Learning Transparent Data Automata

This paper studies the problem of learning data automata (DA), a recently introduced model for defining languages of data words which are finite sequences of pairs of letters from a finite and, respectively, infinite alphabet. The model of DA is closely related to general Petri nets, for which no active learning algorithms have been introduced so far. This paper defines transparent data automata (tDA) as a strict subclass of deterministic DA. Yet, it is shown that every language accepted by DA can be obtained as the projection of the language of some tDA. The model of class memory automata (CMA) is known to be equally expressive as DA. However deterministic DA are shown to be strictly less expressive than deterministic CMA. For the latter, and hence for tDA, equivalence is shown to be decidable. On these grounds, in the spirit of Angluin’s L∗ algorithm we develop an active learning algorithm for tDA. They are incomparable to register automata and variants, for which learning algorithms were given recently.