# Zadání #

1. DS(n)
1. DS(n<sup>3</sup>)
1. DT(2<sup>(n^3)</sup>)
1. NS(n*log(n))
1. NT(n*log(n))

# Řešení #

Bez záruky

## DS(n) a DS(n<sup>3</sup>) ##

Z prostorové hiearchie DS(n) ⊂ DS(n<sup>3</sup>).

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

DS(n) ⊂ DS(n*log(n)) ⊆ NS(n*log(n))

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

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## DS(n<sup>3</sup>) a NS(n*log(n)) ##

NS(n*log(n)) ⊆ DS((n*log(n))<sup>2</sup>) ⊂ DS(n<sup>3</sup>)

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## DT(2<sup>(n^3)</sup>) a NS(n*log(n)) ##

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

L ∈ NS(n*log(n)) ⊂ DS(n<sup>5/2</sup>) => L ∈ DT(C<sub>L</sub><sup>n^(5/2)</sup>) = DT(2<sup>log(CL)*n^(5/2)</sup>) ⊂ DT(2<sup>(n^3)</sup>)

## DT(2<sup>(n^3)</sup>) a NT(n*log(n)) ##

NT(n*log(n)) ⊆ NS(n*log(n)) a zřetězit s předchozím (tranzitivita)

## NS(n*log(n)) a NT(n*log(n)) ##

NS(n*log(n)) ⊇ NT(n*log(n))