Abstract
A series of existing lower bound results for one-tape Turing machines (TM's) is extended to the strongest such model for the computation of functions: one-tape off-line TM's with a write-only output tape. (“Off-line” means: having a two-way input tape.) The following optimal lower bound is shown: Computing the transpose of Boolean ℓ×ℓ-matrices takes Ω(ℓ5/2)=Ω(n5/4) steps on such TM's. (n=ℓ2 is the length of the input.)
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