Question: [30] Prove the following stability property. Deep strings cannot be quickly computed from shallow ones. More precisely, there is a polynomial p and a constant

[30] Prove the following ‘stability property.’ Deep strings cannot be quickly computed from shallow ones. More precisely, there is a polynomial p and a constant

c, both depending only on the universal machine U, such that, if q is a program to compute x in d steps and if q is less than

(d, b)-deep, then x is less than (d + p(d

), b + c)-deep.

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