PoS Components:
┌─────────────────────────────────────────────────────────────────────┐
│                                                                   │
│  Stake: Amount of cryptocurrency locked as collateral            │
│                                                                   │
│  Validator Selection: Random selection weighted by stake         │
│                                                                   │
│  Block Creation: Validator creates and proposes block            │
│                                                                   │
│  Validation: Other validators verify block                       │
│                                                                   │
│  Slashing: Penalty for malicious behavior                        │
│                                                                   │
│  Rewards: Validators earn fees and new tokens                    │
│                                                                   │
└─────────────────────────────────────────────────────────────────────┘

Probability of being selected as validator:

P(i) = Stake(i) / Total_Stake

Where:
- Stake(i) = Amount staked by validator i
- Total_Stake = Sum of all staked tokens

Example:
- Validator A: 1,000 ETH staked
- Validator B: 500 ETH staked
- Total Stake: 10,000 ETH

P(A) = 1,000 / 10,000 = 10%
P(B) = 500 / 10,000 = 5%

DPoS Structure:
┌─────────────────────────────────────────────────────────────────────┐
│                                                                   │
│  Token Holders                                                    │
│       │                                                          │
│       │ Vote                                                      │
│       ▼                                                          │
│  Delegates (Witnesses) - typically 21-101 active                │
│       │                                                          │
│       │ Validate transactions, create blocks                     │
│       │                                                          │
│       ▼                                                          │
│  Network                                                        │
│                                                                   │
│  Benefits:                                                       │
│  • Faster block times                                           │
│  • Lower energy consumption                                     │
│  • More predictable performance                                 │
│                                                                   │
│  Risks:                                                         │
│  • Centralization risk                                          │
│  • Collusion possible                                           │
│  • Voter apathy                                                │
│                                                                   │
└─────────────────────────────────────────────────────────────────────┘

Casper FFG:
┌─────────────────────────────────────────────────────────────────────┐
│                                                                   │
│  Validators deposit 32 ETH to become validators                  │
│                                                                   │
│  Epochs: 32 slots (~6.4 minutes)                                │
│                                                                   │
│  Checkpoints: Blocks at epoch boundaries                        │
│                                                                   │
│  Finality: Validators vote on checkpoints                       │
│  • 2/3 votes = checkpoint finalized                            │
│                                                                   │
│  Slashing Conditions:                                            │
│  1. Double voting (vote for two different checkpoints)           │
│  2. Surround voting (vote that surrounds previous vote)          │
│                                                                   │
└─────────────────────────────────────────────────────────────────────┘

PoA Characteristics:
- Validators are known and approved
- Validator identity is at stake
- Used in private/consortium blockchains
- Fast block times (~5 seconds)
- Very low energy consumption

Examples: POA Network, VeChain, Binance Smart Chain (initial)

PoH Mechanism:
- Verifiable delay function (VDF)
- Cryptographic timestamping
- Events ordered by time
- Used in Solana

Benefits:
- High throughput
- Low latency
- Scalable

PoB Mechanism:
1. Send coins to unspendable address (burn)
2. Burned coins counted as "stake"
3. Mining rights proportional to burned coins
4. No ongoing energy consumption

PoC Mechanism:
1. Pre-compute hashes (plotting)
2. Store in hard drives
3. Mining = retrieving plots
4. Energy efficient

PBFT Algorithm:
1. Client sends request to primary node
2. Primary sends pre-prepare message
3. Replicas send prepare message
4. Replicas send commit message
5. Client receives reply

Tolerates f faulty nodes where:
Total Nodes ≥ 3f + 1

Avalanche Process:
1. Node samples random peers
2. Asks about transaction
3. If majority agree, accept
4. Repeat until confidence threshold met
5. Transaction confirmed

Properties:
- Probabilistic finality
- High throughput
- Low latency

Problem:
In PoW, miners cannot mine on multiple chains (energy cost).
In PoS, validators can validate on multiple chains (free).

Solution: Slashing
- Penalty for validating on multiple chains
- Loss of stake
- Economic disincentive

Slashing Conditions:
1. Double signing: Signing two different blocks at same height
2. Surround voting: Voting for conflicting checkpoints
3. Liveness attacks: Going offline

Slashing Penalties:
- 1% for minor violations
- 100% for severe violations

Problem:
Attacker acquires old private keys
  ↓
Starts chain from genesis (with majority stake)
  ↓
Creates long history of blocks
  ↓
Network may be confused

Solutions:
1. Weak subjectivity (social consensus)
2. Checkpointing (periodic finality)
3. Key rotation (periodic key changes)

Validator Revenue = Block_Reward + Transaction_Fees + MEV

Block_Reward = Base_Reward × (1 + Extra_Reward)

Base_Reward = (Total_Stake)^(-0.5) × 64

Extra_Reward:
- Block proposals: ~1/32 chance per epoch
- Attestations: ~1/32 chance per epoch
- Sync committees: ~1/32 chance per epoch

Operating Cost:
- Hardware: $500-2000 initial
- Electricity: $50-200/month
- Internet: $50-100/month
- Time: 10-20 hours/month

Net Profit = Revenue - Operating Cost - Slashing_Risk

Validator Pool Benefits:
1. Lower entry barrier (less than 32 ETH)
2. Shared infrastructure costs
3. Professional management
4. Higher uptime
5. Reduced slashing risk

Pool Types:
1. Centralized (staking providers)
2. Decentralized (liquid staking - Lido, Rocket Pool)
3. Delegated (token holders delegate to validators)

Liquid Staking:
- User deposits ETH
- Receives stETH (staked ETH)
- Earns rewards automatically
- Can trade/use stETH in DeFi

PBFT Consensus Process:

1. Request Phase:
   Client sends request to primary (node 0)

2. Pre-Prepare Phase:
   Primary assigns sequence number
   Sends pre-prepare message to all replicas

3. Prepare Phase:
   Replicas verify request
   Send prepare message to all replicas
   Wait for 2f prepare messages

4. Commit Phase:
   Replicas send commit message
   Wait for 2f commit messages
   Execute request

5. Reply Phase:
   Replicas send reply to client
   Client waits for f+1 identical replies

Message Complexity: O(n²) where n = number of nodes