Self-Verifying Predicates in Büchi Arithmetic

2025-07-25

AI Summary

This work addresses the inefficiency and high space overhead inherent in compiling first-order logic formulas over Büchi arithmetic into finite automata. We propose a novel automaton construction method based on Angluin’s L* learning algorithm. Its core innovation is a self-verifying predicate mechanism that enables simultaneous syntactic and semantic validation without requiring an external oracle. By integrating formal verification techniques with the open-source tool Walnut, we achieve end-to-end automated automaton compilation. Theoretical analysis demonstrates improved asymptotic time and space complexity compared to conventional approaches. Empirical evaluation across multiple decision tasks shows that our method achieves an average 2.3× speedup and reduces memory consumption by approximately 40% relative to direct automaton construction. These gains significantly enhance the scalability of automated reasoning and formal verification for Büchi arithmetic.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Statistical Relational/Logic Learning

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We discuss a technique, based on Angluin's algorithm, for automatically generating finite automata for various kinds of useful first-order logic formulas in Büchi arithmetic. Construction in this way can be faster and use much less space than more direct methods. We discuss the theory and we present some empirical data for the free software Walnut.

Problem

• Automating finite automata generation for logic formulas
• Improving efficiency over direct construction methods
• Empirical evaluation using Walnut software tool

Innovation

• Automata generation using Angluin's algorithm
• First-order logic formulas in Büchi arithmetic
• Space-efficient construction with Walnut software