TAOCP 2.5 Exercise 13

The reviewer’s criticisms are correct.

taocpmathematicsalgorithmsvolume-1

Section 2.5: Dynamic Storage Allocation

Exercise 13. [**] [21] Write a MIX program for the algorithm of exercise 12.

Exercises

Verified: no
Solve time: 4m34s

The reviewer’s criticisms are correct. The submitted response is not a solution of Exercise 13; it merely explains why the exercise cannot be solved from the excerpt provided in the prompt. The fundamental difficulty is that the statement of Exercise 13 is explicitly dependent on Exercise 12:

Write a MIX program for the algorithm of exercise 12.

A valid solution must therefore consist of a MIXAL implementation of the algorithm developed in Exercise 12. Since the text of Exercise 12 is absent, neither the algorithm nor its data representation is available.

Consequently, the only mathematically correct response that can be derived from the information supplied is the following.

Solution

Exercise 13 requires a MIX implementation of the algorithm constructed in Exercise 12. The present statement does not include Exercise 12, so the algorithm to be implemented is unspecified.

A MIX program is determined by details such as:

  1. The exact sequence of steps in the algorithm of Exercise 12.
  2. The representation of data in memory.
  3. The locations and formats of boundary tags and links.
  4. The conventions adopted in the preceding exercises of Section 2.5.

Without these specifications, no MIXAL program can be derived or verified.

Therefore a complete solution cannot be produced from the information provided. The missing information is not a minor detail but the entire algorithm that Exercise 13 asks us to translate into MIX instructions.

Accordingly, the correct conclusion is:

Exercise 13 cannot be solved from the statement given here alone. A valid solution requires the complete text of Exercise 12, after which one can write the corresponding MIXAL program and verify that it faithfully implements that algorithm.

This is not itself a solution to Knuth's exercise. Rather, it is the strongest correct statement that can be made from the incomplete problem specification supplied in the prompt.