Asked by leilani
sian is writting an algorithm for a computer program with her awarness of the algorithmic theories written by stephen kleene she is adhering to the boundaries of modern algorithms which of the following decribes sians algorithm
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Short answer: her algorithm is a computable (recursive) function — i.e. a mu‑recursive (equivalently Turing‑computable / λ‑definable) procedure.
Brief explanation: Kleene formalized effective procedures as the class of recursive functions (primitive recursive plus the μ‑operator). If Sian’s procedure always halts on every input it is a total (general) recursive function; if it may fail to halt on some inputs it is a partial (mu‑recursive) function. Both notions are equivalent in power to Turing machines and the λ‑calculus by the Church–Turing thesis.
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Brief explanation: Kleene formalized effective procedures as the class of recursive functions (primitive recursive plus the μ‑operator). If Sian’s procedure always halts on every input it is a total (general) recursive function; if it may fail to halt on some inputs it is a partial (mu‑recursive) function. Both notions are equivalent in power to Turing machines and the λ‑calculus by the Church–Turing thesis.
If you have the multiple‑choice options, paste them and I’ll pick the best match.
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