<p>This would imply that L⊊NP since L⊆TISP(poly(n),n^k) k∈N</p>

CC BY-SA 4.0
2018-09-02T19:50:00.247Z
It also can show $SC \neq NP$ in similar way.
Mohsen Ghorbani
CC BY-SA 4.0
2018-09-02T19:44:24.137Z
2018-09-02T19:44:24.137Z
Avi Tal
<p>Does $\forall k\in \mathbb N \space NP\not\subseteq TISP(poly(n),n^k)$  has any separation of classes or consequences?</p>

<blockquote>
  <p>My main question is can use this to show that $P \neq NP$ or some thing useful about $P \neq NP$ .</p>
</blockquote>

CC BY-SA 4.0
2018-09-03T07:35:01.910Z
Why do we need the $\forall$ quantifier here? If $NP$ is not a subset of $TISP(poly(n),n)$ then your statement should also be true for all $k>1$?
Christian Komusiewicz
CC BY-SA 4.0
2018-09-03T07:52:05.283Z
yes, they are equals. I thought they are different.
Mohsen Ghorbani
CC BY-SA 4.0
2018-09-03T07:58:08.043Z
I think they are equals to $NP \not \subset TISP(poly(n),n^{o(1)})$ too.
Mohsen Ghorbani
<cc.complexity-theory><complexity-classes><lower-bounds><space-time-tradeoff>
Conesequences of $\forall k\in \mathbb N \space NP\not\subseteq TISP(poly(n),n^k)$
Mohsen Ghorbani
# Conesequences of $\forall k\in \mathbb N \space NP\not\subseteq TISP(poly(n),n^k)$

(Asked by: username_0 on 2018-09-02)

Does $\forall k\in \mathbb N \space NP\not\subseteq TISP(poly(n),n^k)$ has any separation of classes or consequences?

> My main question is can use this to show that $P \neq NP$ or some thing useful about $P \neq NP$ .

**Tags:** cc.complexity-theory, complexity-classes, lower-bounds, space-time-tradeoff
> **Comments:**
> **username_1**: Why do we need the $\forall$ quantifier here? If $NP$ is not a subset of $TISP(poly(n),n)$ then your statement should also be true for all $k>1$?  
> **username_0**: yes, they are equals. I thought they are different.  
> **username_0**: I think they are equals to $NP \not \subset TISP(poly(n),n^{o(1)})$ too.  

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## 1 answers

### Answer by username_2 on 2018-09-02. Score: 7 | Accepted answer

This would imply that L⊊NP since L⊆TISP(poly(n),n^k) k∈N

> **Comments:**
> **username_0**: It also can show $SC \neq NP$ in similar way.  

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