Automata, Formal Languages, and
Computational Complexity

Assignments

The accompanying table indicates assignments and due dates for Computer Science 341 and are subject to the following notes.


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 2h - 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 ssR, where sR 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}.


This document is available on the World Wide Web as

http://www.cs.grinnell.edu/~walker/courses/341.sp99/assignments.html

created January 5, 1999
last revised April 9, 1999