Mixed Choice in Asynchronous Multiparty Session Types

The AI agent ecosystem has converged on two protocols: the Model Context Protocol (MCP) for tool invocation and Agent-to-Agent (A2A) for single-principal task delegation. Both assume a single controlling principal, meaning one person or organization that owns every agent. When independent principals' agents must coordinate over shared state, such as engineers' coding agents editing the same repository, family members planning a shared trip, or agents from different organizations negotiating a joint decision, neither protocol applies, and coordination collapses to ad-hoc chat, manual merging, or silent overwrites. We present MPAC (Multi-Principal Agent Coordination Protocol), an application-layer protocol that fills this gap with explicit coordination semantics across five layers: Session, Intent, Operation, Conflict, and Governance. MPAC makes intent declaration a precondition for action, represents conflicts as first-class structured objects, and supports human-in-the-loop arbitration through a pluggable governance layer. The specification defines 21 message types, three state machines with normative transition tables, Lamport-clock causal watermarking, two execution models, three security profiles, and optimistic concurrency control on shared state. We release two interoperable reference implementations in Python and TypeScript with 223 tests, a JSON Schema suite, and seven live multi-agent demos. A controlled three-agent code review benchmark shows a 95 percent reduction in coordination overhead and a 4.8 times wall-clock speedup versus a serialized human-mediated baseline, with per-agent decision time preserved. The speedup comes from eliminating coordination waits, not compressing model calls. Specification, implementations, and demos are open source.

Ensuring behavioural correctness in communication protocols is a central challenge in distributed software systems, as subtle inconsistencies can lead to deadlocks. In such settings, protocol refinement - the safe substitution of a protocol that preserves correctness and compatibility with other components - is essential. Large language models (LLMs) have demonstrated strong capabilities in code generation and program synthesis, yet lack mechanisms to reliably produce outputs with correct behaviour. Formal specification approaches, such as multiparty session types (MPST), offer rigorous guarantees, including deadlock freedom, but provide limited support for automatically constructing protocol refinements. In this paper, we present Syntropy, a framework for synthesising protocol refinements guided by MPST specifications and LLMs. It incorporates refinement constraints directly into the generation process, ensuring the generated variants satisfy these guarantees. Our comprehensive evaluation indicates that Syntropy achieves 95.6%-99.5% validity while maintaining high syntactic correctness, and produces diverse, non-trivial refinements across multiple LLMs.

Multi-agent LLM orchestration incurs synchronization costs scaling as O(n x S x |D|) in agents, steps, and artifact size under naive broadcast -- a regime I term broadcast-induced triply-multiplicative overhead. I argue this pathology is a structural residue of full-state rebroadcast, not an inherent property of multi-agent coordination. The central claim: synchronization cost explosion in LLM multi-agent systems maps with formal precision onto the cache coherence problem in shared-memory multiprocessors, and MESI-protocol invalidation transfers to artifact synchronization under minimal structural modification. I construct the Artifact Coherence System (ACS) and prove the Token Coherence Theorem: lazy invalidation attenuates cost by at least S/(n + W(d_i)) when S > n + W(d_i), converting O(n x S x |D|) to O((n + W) x |D|). A TLA+-verified protocol enforces single-writer safety, monotonic versioning, and bounded staleness across ~2,400 explored states. Simulation across four workload configurations yields token savings of 95.0% +/- 1.3% at V=0.05, 92.3% +/- 1.4% at V=0.10, 88.3% +/- 1.5% at V=0.25, and 84.2% +/- 1.3% at V=0.50 -- each exceeding the theorem's conservative lower bounds. Savings of ~81% persist at V=0.9, contrary to the predicted collapse threshold. Contributions: (1) formal MESI-to-artifact state mapping; (2) Token Coherence Theorem as savings lower bound; (3) TLA+-verified protocol with three proven invariants; (4) characterization of conditional artifact access semantics resolving the always-read objection; (5) reference Python implementation integrating with LangGraph, CrewAI, and AutoGen via thin adapter layers.