Chapter 12: The Principle of Computational Equivalence

Section 8: Undecidability and Intractability

Circuit complexity

Any function with a fixed size of input can be computed by a circuit of the kind shown on page 619. How the minimal size or depth of circuit needed grows with input size then gives a measure of the difficulty of the computation, with circuit depth growing roughly like number of steps for a Turing machine. Note that much as on page 662 one can construct universal circuits that can be arranged by appropriate choice of parts of their input to compute any function of a given input size. (Compare page 703.)

Image Source Notebooks:

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