Savitch showed in 1970 that nondeterministic logspace (NL) is contained in
deterministic O(log2n) space but his algorithm requires
quasipolynomial time. The question whether we can have a deterministic
algorithm for every problem in NL that requires polylogarithmic space and
simultaneously runs in polynomial time was left open.
In this paper we give a partial solution to this problem and show that for
every language in NL there exists an unambiguous nondeterministic algorithm
that requires O(log2n) space and simultaneously runs in
polynomial time.Comment: Accepted in MFCS 201