Inference of $\omega$-languages from prefixes

Authors: C. de la Higuera and J. C. Janodet

Source: Theoretical Computer Science Vol. 313, Issue 2, 17 February 2004, pp. 295-312.

Abstract. Büchi automata are used to recognize languages of infinite strings. Such languages have been introduced to describe the behavior of real-time systems or infinite games. The question of inferring them from infinite examples has already been studied, but it may seem more reasonable to believe that the data from which we want to learn is a set of finite strings, namely the prefixes of accepted or rejected infinite strings. We describe the problems of identification in the limit and polynomial identification in the limit from given data associated to different interpretations of these prefixes: a positive prefix is universal (respectively existential) when all the infinite strings of which it is a prefix are in the language (respectively when at least one is); the same applies to the negative prefixes. We prove that the classes of regular $\omega$-languages (those recognized by Büchi automata) and of deterministic $\omega$-languages (those recognized by deterministic Büchi automata) are not identifiable in the limit, whatever interpretation for the prefixes is taken. We give a polynomial algorithm that identifies the class of safe languages from positive existential prefixes and negative universal prefixes. We show that this class is maximal for polynomial identification in the limit from given data, in the sense that no superclass can even be identified in the limit.

©Copyright 2004 Elsevier Science B.V.