Consensus Algorithm

Overview

This document describes the mathematical foundation of our consensus algorithm.

Definitions

Let P be the set of participants in the network. Let B be the set of all possible blocks. Let V: B → ℝ be a function that assigns a value to each block.

Algorithm

  1. Each participant p ∈ P proposes a block b ∈ B.
  2. The network selects the block b such that: $$b^ = \arg\max_{b \in B} V(b)$$

Proof of Correctness

Theorem: The selected block b* maximizes the value function V.

Proof: By construction, b is chosen such that V(b) ≥ V(b) for all b ∈ B. Therefore, b maximizes the value function V*.

To elaborate, since b is selected as the block that maximizes the value function V, it follows that for any other block b in the set B, the value assigned to b by the function V will be less than or equal to the value assigned to b. This ensures that b is the optimal block according to the value function V.

Complexity Analysis

Time Complexity: O(|P| * |B|) Space Complexity: O(|B|)