# Homework Assignment #8

#### Due on paper in lecture, Friday 20 April 2012.

There are nine questions for 60 total points plus 15 extra credit. All but one are from the textbook, Mathematical Foundation for Computer Science. Note that the book has both Exercises and Problems -- make sure you are doing a Problem and not the Exercise with the same number. The number in parentheses following each problem is its individual point value.

Students are responsible for understanding and following the academic honesty policies indicated on this page.

• Problem 14.1.2 (10) Use the inductive definitions of the δ* function, paths in graphs, and strings.

• Problem 14.1.4 (10) Explain why your DFA for L(M1) ∪ L(M2) is correct. Also indicate (without proof) how you would make a DFA for L(M1) ⊕ L(M2).

• Problem 14.2.3 (10XC)

• Problem 14.2.4 (5)

• Problem 14.3.1 (5)

• Problem 14.3.4 (10)

• Problem H-1 (10): Let N be the following NFA. The input alphabet is {a, b}, the state set is {0, 1, 2, 3, 4}, the start state is 0, and the final state set is {0}. The transition relation Δ contains all triples of the form (i, a, i), (i, b, (i + 1)%5), and (i, b, (i-1)%5), where "%" is the Java modular division operator.
• (a) Describe the language of this NFA in English, and justify your answer.
• (b) Apply the Subset Construction to get a DFA equivalent to N.

• Problem 14.6.4 (10)

• Problem 14.6.5 (5XC)