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Humans appear to be able to learn new concepts without needing to be programmed explicitly in any conventional sense. In this paper we regard learning as the phenomenon of knowledge acquisition in the absence of explicit programming. We give a precise methodology for studying this phenomenon from a computational viewpoint. It consists of choosing an(More)
The success of the von Neumann model of sequential computation is attributable to the fact that it is an efficient bridge between software and hardware: high-level languages can be efficiently compiled on to this model; yet it can be effeciently implemented in hardware. The author argues that an analogous bridge between software and hardware in required for(More)
In the theory of recursive functions and computational complexity it has been demonstrated repeatedly that the natural problems tend to cluster together in &#8220;completeness classes&#8221;. These are families of problems that (A) are <underline>computationally</underline> interreducible and (B) are the hardest members of some(More)
In this paper, we prove the intractability of learning several classes of Boolean functions in the distribution-free model (also called the Probably Approximately Correct or PAC model) of learning from examples. These results are <italic>representation independent</italic>, in that they hold regardless of the syntactic form in which the learner chooses to(More)