  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.
