Prof. Franklin, Summer 2013
ECS 120 HW (Practice only, do not turn in)

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HW #1 (Covers Sipser Chapt 1)
Do not turn in (practice only)

1.4g, 1.5g, 1.6c, 1.7b, 1.8a, 1.9a, 1.10a, 1.16b, 1.31, 1.36, 1.41,
1.60.

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Hw #2 (covers Sipser Chapts 2, 3)
Do not turn in (practice only)

2.1d, 2.4abe, 2.5ab, 2.8, 2.12, 2.14

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}

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HW #3 (Covers Sipser 4,5)
Do not turn in, practice only

4.3, 4.4, 4.6, 4.7, 4.12, 5.9, 5.13, 5.17, 5.18, 5.24, extra
problems (see below):

a. Construct the Modified Post Correspondence Problem instance for TM
M_1 (from Chapt 3, p 145) with input w = 0#0.  (You will have to modify
notation slightly to distinguish between #'s used as alphabet symbol in
M_1 and #'s used as domino symbols in the MPCP.)

b. Solve the MPCP instance from part (a), and show that the solution
corresponds to an accepting computation of M_1.

c. Demonstrate that the MPCP instance from part (a) does not work
as a PCP instance, i.e., has solutions that do not correspond
to accepting computations of M_1.

d. Convert the MPCP instance from part (a) into a PCP instance.

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HW #4 (Covers Sipser Chapt 7
do not turn in, practice only

Exercises: 7.1cde, 7.2cde, 7.6, 7.7, 7.8, 7.11