Self-Verifying Predicates in B\"uchi Arithmetic

TL;DR

This paper introduces a technique based on Angluin's algorithm for efficiently generating finite automata from first-order logic formulas in B"uchi arithmetic, improving speed and space efficiency over traditional methods.

Contribution

It presents a novel approach using Angluin's algorithm for automata construction in B"uchi arithmetic, with empirical validation on the Walnut software.

Findings

Faster automata generation compared to direct methods

Reduced space usage in automata construction

Empirical results demonstrating practical efficiency

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 B\"uchi 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.