Abstract

The present paper studies the problem of when a team of learning machines can be aggregated into a single learning machine without any loss in learning power. The main results concern aggregation ratios for vacillatory identification of languages from texts. For a positiveinteger n,amachine is said to TxtFex n -identify a language L just in case the machine converges to up to n grammars for L on any text for L.For such identification criteria, the aggregation ratio is derived for the n = 2 case. It is shown that the collection of languages that can be TxtFex 2 identified by teams with success ratio greater than 5=6 are the same as those collections of languages that can be TxtFex 2 - identified by a single machine. It is also established that 5=6 is indeed the cut-off point by showing that there are collections of languages that can be TxtFex 2 -identified bya team employing 6 machines, at least 5 of which are required to be successful, but cannot be TxtFex 2 -identified byany single machine. Additionally, aggregation ratios are also derived for finite identification of languages from positive data and for numerous criteria involving language learning from both positive and negative data.

Citations