Abstract
Circuit expressions were introduced to provide a natural link between Computational Learning and certain aspects of Structural Complexity. Upper and lower bounds on the learnability of circuit expressions are known. We study here the case in which the circuit expressions are of low (time-bounded) Kolmogorov complexity. We show that these are polynomial-time learnable from membership queries in the presence of an NP oracle. We also exactly characterize the sets that have such circuit expressions, and precisely identify the subclass whose circuit expressions can be learned from membership queries alone. The extension of the results to various Kolmogorov complexity bounds is discussed.
Work partially supported by the EC through the Esprit program (project 7141, ALCOM-II, and Working Group 8556, NeuroColt), and through the HCM program (project CHRX-CT93-0451, COLORET Network), by the Dutch NWO, and by the Spanish DGICYT (project PB92-07099).
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© 1995 Springer-Verlag Berlin Heidelberg
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Balcázar, J.L., Buhrman, H., Hermo, M. (1995). Learnability of Kolmogorov-easy circuit expressions via queries. In: Vitányi, P. (eds) Computational Learning Theory. EuroCOLT 1995. Lecture Notes in Computer Science, vol 904. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59119-2_172
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DOI: https://doi.org/10.1007/3-540-59119-2_172
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