Minimal Memory Automata

We provide a Myhill-Nerode-like theorem that characterizes the class of data languages recognized by deterministic finite-memory automata (DMA). As a byproduct of this characterization result, we obtain a canonical representation for any DMA-recognizable language. We then show that this canonical automaton is minimal in a strong sense: it has the minimal number of control states and also the minimal amount of internal storage. We finally show how this minimal automaton can be computed