If Deterministic and Nondeterministic Space Complexities are Equal for log log n, then they are also Equal for log n

It is well known that for any „well behaved“ space function L(n) ≥ log n if DSPACE(L(n)) = NSPACE(L(n)) then also DSPACE(H(n)) = NSPACE(H(n)) for all „well behaved“ functions H(n) ≥ L(n). The aim of this paper is to show that also if DSPACE(log log n) = NSPACE(log log n) then L = NL (i.e. DSPACE(log n) = NSPACE(log n)).

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