Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

All Questions

6
votes
1answer
655 views

Notation: SPACE(n) vs SPACE(O(n))

I want to denote the class of problems solvable by linear space multi-tape Turing machines. I have seem in many places this class being denoted by $SPACE(n)$. But why is the notation $SPACE(O(n))$ not ...
1
vote
2answers
83 views

What does $\cdot$ mean as a notation with complexity classes?

In the wikipedia page for Toda's Theorem, the notation $A\cdot B$ is used where $A$ and $B$ are two complexity classes, but without explanation as to its meaning. SO given two classes $A$ and $B$ ...
3
votes
1answer
105 views

Hierarchy of complexity classes $\bigcup_{c > 0} \mathrm{Time}(2^{c \log^k n})$, w.r.t. $k$

This is a true/false question: For each integer $k > 1$, define the complexity class $\sf QP_k := \bigcup_{c > 0} Time(2^{c \log^k n})$. Then for all integers $k > 1$, $\sf QP_k \subsetneq ...