Abstract
Measure and category (or rather, their recursion theoretical counterparts) have been used in Theoretical Computer Science to make precise the intuitive notion “for most of the recursive sets.” We use the notions of effective measure and category to discuss the relative sizes of inferrible sets, and their complements. We find that inferrible sets become large rather quickly in the standard hierarchies of learnability. On the other hand, the complements of the learnable sets are all large.
Supported in part by NSF Grant CCR 92-53582.
Supported in part by Latvian Council of Science Grant 93.599 and NSF Grant 9119540.
Supported in part by NSF Grant 9301339.
Supported in part by NSF Grants 9119540 and 9301339.
Supported by the Deutsche Forschungsgemeinschaft (DFG) Grant Me 672/4-2.
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Fortnow, L. et al. (1995). Measure, category and learning theory. In: Fülöp, Z., Gécseg, F. (eds) Automata, Languages and Programming. ICALP 1995. Lecture Notes in Computer Science, vol 944. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60084-1_105
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DOI: https://doi.org/10.1007/3-540-60084-1_105
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