# Homework Assignment #4

#### Due on paper in class, Wednesday 25 March 2015

There are thirteen questions for 100 total points plus 10 extra credit. All are from the textbook, Introduction to the Theory of Computation by Michael Sipser (second/third edition). though some are adapted as indicated. The number in parentheses following each problem is its individual point value.

• Problem 4.12 (2nd)/4.13 (3rd) (5):

• Problem 4.24 (2nd)/4.26 (3rd) (10):

• Problem 4.28 (2nd)/4.30 (3rd) (10):

• Exercise 5.3 (5):

• Exercise 5.4 (5):

• Problem 5.9 (10):

• Problem 5.15 (10):

• Problem 5.20 (5):

• Problem 5.24 (10):

• Problem 5.30 part b only (5): You will need to read Problem 5.28 and its solution in the back of the book.

• Problem 5.35 (2nd)/5.34 (3rd): The Myholl-Nerode Theorem can be useful here.

• Problem 5.36 (3rd) (not in second edition) (10): Say that a CFG is minimal if none of its rules can be removed without changing the language generated. Let MINCFG be {G: G is a minimal CFG}. Part (a) is to show that MINCFG is TR. Part (b) is to show that MINCFG is undecidable.

• Problem 6.7 (5):

• Problem 6.8 (10XC):