L versus P

Is every problem solvable in polynomial time also solvable using only logarithmic memory? This 'L vs P' question is open, just like P vs NP. A proof of P ⊆ L would have major implications for memory-efficient computation.

Most researchers believe L ⊊ P but no proof is known. The space hierarchy theorem implies L ⊊ PSPACE, which is weaker.