Abstract
This chapter focuses on primitive recursiveness and search, which give the class of general recursive partial functions. It develops tools for showing that certain functions are in this class. These tools are used to study computability by register-machine programs. The search operator provides a useful way of defining a function in terms of a “search” for the first time a given condition is satisfied. Earlier the collection of primitive recursive functions cannot contain all of the effectively calculable total functions. This chapter presents theorem to show that the constructions preserve primitive recursiveness. That is, when applied to primitive recursive relations, they produce primitive recursive relations. This theorem is useful in extending the supply of primitive recursive relations and functions. The class of general recursive partial functions is obtained that allows functions to be built up by use of search.
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