thesis, we prove lower bounds on the number of registers needed to solve colourless tasks in asynchronous shared memory systems. Many fundamental synchronization tasks, such as consensus, k-set agreement, and -approximate agreement, are colourless. We show that it is possible to transform any nondeterministic solo-terminating algorithm (including any randomized wait-free algorithm) into an obstruction-free algorithm that uses the same number of registers. This result extends to algorithms using any finite number of deterministic objects that support read operations. Hence, we can focus on proving lower bounds for obstruction-free algorithms. We prove a tight lower bound on the number of registers needed to solve obstruction-free consensus. We also prove the first non-constant lower bounds on the number of registers needed to solve obstruction- free k-set agreement and obstruction-free -approximate agreement. The bound for k-set agreement is asymptotically tight when k is a constant and the bound for -approximate agreement is asymptotically tight when is sufficiently small. To prove these bounds, we introduce a new technique, revisionist simulations. This technique allows us to prove a general theorem that yields lower bounds on the number of registers needed to solve any colourless task in an obstruction-free manner. -
K-Set Agreement Bounds in Round-Based Models Through Combinatorial Topology Adam Shimi, Armando Castañeda
K-set agreement bounds in round-based models through combinatorial topology Adam Shimi, Armando Castañeda To cite this version: Adam Shimi, Armando Castañeda. K-set agreement bounds in round-based models through combina- torial topology. 39th ACM Symposium on Principles of Distributed Computing (PODC 2020), Aug 2020, Salerno, Italy. pp.395-404. hal-02950742 HAL Id: hal-02950742 https://hal.archives-ouvertes.fr/hal-02950742 Submitted on 28 Sep 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Open Archive Toulouse Archive Ouverte OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible This is an author’s version published in: http://oatao.univ-toulouse.fr/26404 Official URL https://doi.org/10.1145/3382734.3405752 To cite this version: Shimi, Adam and Castañeda, Armando K-set agreement bounds in round-based models through combinatorial topology. (2020) In: 39th ACM Symposium on Principles of Distributed Computing (PODC 2020), 3 August 2020 - 7 August 2020 (Salerno,