# What would be the consequences if P=NL

I haven't found anything in the literature that suggests what would happen if that is the case. Thank you, Akash

$$NL=P$$ is not considered likely by the experts.

I found a few SE questions on this topic: [1] [2]

The corollaries include:

$$P\subseteq L^2$$ by Savitch's theorem

$$NC=P$$ by the Squeeze theorem

$$EXP=PSPACE$$ by $$P\subseteq polyL$$

I would like to include or exclude $$P=L^k$$, $$k\in[1,2]$$, but I have not collected sufficient evidence for or against that conclusion.

• Thank you so much May 11 '19 at 23:23
• It's also worth mentioning $P \subsetneq PSPACE$ as a new separation. May 26 '19 at 8:40