Assignments

• Unless otherwise indicated, textbook references are to Michael Sipser, Introduction to the Theory of Computation, PWS Publishing Company, 1997, ISBN: 0-534-95651-3.

• Supplemental problems are stated later on this page.

• Unless otherwise stated, collaboration IS NOT allowed on assignments either from the text or from the supplemental problems.

Due Date	Collaboration	Chapter	Problems
Mon., Apr. 19	no	5	5.9, 5.10
Fri., Apr. 16	no	5	5.3, 5.7
Fri., Mar. 12	no	4	4.1, 4.2, 4.5
Wed., Mar. 10	no	3	3.15a
Mon., Mar. 8	no	1	Chance to Redo Feb. 15 problems
Fri., Mar. 5	no	3	3.6, 3.8
Wed., Mar. 3	no	Sup. Prob.	3
Mon., Mar. 1	no	Sup. Prob.	2
Wed., Feb 24	no		Take-Home Test
Wed., Feb. 17	no	2	2.1, 2.3, 2.4abdf
Mon., Feb. 15	no	1	1.17, 1.23, 1.24, 1.41
Wed., Feb. 10	no	1	1.13bcfij, 1.16
Mon., Feb. 8	no	1	1.5abe, 1.8b, 1.9, 1.12
Fri., Feb. 5	no	1	1.1abef, 1.2(for M1 only), 1.3, 1.4bcfij
Wed., Feb. 3	no	Sup. Prob.	1
Due Date	Collaboration	Chapter	Problems

Supplemental Problems

1. Definition: The height of a non-empty tree is defined as the number of nodes on the longest path from a leaf of a tree to its root, the height of an empty tree is defined to be 0.

   Nodes in a Binary Tree: Suppose a binary tree T has height h. Prove that T contains at least h nodes and at most 2^h - 1 nodes.

2. Turing Machine for 2 a's: Design a Turing machine that accepts exactly those strings that contain two consecutive a's. Write out your machine in full, both using a complete transition table and using a state diagram.

   Consider the input alphabet for this problem to be {a, b}.

3. Turing Machine for Palindromes: Design a Turing machine that reads a string s and returns the string ss^R, where s^R is the reverse of the string s. For example, given the string "abbaa", the Turing machine should halt after "abbaaaabba" is printed on the tape. As in Supplemental Problem 2, write out your machine in full, both using a complete transition table and using a state diagram, and consider the input alphabet to be {a, b}.