Agent communication remains a foundational problem in multi-agent systems: protocols such as FIPA-ACL guarantee semantic richness but are intractable for constrained environments, while lightweight IoT protocols achieve efficiency at the expense of expressiveness. This paper presents $μ$ACP, a formal calculus for expressive agent communication under explicit resource bounds. We formalize the Resource-Constrained Agent Communication (RCAC) model, prove that a minimal four-verb basis \textit{\{PING, TELL, ASK, OBSERVE\}} is suffices to encode finite-state FIPA protocols, and establish tight information-theoretic bounds on message complexity. We further show that $μ$ACP can implement standard consensus under partial synchrony and crash faults, yielding a constructive coordination framework for edge-native agents. Formal verification in TLA$^{+}$ (model checking) and Coq (mechanized invariants) establishes safety and boundedness, and supports liveness under modeled assumptions. Large-scale system simulations confirm ACP achieves a median end-to-end message latency of 34 ms (95th percentile 104 ms) at scale, outperforming prior agent and IoT protocols under severe resource constraints. The main contribution is a unified calculus that reconciles semantic expressiveness with provable efficiency, providing a rigorous foundation for the next generation of resource-constrained multi-agent systems.

翻译：智能体通信仍然是多智能体系统中的基础性问题：诸如FIPA-ACL等协议虽能保证语义丰富性，但在受限环境中难以实现；而轻量级物联网协议虽实现了高效性，却以牺牲表达能力为代价。本文提出$μ$ACP，一种在显式资源约束下实现表达能力的形式化智能体通信演算。我们形式化了资源受限智能体通信（RCAC）模型，证明了最小四动词基 \textit{\{PING, TELL, ASK, OBSERVE\}} 足以编码有限状态FIPA协议，并建立了消息复杂度的紧信息论界。我们进一步证明$μ$ACP能够在部分同步与崩溃故障下实现标准共识，从而为边缘原生智能体提供了一个构造性协调框架。通过TLA$^{+}$（模型检测）与Coq（机械化不变量）的形式化验证，确立了系统的安全性与有界性，并在建模假设下支持活性。大规模系统仿真证实，在严重资源约束下，ACP实现了34毫秒的中位数端到端消息延迟（95分位数为104毫秒），优于现有智能体与物联网协议。主要贡献在于提出了一种统一演算，将语义表达能力与可证明的效率相统一，为下一代资源受限多智能体系统提供了严格的理论基础。