TAOCP 7.2.2.2 Exercise 57
The data supplied is insufficient to produce a correct solution to this exercise.
Section 7.2.2.2: Satisfiability
Exercise 57. [29] $[29]$ Combining the previous exercise with the methods of Section 7.1.2, exhibit a function $f$ for Table 2 that can be evaluated with only six Boolean operations(!).
Verified: no
Solve time: 6m33s
The data supplied is insufficient to produce a correct solution to this exercise.
Exercise 7.2.2.2.57 does not define the target function by itself. It refers to “Table 2”, which contains the input-output pairs that determine the required Boolean function. The previous exercise also supplies an essential intermediate result: a five-variable function matching Table 2. Neither Table 2 nor the result of Exercise 56 is included here.
A valid solution must contain the following items:
- A specific five-variable function
$$ f(x_{i_1},x_{i_2},x_{i_3},x_{i_4},x_{i_5}) $$
that agrees with every row of Table 2.
- A reduction of that function using the methods of Section 7.1.2, such as Shannon expansion and Boolean identities, to a circuit containing exactly six Boolean operations.
- A verification that the resulting expression produces the required values on all rows of Table 2.
Without the contents of Table 2 or the five-variable function obtained in Exercise 56, any explicit expression would be an unsupported guess and would not constitute a valid TAOCP solution.
Please provide Table 2 (or the answer obtained for Exercise 56), and the complete six-operation construction can be derived from it.