Constructing song syntax by automata induction

We propose a new methodology for ethology in terms of automata induction. Recent studies on Bengalese finch reported unique features of its songs. As opposed to most other songbirds, the songs of the Bengalese finch are neither monotonous nor random; they can be represented by a finite automaton, which we call song syntax [3]. Juvenile finches learn songs from their fathers during a critical period. The song learning has a similarity to the grammatical inference from positive samples, which is known as Angluin's algorithm [1]. This is an induction algorithm for inferring certain subclasses of regular languages, which are known as k-reversible languages, from positive samples, where k = 0,1,2,.... A regular language is k-reversible under the following condition: whenever two prefixes whose last k words match have a tail in common, then these prefixes have all tails in common. For each k, Angluin's algorithm provides a finite automaton that accepts the smallest k-reversible language, including the given finite positive sample within polynomial time.