Abstract
We consider the capabilities of probabilistic FIN-type learners who must always produce programs (i.e., hypotheses) that halt on every input. We show that the structure of the learning capability of probabilistic and team learning with success ratio above 1/2 in PFIN-type learning is analogous to the structure observed in FIN-type learning. On the contrary, the structure of probabilistic and team learning with success ratio at or below 1/2 is more sparse for PFIN-type learning than FIN-type learning. For n ≥2, we show that the probabilistic hierarchy below 1/2 for PFIN-type learning is defined by the sequence 4n/9n−2, which has an accumulation point at 4/9. We also show that the power of redundancy at the accumulation point 4/9 is different from the one observed at 1/2. More interestingly, for the first time, we show the power of redundancy even at points that are not accumulation points.
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© 1992 Springer-Verlag Berlin Heidelberg
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Daley, R., Kalyanasundaram, B., Velauthapillai, M. (1992). The power of probabilism in Popperian FINite learning. In: Jantke, K.P. (eds) Analogical and Inductive Inference. AII 1992. Lecture Notes in Computer Science, vol 642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56004-1_11
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DOI: https://doi.org/10.1007/3-540-56004-1_11
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