Prof Franklin, Spring 2009
ECS 120, Homework #4 (Covers Sipser 3)
Due Tues 12 May, 2009

1. This question is about Turing Machine M_1 described in Example 3.9
in the textbook. Give the sequence of configurations that M_1 enters
when started on each of the following input strings:

(a) 0#01
(b) 01#01

2. Give an implemtation-level description of a Turing Machine that
decides each of the following languages over the alphabet {0,1}:

(a) {w | w contains more 0's than 1's}
(b) {w | w contains more than twice as many 0's as 1's}

3. Let M_1 be a Turing Machine that decides language L_1,
and let M_2 be a Turing Machine that decides language L_2.
Give an implementation-level description of a Turing Machine
that decides each of the following languages: 

(a) {w | w is in L_1 and w is not in L_2}
(b) {w | w = xy for some x in L_1 and some y in L_2}

4. Let M_1 be a Turing Machine that recognizes language L_1,
and let M_2 be a Turing Machine that recognizes language L_2.
Give an implementation-level description of a Turing Machine
that recognizes each of the following languages: 

(a) {w | w is in L_1 and w is in L_2}
(b) {w | w = xy for some x in L_1 and some y in L_2}