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In statistical setting of the pattern recognition problem the number ofexamples required to approximate an unknown labelling function is linear in theVC dimension of the target learning class. In this work we consider thequestion whether such bounds exist if we restrict our attention to computablepattern recognition methods, assuming that the unknown labelling function isalso computable. We find that in this case the number of examples required fora computable method to approximate the labelling function not only is notlinear, but grows faster (in the VC dimension of the class) than any computablefunction. No time or space constraints are put on the predictors or targetfunctions; the only resource we consider is the training examples.  The task of pattern recognition is considered in conjunction with anotherlearning problem -- data compression. An impossibility result for the task ofdata compression allows us to estimate the sample complexity for patternrecognition

Sample Complexity for Computational Classification Problems