Formal Definition of Agent Autonomy

Autonomy Dimensions

We define AI Agent autonomy as the product of three dimensions:

Autonomy(Agent) = Compute_Capability × Physical_Capability × Payment_Capability

(1) Compute Capability

Defined as the set of computational resources accessible to the Agent:

C = {CPU_cores, Memory_GB, Storage_TB, GPU_hours, Network_bandwidth}

In PACT, the PactCompute module provides decentralized access to these resources.

(2) Physical Capability

Defined as the set of physical task types the Agent can complete:

P = {Task_types, Geographic_coverage, Time_availability}

In PACT, the PactTasks module provides this capability through the human worker network.

(3) Payment Capability

Defined as the Agent's autonomous payment and fund management capability:

Pay = {Balance, Payment_protocol, Gas_abstraction, Budget_management}

In PACT, the PactPay module and X402 protocol provide gasless automatic payments.

State Machine Model

An Agent can be modeled as an Extended Finite State Machine:

Agent_FSM = (S, A, T, s₀, F)

Where:
- S is the state set: {Idle, Computing, TaskPublishing, Waiting, Verifying, Paying}
- A is the action set: {compute(), publish_task(), wait(), verify(), pay()}
- T: S × A × Conditions → S is the state transition function
- s₀ ∈ S is the initial state
- F ⊆ S is the set of terminal states

Autonomy Metric

Define the Agent's Autonomy Index as:

AI(agent) = w₁·log(|C|) + w₂·log(|P|) + w₃·log(Balance) + w₄·(1 - Human_intervention_rate)

Where:

• w₁, w₂, w₃, w₄ are weight coefficients satisfying Σwᵢ = 1

• Human_intervention_rate is the proportion of operations requiring human intervention

According to Russell & Norvig (2020) [11], a fully autonomous Agent should satisfy AI(agent) > threshold, where threshold is determined by the application scenario.