CMPSCI 250: Introduction to Computation

David Mix Barrington

Spring, 2011

Homework Assignment #7

Posted Tuesday 22 March 2011

Due on paper in lecture, Friday 15 April 2011.

There are seven 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.

• Excursion 9.11, Writing Exercise 2 (15XC) You may be able to find a winning Octopawn strategy for one player by hand. But you are probably better off searching the entire game tree by computer. If I were doing it, I would define a Position class whose objects have a boolean telling whose move it is and a four by four array of int values: 0 for a blank space, 1 for a White pawn, and 2 for a Black pawn. I would write an eval method for this class that determined who would win from the calling position given optimal play. This would be recursive, and the hardest thing would be to generate all the positions that the player could move to.

• Problem 9.10.5 (10) Prove that your strategy is correct. You may find the winning strategy from an outside source, but be sure to cite your source in your answer.

• Problem 5.1.3 (10)

• Problem 5.1.5 (10)

• Problem 5.2.5 (10)

• Problem 5.4.2 (10) Note that this problem changed between the green and blue books -- do the version in the blue book, which is also in the Fall 2010 errata page.

• Problem G-1 (10): Give a regular expression, over the alphabet Σ = {a,b}, for the set of strings that have either aaa or bbb as substrings (the three a's or three b's must occur consecutively). Then give a regular expresssion for the complement of this language -- the set of strings that do not have an aaa or a bbb in them. Argue that this second expression is correct.

Last modified 5 April 2011