Agent Hunt: Bounty Based Collaborative Autoformalization With LLM Agents

2026-03-06

AI Summary

This work addresses the inefficiency and poor scalability of automating formalization in interactive theorem proving for algebraic topology by proposing a bounty-driven multi-agent collaboration framework. Leveraging large language model–powered agents, the framework dynamically generates lemmas, issues bounty tasks, and orchestrates competitive completion within the proof environment. By integrating tactic invocation with proof state analysis, it enables decentralized introduction of definitions, iterative strategy refinement, and incremental theory construction. Experimental results demonstrate that this approach overcomes the limitations of traditional static planning, successfully achieving large-scale automatic formalization of algebraic topology content, with all generated proofs rigorously validated by the underlying proof assistant.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Multiagent Systems: Multiagent Planning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We describe an experiment in large-scale autoformalization of algebraic topology in an Interactive Theorem Proving (ITP) environment, where the workload is distributed among multiple LLM-based coding agents. Rather than relying on static central planning, we implement a simulated bounty-based marketplace in which agents dynamically propose new lemmas (formal statements), attach bounties to them, and compete to discharge these proof obligations and claim the bounties. The agents interact directly with the interactive proof system: they can invoke tactics, inspect proof states and goals, analyze tactic successes and failures, and iteratively refine their proof scripts. In addition to constructing proofs, agents may introduce new formal definitions and intermediate lemmas to structure the development. All accepted proofs are ultimately checked and verified by the underlying proof assistant. This setting explores collaborative, decentralized proof search and theory building, and the use of market-inspired mechanisms to scale autoformalization in ITP.

Problem

• autoformalization
• interactive theorem proving
• LLM agents
• collaborative proof search
• algebraic topology

Innovation

• bounty-based collaboration
• autoformalization
• LLM agents
• interactive theorem proving
• decentralized proof search