Related papers: Stone Duality Proofs for Colorless Distributed Com…
The paper studies computability-theoretic aspects of topological $T_0$-spaces. We introduce effective versions of the notions of a countable $c$-poset and a (second-countable) topological space with base. Based on this, we prove an…
Distributed computing tasks can be presented with a triple $(\I,\Ou,\Delta)$. The solvability of a colorless task on the Iterated Immediate Snapshot model (IIS) has been characterized by the Colorless Computability Theorem…
We suggest a diagrammatic model of computation based on an axiom of distributivity. A diagram of a decorated coloured tangle, similar to those that appear in low dimensional topology, plays the role of a circuit diagram. Equivalent diagrams…
We present and explore a model of stateless and self-stabilizing distributed computation, inspired by real-world applications such as routing on today's Internet. Processors in our model do not have an internal state, but rather interact by…
We present efficient and practical algorithms for a large, distributed system of processors to achieve reliable computations in a secure manner. Specifically, we address the problem of computing a general function of several private inputs…
The mathematical framework of Stone duality is used to synthesize a number of hitherto separate developments in Theoretical Computer Science: - Domain Theory, the mathematical theory of computation introduced by Scott as a foundation for…
Studying distributed computing through the lens of algebraic topology has been the source of many significant breakthroughs during the last two decades, especially in the design of lower bounds or impossibility results for deterministic…
The traditional models of distributed computing focus mainly on networks of computer-like devices that can exchange large messages with their neighbors and perform arbitrary local computations. Recently, there is a trend to apply…
Modeling distributed computing in a way enabling the use of formal methods is a challenge that has been approached from different angles, among which two techniques emerged at the turn of the century: protocol complexes, and directed…
Coded distributed computing introduced by Li et al. in 2015 is an efficient approach to trade computing power to reduce the communication load in general distributed computing frameworks such as MapReduce. In particular, Li et al. show that…
We prove several new tight distributed lower bounds for classic symmetry breaking graph problems. As a basic tool, we first provide a new insightful proof that any deterministic distributed algorithm that computes a $\Delta$-coloring on…
The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead. The…
A task is a distributed problem for $n$ processes, in which each process starts with a private input value, communicates with other processes, and eventually decides an output value. A task is colorless if each process can adopt the input…
We consider the problem of making distributed computations robust to noise, in particular to worst-case (adversarial) corruptions of messages. We give a general distributed interactive coding scheme which simulates any asynchronous…
This paper proposes a simple topological characterization of a large class of fair adversarial models via affine tasks: sub-complexes of the second iteration of the standard chromatic subdivision. We show that the task computability of a…
The paper compares two generic techniques for deriving lower bounds and impossibility results in distributed computing. First, we prove a speedup theorem (a-la Brandt, 2019), for wait-free colorless algorithms, aiming at capturing the…
Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed…
We prove three new versions of Stone Duality. The main version is the following: the category of Kolmogorov locally small spaces and bounded continuous mappings is equivalent to the category of spectral spaces with decent lumps and with…
Our main result is that any topological algebra based on a Boolean space is the extended Stone dual space of a certain associated Boolean algebra with additional operations. A particular case of this result is that the profinite completion…
The problem of computing spectra of operators is arguably one of the most investigated areas of computational mathematics. However, the problem of computing spectra of general bounded infinite matrices has only recently been solved. We…