A Quasiorder-based Perspective on Residual Automata

TL;DR

This paper introduces a quasiorder-based framework for residual automata, including new constructions and methods, offering fresh insights and a novel perspective on residual automata and their learning algorithms.

Contribution

It presents a new residualization operation, a generalized double-reversal method, and a quasiorder perspective on residual automata and NL* algorithm, advancing theoretical understanding.

Findings

Quasiorders are fundamental to residual automata.

New residualization operation improves automaton construction.

A generalized double-reversal method for canonical residual automata.

Abstract

In this work, we define a framework of automata constructions based on quasiorders over words to provide new insights on the class of residual automata. We present a new residualization operation and a generalized double-reversal method for building the canonical residual automaton for a given language. Finally, we use our framework to offer a quasiorder-based perspective on NL*, an online learning algorithm for residual automata. We conclude that quasiorders are fundamental to residual automata as congruences are to deterministic automata.