Brief Announcement: Probabilistic Indistinguishability and The Quality of Validity in Byzantine Agreement

Lower bounds and impossibility results in distributed computing are both intellectually challenging and practically important. Hundreds if not thousands of proofs appear in the literature, but surprisingly, the vast majority of them apply to deterministic algorithms only. Probabilistic protocols have been around for at least four decades and are receiving a lot of attention with the emergence of blockchain systems. Nonetheless, we are aware of only a handful of randomized lower bounds. In this work we provide a formal framework for reasoning about randomized distributed algorithms. We generalize the notion of indistinguishability, the most useful tool in deterministic lower bounds, to apply to a probabilistic setting. We apply this framework to prove a result of independent interest. Namely, we completely characterize the quality of decisions that protocols for a randomized multi-valued Consensus problem can guarantee in an asynchronous environment with Byzantine faults. We use the new notion to prove a lower bound on the guaranteed probability that honest parties will not decide on a possibly bogus value proposed by a malicious party. Finally, we show that the bound is tight by providing a protocol that matches it. This brief announcement consists of an introduction to the full paper [Guy Goren et al., 2020] by the same title. The interested reader is advised to consult the full paper for a detailed exposition

Symmetric and Synchronous Communication in Peer-to-Peer Networks

Motivated by distributed implementations of game-theoretical algorithms, we study symmetric process systems and the problem of attaining common knowledge between processes. We formalize our setting by defining a notion of peer-to-peer networks(*) and appropriate symmetry concepts in the context of Communicating Sequential Processes (CSP), due to the common knowledge creating effects of its synchronous communication primitives. We then prove that CSP with input and output guards makes common knowledge in symmetric peer-to-peer networks possible, but not the restricted version which disallows output statements in guards and is commonly implemented. (*) Please note that we are not dealing with fashionable incarnations such as file-sharing networks, but merely use this name for a mathematical notion of a network consisting of directly connected peers "treated on an equal footing", i.e. not having a client-server structure or otherwise pre-determined roles.)Comment: polished, modernized references; incorporated referee feedback from MPC'0

Distributed Computing with Adaptive Heuristics

We use ideas from distributed computing to study dynamic environments in which computational nodes, or decision makers, follow adaptive heuristics (Hart 2005), i.e., simple and unsophisticated rules of behavior, e.g., repeatedly "best replying" to others' actions, and minimizing "regret", that have been extensively studied in game theory and economics. We explore when convergence of such simple dynamics to an equilibrium is guaranteed in asynchronous computational environments, where nodes can act at any time. Our research agenda, distributed computing with adaptive heuristics, lies on the borderline of computer science (including distributed computing and learning) and game theory (including game dynamics and adaptive heuristics). We exhibit a general non-termination result for a broad class of heuristics with bounded recall---that is, simple rules of behavior that depend only on recent history of interaction between nodes. We consider implications of our result across a wide variety of interesting and timely applications: game theory, circuit design, social networks, routing and congestion control. We also study the computational and communication complexity of asynchronous dynamics and present some basic observations regarding the effects of asynchrony on no-regret dynamics. We believe that our work opens a new avenue for research in both distributed computing and game theory.Comment: 36 pages, four figures. Expands both technical results and discussion of v1. Revised version will appear in the proceedings of Innovations in Computer Science 201

Real-time and distributed applications for dictionary-based data compression

The greedy approach to dictionary-based static text compression can be executed by a finite state machine. When it is applied in parallel to different blocks of data independently, there is no lack of robustness even on standard large scale distributed systems with input files of arbitrary size. Beyond standard large scale, a negative effect on the compression effectiveness is caused by the very small size of the data blocks. A robust approach for extreme distributed systems is presented in this paper, where this problem is fixed by overlapping adjacent blocks and preprocessing the neighborhoods of the boundaries. Moreover, we introduce the notion of pseudo-prefix dictionary, which allows optimal compression by means of a real-time semi-greedy procedure and a slight improvement on the compression ratio obtained by the distributed implementations