QuestionQuestion

Question 3
Mining protocol for a blockchain

A new cooperative blockchain EBLOCKS produces blocks using the following protocol, which works in phases. We assume that the number of members n is fixed. At the beginning of each phase all n members become active. In each step within a phase, each active member flips a fair coin and with probability p = 1/2, the member remains active, and with the remaining probability it becomes inactive. The phase ends when the number of active members becomes either 0 or 1. When the phase ends with a single active member, this member produces a block, otherwise the phase terminates without a block.

(a) Show that the probability that a block is produced in a phase is at least 2/3.
(b) Show that the expected number of steps in a phase is 9(logn), giving both a lower and an upper bound, and conclude that this blockchain protocol produces a block every O(long) steps in expectation.
(c) The above protocol produces one block per 9(logn) steps in expectation. By changing only the probability p that each member remains active in each step, can we get a protocol so that a block is produced in expected O(1) steps?

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:
    Solution.pdf.

    $10.00
    for this solution

    or FREE if you
    register a new account!

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Probability Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Decision:
    Upload a file
    Continue without uploading

    SUBMIT YOUR HOMEWORK
    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats