Set-Driven and Rearrangement-Independent Learning of Recursive LanguagesAuthor: Steffen Lange and Thomas Zeugmann Source: Mathematical Systems Theory 29, No. 6, 1996, 599 - 634.
Abstract.
The present paper studies the impact of order independence to the
learnability of indexed families Furthermore, we consider the influence of set-drivenness and rearrangement-independence for learning devices that realize the subset principle to different extents. Thereby we distinguish between strong-monotonic, monotonic and weak-monotonic or conservative learning. The results obtained are threefold. First, rearrangement-independent learning does not constitute a restriction except the case of monotonic learning. Next, we prove that for all but two of the considered learning models set-drivenness is a severe restriction. However, class comprising set-driven conservative learning is exactly as powerful as unrestricted class comprising conservative learning. Finally, the power of class comprising set-driven learning in the limit is characterized by equating the collection of learnable indexed families with the collection of class comprisingly conservatively inferable indexed families. These results considerably extend previous work done in the field (cf., e.g., Schäfer-Richter (1984) and Fulk (1990)).
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