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Smart Contract Execution - the (+-)-Biased Ballot Problem

Authors Lin Chen, Lei Xu, Zhimin Gao, Nolan Shah, Yang Lu, Weidong Shi

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Lin Chen
Lei Xu
Zhimin Gao
Nolan Shah
Yang Lu
Weidong Shi

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Lin Chen, Lei Xu, Zhimin Gao, Nolan Shah, Yang Lu, and Weidong Shi. Smart Contract Execution - the (+-)-Biased Ballot Problem. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 21:1-21:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.ISAAC.2017.21

Abstract

Transaction system build on top of blockchain, especially smart contract, is becoming an important part of world economy. However, there is a lack of formal study on the behavior of users in these systems, which leaves the correctness and security of such system without a solid foundation. Unlike mining, in which the reward for mining a block is fixed, different execution results of a smart contract may lead to significantly different payoffs of users, which gives more incentives for some user to follow a branch that contains a wrong result, even if the branch is shorter. It is thus important to understand the exact probability that a branch is being selected by the system. We formulate this problem as the (+-)-Biased Ballot Problem as follows: there are n voters one by one voting for either of the two candidates A and B. The probability of a user voting for A or B depends on whether the difference between the current votes of A and B is positive or negative. Our model takes into account the behavior of three different kinds of users when a branch occurs in the system -- users having preference over a certain branch based on the history of their transactions, and users being indifferent and simply follow the longest chain. We study two important probabilities that are closely related with a blockchain based system - the probability that A wins at last, and the probability that A receives d votes first. We show how to recursively calculate the two probabilities for any fixed n and d, and also discuss their asymptotic values when n and d are sufficiently large.
Keywords
  • Blockchain
  • Probability
  • Random Walk
  • Smart Contract

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