The Learnability of Simple Deterministic Finite-Memory Automata

The present paper establishes the learnability of simple deterministic finitememory automata via membership and equivalence queries. Simple deterministic finite-memory automata are a subclass of deterministic finite-memory automata introduced by Kaminski and Francez [9] as a model generalizing finite-state automata to infinite alphabets. For arriving at a meaningful learning model we first prove the equivalence problem for simple deterministic finite-memory automata to be decidable by reducing it to the equivalence problem for finite-state automata. In particular, we present a decision algorithm taking as input any two simple deterministic finite-memory automata A and B which computes a number k from A and B as well as two finite state automata DlA, iMB over a finite alphabet C of cardinality k such that A and B are equivalent iff PIA and &Ia are equivalent over C. Next, we provide the announced learning algorithm and prove its running time to be polynomially bounded in the length of a longest counter example returned, in k, the number described above, and in n the number of states of a minimum deterministic finite state automata being consistent with the target language over a finite alphabet of cardinality k.