Quotient deterministic finite automaton by indistinguishable states
= Quotient deterministic finite automaton by indistinguishable states
Indistinguishability is a right-invariant equivalence relation. The quotient has states $[q]$, transition $[q]\mapsto[\delta(q,a)]$, initial state $[q_0]$, and accepting classes represented by accepting states. It accepts the original language and has no two distinct indistinguishable states.