Active Learning of Symbolic Automata Over Rational Numbers

TL;DR

This paper extends the classical $L^*$ automata learning algorithm to handle symbolic automata with transitions over rational numbers, enabling applications in infinite alphabets like real RGX and time series, with optimal query complexity.

Contribution

It introduces a novel extension of the $L^*$ algorithm to learn symbolic automata over infinite rational alphabets, broadening its applicability.

Findings

Algorithm is optimal in query complexity

Enables learning automata over infinite alphabets

Applicable to real RGX and time series

Abstract

Automata learning has many applications in artificial intelligence and software engineering. Central to these applications is the $L^*$ algorithm, introduced by Angluin. The $L^*$ algorithm learns deterministic finite-state automata (DFAs) in polynomial time when provided with a minimally adequate teacher. Unfortunately, the $L^*$ algorithm can only learn DFAs over finite alphabets, which limits its applicability. In this paper, we extend $L^*$ to learn symbolic automata whose transitions use predicates over rational numbers, i.e., over infinite and dense alphabets. Our result makes the $L^*$ algorithm applicable to new settings like (real) RGX, and time series. Furthermore, our proposed algorithm is optimal in the sense that it asks a number of queries to the teacher that is at most linear with respect to the number of transitions, and to the representation size of the predicates.