Question: [27/O35] Let T (n), f(n) be functions both computable in time T (n). Prove that C[f(n), T (n), ] C[f(n), c2f(n) T (n), ],

[27/O35] Let T (n), f(n) be functions both computable in time T (n). Prove that C[f(n), T (n), ∞] ⊂ C[f(n), c2f(n)

T (n), ∞], for some constant

c. Open problem: Can we establish a tighter version of this time hierarchy without an exponential-time gap in the hierarchy?

Comments. Source: [L. Longpr´e, Ph.D. thesis, Cornell University, 1986].

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