A Myhill-Nerode Characterization and Active Learning for One-Clock Timed Automata

TL;DR

This paper introduces a Myhill-Nerode characterization for one-clock deterministic timed automata and develops L*-style algorithms for learning their canonical forms.

Contribution

It provides a novel Myhill-Nerode style framework for 1-DTA and algorithms for actively learning their canonical automata.

Findings

New characterization based on half-integral words and reset information

L*-style algorithms successfully learn canonical 1-DTA

Addresses challenges of resets in automata with a single clock

Abstract

We present a Myhill-Nerode style characterization for languages recognized by one-clock deterministic timed automata (1-DTA). Although there is only one clock, distinct automata may reset it differently along the same word. This adds a significant challenge in the search for a canonical automaton. Our characterization is based on a new perspective of 1-DTAs in terms of "half-integral" words that they accept, along with the reset information encoded by them. We apply our results to develop L* style algorithms that learn the canonical 1-DTA.