# Does solving subproblems in logspace in different models implies solving original problem in logspace?

Let's consider the following situation:

We have a problem $\mathsf{L\text{}}$ . We would like to solve it in $LOGSPACE$. Let assume that our problem $\mathsf{L\text{}}$ can be divided to two parts: $A$ and $B$.

We can solve $A$ using computatation model $M_1$ in $LOGSPACE$.

We can solve $B$ using computation model $M_2$ in $LOGSPACE$, $M_1 \neq M_2$

Does it mean that we can solve $P$ in $LOGSPACE$ ? Why?

• I'm not sure what you mean by solving a problem using some specific computaion model in LOGSPACE. LOGSPACE, by definition, refers to the amount of space used by a Turing machine. (Also, if you're talking about complexity classes, please don't call a problem "$P$" -- that gets really confusing, really fast. ;-) ) Apr 23, 2017 at 11:33
• What does "divide" mean here, precisely? That is essential. Apr 23, 2017 at 15:39

## 1 Answer

The composition of two logspace functions is again in logspace. This is a classical result that you can try to prove on your own.