General form recursive equations I
In this article the general form recursive equations (GFRE) are considered. A necessary and sufficient condition for these equations to have a solution in the family of partial recursive functions is found. We show that there exists such a GFRE that, in contrast with usual case, it has a non-computable solution but has no solution in the class P of partial recursive functions. The problem of solution existence to GFRE is shown to be Σ 3 0 -complete and Σ 1 1 -complete in the classes P and the class of total recursive functions, respectively.
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