Learning deterministic variable automata over infinite alphabets

Abstract

Automated reasoning about systems with infinite domains requires an extension of automata, and in particular, finite automata, to infinite alphabets. One such model is Variable Finite Automata (VFA). VFAs are finite automata whose alphabet is interpreted as variables that range over an infinite domain. On top of their simple and intuitive structure, VFAs have many appealing properties. One such property is a deterministic fragment (DVFA), which is closed under the Boolean operations, and whose containment and emptiness problems are decidable. These properties are rare amongst the many different models for automata over infinite alphabets. In this paper, we continue to explore the advantages of DVFAs, and show that they have a canonical form, which proves them to be a particularly robust model that is easy to reason about and use in practice. Building on these results, we construct an efficient learning algorithm for DVFAs, based on the $$\textsc {L}^*$$ algorithm for regular languages.