3.4 InterConnect Rollup: Key for Management and Supervision

InterConnect Rollup is a specialized Layer 2 solution designed to improve transaction throughput and reduce transaction costs by executing transactions on Layer 2 and submitting compressed transaction data to the main chain. It is pivotal for governance and supervision tasks, including managing AI agents, defining data assets, and recording transaction behaviors.

At the core of InterConnect Rollup is the use of Zero-Knowledge Proofs (ZKPs) and Optimized State Channels. ZKPs enable the system to verify the validity of transactions without revealing any sensitive information, ensuring privacy while maintaining trust. This is particularly important in the MAIN system, where the integrity and confidentiality of transactions involving AI agents and data assets are paramount.

The integration of Optimized State Channels further enhances the efficiency of the Rollup. These channels allow for off-chain transactions between agents that can be settled on-chain only when necessary, significantly reducing the computational burden on the main chain. This mechanism is vital for the MAIN system, where numerous interactions between AI agents must be processed swiftly and securely.

InterConnect Rollup also utilizes Recursive Proof Composition, a technique that aggregates multiple proofs into a single, succinct proof that can be quickly verified on the main chain. This approach not only reduces the data load on the blockchain but also ensures that even complex multi-step transactions are validated efficiently. In the context of the MAIN system, this means that complex decision-making processes involving multiple AI agents can be executed and verified with minimal delay, enhancing the system’s overall responsiveness.

Suppose there are $k$ sub-proofs $\pi_1, \pi_2, \dots, \pi_k$, each of which is verified by $\text{Verify}(\pi_i) = \text{True}$. The aggregated proof can be expressed as:

$$\Pi = \text{Aggregate}(\pi_1, \pi_2, \dots, \pi_k).$$

The time complexity of verifying this aggregated proof on the main chain is reduced from $O(k)$ to $O(1)$, thereby effectively reducing the blockchain’s data load and improving verification efficiency.

Moreover, the Rollup incorporates Plonk Protocol (Permutation Argument for Knowledge), a highly efficient ZKP protocol that allows for universal, updatable circuits. This flexibility is crucial for the MAIN system, where the rules and parameters governing AI agents may evolve over time. The Plonk Protocol ensures that these updates can be integrated seamlessly without the need for significant re-engineering, thereby supporting the dynamic nature of the MAIN ecosystem. In the Plonk protocol, the proof generation process for a circuit $C$ can be represented as:

$$\text{Proof} = \text{Prove}(C, w, \{a_i\}, \{b_j\}),$$

where $w$ is the witness for the circuit, and $\{a_i\}$ and $\{b_j\}$ are the sets of input and output parameters, respectively. The Plonk protocol uses a permutation argument to ensure the consistency and correctness of the computation, specifically:

$$\text{Permutation Argument} = \prod_{i=1}^{n} \frac{L_i(x)}{R_i(x)} = \prod_{i=1}^{n} S_{\sigma(i)}(x),$$

where $L_i(x)$ and $R_i(x)$ are the left and right polynomials, respectively, and $S_{\sigma(i)}(x)$ is the permutation polynomial.

Finally, the governance aspect of InterConnect Rollup is fortified by On-Chain Governance Models that leverage the security and transparency of the main chain. These models ensure that any changes to the Rollup’s operational parameters, such as those affecting AI agent management or data asset definitions, are made transparently and with community consensus.