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On speed-up of function synthesis and prediction
Abstract
Duplicate of:
https://www.researchgate.net/publication/316715194_On_speed-up_of_function_synthesis_and_prediction
In designing a new algorithm we usually begin with considering a number of examples and then try to generalize them. These examples are mainly input-output examples or sample computations (computation traces, histories of computations) explaining the algorithm's behavior. The aim of our research is to understand and formalize the process of this generalization and eventually to design practical synthesizers.
Within the frameworks of learning in the limit of indexed classes of recursive languages from positive data and automatic learning in the limit of indexed classes of regular languages (with automatically computable sets of indices), we study the problem of minimizing the maximum number of mind changes FM(n) by a learner M on all languages with indices not exceeding n. For inductive inference of recursive languages, we establish two conditions under which FM(n) can be made smaller than any recursive unbounded non-decreasing function. We also establish how FM(n) is affected if at least one of these two conditions does not hold. In the case of automatic learning, some partial results addressing speeding up the function F M(n) are obtained.
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