Notes

Chapter 12: The Principle of Computational Equivalence

Section 8: Undecidability and Intractability


Properties [of example Turing machines]

The maximum numbers of steps increase with input size according to:

(a) 14 2^Floor[n/2] - 11 + 2Mod[n, 2]

(b) (does not halt for x = 1)

(c) 2n - 1

(d) (7(1 + Mod[n, 2])4^Floor[n/2] + 2Mod[n, 2] - 7)/3

(h) (see note below)

(i) (does not halt for various x > 53)

(j) (does not halt for various x > 39)

(k) (does not halt for x = 1)

(l) 5 (2n - 2 - 1)



Image Source Notebooks:

From Stephen Wolfram: A New Kind of Science [citation]