DeepAI AI Chat
Log In Sign Up

On the Lazy Set object

by   Uri Abraham, et al.

The aim of this article is to employ the Lazy Set algorithm as an example for a mathematical framework for proving the linearizability of distributed systems. The proof in this approach is divided into two stages of lower and higher abstraction level. At the higher level a list of "axioms" is formulated and a proof is given that any model theoretic structure that satisfies these axioms is linearizable. At this level the algorithm is not mentioned. At the lower level, a Simpler Lazy Set algorithm is described, and it is shown that any execution of this simpler algorithm generates a model of these axioms (and is therefore linearizable). Finally the linearization of the Lazy Set algorithm is obtained by proving that any of its executions has a reduct that is an execution of the Simpler algorithm. So the reduct executions are linearizable and this entails immediately linearizability of the Lazy Set algorithm itself.


page 1

page 2

page 3

page 4


A Simpler NP-Hardness Proof for Familial Graph Compression

This document presents a simpler proof showcasing the NP-hardness of Fam...

FEther: An Extensible Definitional Interpreter for Smart-contract Verifications in Coq

Blockchain technology adds records to a list using cryptographic links. ...

Even Simpler Deterministic Matrix Sketching

This paper provides a one-line proof of Frequent Directions (FD) for ske...

Higher-order asymptotics for the parametric complexity

The parametric complexity is the key quantity in the minimum description...

Adding an Abstraction Barrier to ZF Set Theory

Much mathematical writing exists that is, explicitly or implicitly, base...

The Theory of an Arbitrary Higher λ-Model

One takes advantage of some basic properties of every λ-homotopic model ...