[Solved]: What is known about coRL and RL?

Problem Detail: 

Wondering about any known relations between $\mathsf{RL}$ complexity class (one sided error with logarithmic space) and its complementary class, $\mathsf{coRL}$.

Are they the same class?

What are $\mathsf{coRL}$'s relation to $\mathsf{NL}$, $\mathsf{P}$?

Asked By : Uri

Answered By : Abuzer Yakaryilmaz

By definition, $ \mathsf{RL} $ is a subset of $ \mathsf{NL} $, and so $ \mathsf{coRL} $ is a subset of $ \mathsf{coNL} $.

Since $ \mathsf{NL} = \mathsf{coNL} $, $ \mathsf{coRL} $ is also subset of $ \mathsf{NL} $.

Moreover, $ \mathsf{NL} \subseteq \mathsf{P} $.

Please also note that although it is widely believed to be true, whether $ \mathsf{RL} \subseteq \mathsf{L} $ is still an open problem, and so is whether $ \mathsf{coRL} \subseteq \mathsf{L} $. (The obviuos relation is $ \mathsf{L} \subseteq \mathsf{RL} \cap \mathsf{coRL} $.)

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Question Source : http://cs.stackexchange.com/questions/3031

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