Learning erasing pattern languages with queries

A pattern is a finite string of constant and variable symbols. The non-erasing language generated by a pattern is the set of all strings of constant symbols that can be obtained by substituting non-empty strings for variables. In order to build the erasing language generated by a pattern, it is also admissible to substitute the empty string. The present paper deals with the problem of learning erasing pattern languages within Angluin's model of learning with queries. Moreover, the learnability of erasing pattern languages with queries is studied when additional information is available. The results obtained are compared with previously known results in case non-erasing pattern languages have to be learned. First, when regular pattern languages have to be learned, it is shown that the learnability results for the non-erasing case remain valid, if the proper superclass of all erasing regular pattern languages is the object of learning. Second, in the general case, serious differences have been observed. For instance, it turns out that arbitrary erasing pattern languages cannot be learned in settings in which, in the non-erasing case, even polynomially many queries will suffice.

Authors

• Jochen Nessel
• Steffen Lange

Keywords

• Formal language theory
• Algorithmic learning
• Query inference