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TM 은 μ - 재귀 부분함수다 .

TM 은 μ - 재귀 부분함수다. TM 의 상황 ( α , p , β ) ↔ (w, p, n) α , β ∈ Γ *, p ∈ Q, w, p, n ∈ N. w = # | Γ | ( αβ ) R , p ∈ {0, … , |Q|-1}, n ∈ {1, … , | αβ |}, 단 q s = 1 , q f = 0 , 현재 n = | α |+1. 1: β = (w÷b n-1 )↓( b∙( w ÷b n )) step: N 3 → N 3 : (w, p, n) → (w’, p’, n’).

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TM 은 μ - 재귀 부분함수다 .

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  1. TM은 μ-재귀 부분함수다. • TM의 상황 (α, p, β) ↔ (w, p, n) • α, β ∈ Γ*, p ∈ Q, w, p, n ∈ N. • w = #|Γ|(αβ)R, p ∈ {0, …, |Q|-1}, n ∈ {1, …, |αβ|}, 단 qs= 1, qf= 0, 현재 n = |α|+1. • 1:β = (w÷bn-1)↓(b∙(w÷bn)) • step: N3 → N3: (w, p, n) → (w’, p’, n’). • 기본재귀함수. • run: N3ⅹ N → N3: • run(w, p, n, 0) = (w, p, n) • run(w, p, n, t+1) = step(run(w, p, n, t)) 기본재귀함수. • stoptime(w) = μ t [π23(w, 1, 1) = 0] • stoptime은 μ-재귀 부분함수다. • fTM(w) = π13(run(w, 1, 1, stoptime(w)). • fTM도 μ-재귀 부분함수다. 한국과학기술원 전산학과 최광무

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