Zadání

1. DS(n)

2. DS(n³)

3. DT(2^{(n^3)})

4. NS(n*log(n))

5. NT(n*log(n))

Řešení

Bez záruky

DS(n) a DS(n³)

Z prostorové hiearchie DS(n) ⊂ DS(n³).

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DS(n) a NS(n*log(n))

DS(n) ⊂ DS(nlog(n)) ⊆ NS(nlog(n))

DS(n) a NT(n*log(n))

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DS(n³) a NS(n*log(n))

NS(nlog(n)) ⊆ DS((nlog(n))²) ⊂ DS(n³)

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DT(2^{(n^3)}) a NS(n*log(n))

Savičova věta: NS(nlog(n)) ⊆ DS(n²(log(n))²)<BR> Věta o prostorové hierarchii: DS(n²*(log(n))² ⊂ DS(n^5/2)<BR>

L ∈ NS(n*log(n)) ⊂ DS(n^5/2) => L ∈ DT(C_L^{n^(5/2)}) = DT(2^{log(CL)*n^(5/2)}) ⊂ DT(2^{(n^3)})

DT(2^{(n^3)}) a NT(n*log(n))

NT(nlog(n)) ⊆ NS(nlog(n)) a zřetězit s předchozím (tranzitivita)

NS(nlog(n)) a NT(nlog(n))

NS(nlog(n)) ⊇ NT(nlog(n))