## Nilu's Prover Strategy Objectives

## 1. Cost

The primary goal of a rollup is to reduce user costs by scaling Ethereum.

**Minimize**
- **Computational Cost** associated with the computation performed by provers.

**Subject to**
- Total Revenue ≥ Total Operational
- Cost Total Transaction Cost for Users ≤ User’s Maximum Acceptable
- Cost Prover Operational Costs ≤ Prover Earnings

## 2. Liveness

The primary goal is to minimize any downtime and delays in the network.

**Minimize**

**Cost of Downtime and Delays** represents the cost associated with any periods during which provers are unavailable or fail to generate proofs. The cost of downtime can be quantified in terms the opportunity cost of potential revenue from the duration of failure.

**Subject to**
- A maximum allowable downtime and delay in generating proofs to ensure that proofs are produced quickly. *What is the expected recovery period?*

`proofTimeWindow` ensures that even if a griefing attack occurs and provers with the best hardware attempt to monopolize the rewards, they still have to spend/wait a significant amount of time proving each batch. This could potentially make it more difficult for a small group of provers to dominate the process.

- Provers have access to the necessary computational resources, such as CPU, memory, and storage to generate proofs efficiently.
- The protocol should be resilient against such inactivity attacks. The number of provers can be dynamically adjusted based on network conditions via economic Incentives. *If you have 1.5x redundancy, then should you expect your system to have 1.5x costs?*
#
**Maximize**
**Prover Reputation Score (PRS)**

- **Prover Uptime (PU)** represents the amount of time a prover is available and actively participating in the network. It can be measured in units of time or epochs?
- **Prover Reliability (PR)** factor accounts for the reliability of each prover in terms of their ability to generate proofs accurately and without errors.

**Subject to**
- A minimum level reputation score (uptime and reliability) to ensure network security.
- A minimum number of provers ready to generate proofs.
- A minimum level of participation from each prover to prevent free-riding and ensure an active and competitive environment.

## 3. Decentralization
The goal is to prevent leading to centralization or monopolization, Sybil attacks.

**Maximize**
**Geographic Diversity (GD)**


**Subject to**
- A minimum distance or separation between provers in the same geographic region to ensure that they are not concentrated in a small area within the region to detect Sybil attacks.

#
**Minimize**
**Resource Distribution Inequality (RDI)**
The primary goal is to quantify the overall inequality, taking into account both within-group and between-group inequality, in the distribution of resource concentration among provers in the network.

- **Computing Power Concentration (CPC)** as the Theil T for computing power distribution.
- **Stake Concentration (SC)** as the Theil T for stake distribution.

### **$RDI = CPC + SC$**

**Subject to**
- A maximum level of inequality index…
- else use incentives…
- A minimum computing power and stake that each prover can contribute to and hold in the network.
- *Distributed prover system for large circuits?*

## 4. Honest Behaviour

The primary goal is to incentivize provers to behave honestly.

**Maximize**
### **$Honest Behavior = Reward - Penalty$**


* **V** is the number of valid proofs submitted by the prover.
* **Base Reward/ Penalty** is the fixed reward assigned to each valid/invalid proof.
* **C** is the complexity of the computations involved.
* **Complexity Bonus** is a coefficient that rewards more complex computations.
* **I** represents the number of incorrect or invalid proofs.
* **Penalty Severity** is a coefficient that determines the severity of the penalty based on the degree of misbehavio

**Subject to**
- A maximum amount of reward that can be earned by honest provers.
- *Also, penalize provers who are re-ordering tx to extract MEV?*