Use of Reduction Arguments in Determining Popperian FIN-Type Learning Capabilities

Abstract

The main contribution of this paper is the development of analytical tools which permit the determination of team learning capabilities as well as the corresponding types of redundancy for Popperian FINite learning. The basis of our analytical framework is a reduction technique used previously by us. Using our analytical tools we determine the redundancy types for all ratios of the form 4 n/9n−2 , where n ≥2, which defines the sequence of capabilities for probabilistic PFIN-type learners in the interval (4/9,1/2]. We also show that there is unbounded redundancy at the ratio 2/5, i.e., quadrupling the team size and keeping the success ratio will always increase learning power. We also extend, using our tools, the region of known PFIN-type learning capabilities, by presenting an ω_2 sequence of learning capabilities beginning at 1/2 which converges to 2/5. We believe that this sequence forms the backbone of the learning capabilities in this interval, but that the actual capability structure is very much more complex.