Question: [46] Prove that simulating a linear-time 2-tape deterministic Turing machine with one-way input by a 1-tape nondeterministic Turing machine with one-way input requires (n2/ log(k)

[46] Prove that simulating a linear-time 2-tape deterministic Turing machine with one-way input by a 1-tape nondeterministic Turing machine with one-way input requires Ω(n2/ log(k) n) time, for any k, where log(k) = log log ··· log is the k-fold iterated logarithm. This improves the result in Exercise 6.10.4.

Comments. Source: [Z. Galil, R. Kannan, and E. Szemer´edi, J. Comput.

System Sci., 38(1989), 134–149; Combinatorica, 9(1989), 9–19].

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