Partial Recursive Function

Some articles on recursive, recursive functions, partial recursive function, recursive function, functions:

Tennenbaum's Theorem - Recursive Structures For PA
... A structure in the language of PA is recursive if there are recursive functions + and × from to, a recursive two-place relation < on, and ... Because the isomorphism must be a bijection, every recursive model is countable ...
Recursively Enumerable Set - Equivalent Formulations
... That is, S is the domain (co-range) of a partial recursive function ... There is a partial recursive function f such that Enumerability The set S is the range of a partial recursive function ... The set S is the range of a total recursive function or empty ...
Counter Machine - Two-counter Machines Are Turing Equivalent (with A Caveat) - The Caveat: *If* Its Counters Are Initialised To N and 0, Then A 2CM Cannot Calculate 2N
... This result, together with a list of other functions of N that are not calculable by a two-counter machine — when initialised with N in one counter and 0 in the other — such as N2, sqrt(N), log2(N), etc ... cf Minsky 1967170-174) "Theorem A 3CM can compute any partial recursive function of one variable ... "Corollary A 2CM can compute any partial recursive function of one argument, provided the input is coded as 2N and the output (if the machine halts) is coded as 2answer." (p ...
Adequate Pointclass
... can be called adequate if it contains all recursive pointsets and is closed under recursive substitution, bounded universal and existential quantification and preimages by recursive functions This ...
Counter Machine Models - The Models in More Detail - 1961: Minsky's Model of A Partial Recursive Function Reduced To A "program" of Only Two Instructions
... led Minsky to the following definition of "an interesting basis for recursive function theory involving programs of only the simplest arithmetic ... His "Theorem Ia" asserts that any partial recursive function is represented by "a program operating on two integers S1 and S2 using instructions Ij of the forms (cf Minsky (1961) p ... a second "Theorem IIa" that "...represents any partial recursive function by a program operating on one integer S using instructions Ij of the forms" Action Description a ...

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