Chapter 12

Describe what factors might be included in a model for the spread of an epidemic.

Say an automobile manufacturer designs a new car using a sophisticated and detailed computer simulation, but no prototype vehicles, and the automobile is later found to have a defect. Do you think the manufacturer is accountable? Is the manufacturer accountable if it builds prototypes that do not reveal the defect, but it does not do a simulation?

Give an example of a potential use of computerized models in a. The pharmaceutical industry b. The food processing industry c. The insurance industry

Which of the following can be considered computing agents and why? a. A clock radio b. A vacuum cleaner c. A video camera d. A programmable calculator

A Turing machine contains only the following instructions: $$ \begin{aligned} &(1,1,1,1, R) \\ &(1, b, 1,2, R) \end{aligned} $$ Can this machine ever reach the following configuration? Explain your answer. $$ \ldots b 01 b \ldots $$

Describe the behavior of the Turing machine $$ \begin{aligned} &(1,1,1,2, R) \\ &(2,0,0,1, L) \end{aligned} $$ when run on the tape \(\ldots b 101 b \ldots\)

Describe the behavior of the Turing machine \((1,1,1,1, R)\) \((1,0,0,2, L)\) \((2,1,0,2, L)\) \((2, b, 1,3, L)\) \((3, b, b, 1, R)\) when run on the tape \(\ldots b 101 b \ldots\)

a. Write a Turing machine that, when run on the tape \(\ldots\) b 11111 b... produces an output tape of \(\ldots\) b 11110 b... b. Write a Turing machine that, when run on any tape containing a unary string, changes the rightmost 1 to 0 and then halts. (If your solution to Exercise 15 a was sufficiently general, you will not have to change it here.)

Write a Turing machine to perform a unary decrement (the opposite of an increment). Assume that \(n>0\).

Write a Turing machine to perform a unary decrement. Assume that \(n\) may be 0 , in which case a single 0 should be output on the tape to signify that the operation results in a negative number.