Identification of unions of languages drawn from an identifiable class

We follow a line of research begun by Gold and continued by Angluin. Gold defined a property of language classes: identifiability in the limit from positive examples (i.e. text). This means that given any stream of examples drawn from some language in the class it is possible to produce a stream of guesses that converges to the language from which the examples are drawn. Suppose we are given a class of languages that is identifiable from text, and a stream of examples drawn from two of those languages intermixed. Is it possible to converge in the limit to a pair of languages that together explain the examples? The answer is: in general, no. We define a property of language classes that ensures such bilingual identification is possible. We call this property of language classes finite elasticity. Finite elasticity is preserved by the operation of taking unions of pairs of languages. This generalizes a result due to Shinohara. Shinohara has shown that pairs of pattern languages are identifiable from text. It is easy to see that the class of pattern languages has finite elasticity. We now see that Shinohara's result holds for any language class with finite elasticity.