#+TITLE: HW 02
#+AUTHOR: Elizabeth Hunt
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* Problem 1
** Part 1
$L(M) = \{ x | x \in \{ a \}^{*} \} \cup \{ x | x \in \{ b \}^{*} \} \cup \{ x | x \in \{ c \}^{*} \}$

** Part 2

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[[./img/p01_02.png]]

$Q = {q_0, q_1, q_2, q_3}$

$\Sigma = {a, b, c}$

$F = {q_1, q_2, q_3}$

$\delta(q_0, a) = {q_1}, \delta(q_1, a) = {q_1}, \delta(q_0, b) = {q_2}, \delta(q_2, b) = {q_2}, \delta(q_0, c) = {q_3}, \delta(q_3, c) = c$

* Problem 2
** Work
| subset       | 0                      | 1                  |
| {q_0}         | {q_0, q_1}               | {q_1}               |
| {q_1}         | {q_2}                   | {q_2}               |
| {q_2}         | {q_2}                   | {q_2}               |
| {q_0, q_1}     | {q_0, q_1} \cup {q_2}        | {q_1} \cup {q_2}        |
| {q_0, q_1, q_2} | {q_0, q_1} \cup {q_2} \cup {q_2} | {q_1} \cup {q_2} \cup {q_2} |
| {q_1, q_2}     | {q_2} \cup {q_2}            | {q_2} \cup {q_2}        |


** Solution
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[[./img/p02.png]]

$Q_D = \{q_0, q_1, q_2, q_3, q_4, q_5\}$

$\Sigma = \{0, 1\}$

$F_D = \{q_1, q_2, q_4, q_5\}$

$\delta_D(q_0, 0) = q_1$

$\delta_D(q_0, 1) = q_2$

$\delta_D(q_1, 0) = q_5$

$\delta_D(q_1, q) = q_4$

$\delta_D(q_2, 0) = \delta_D(q_2, 1) = q_3$

$\delta_D(q_3, 0) = \delta_D(q_3, 1) = q_3$

$\delta_D(q_4, 0) = \delta_D(q_4, 1) = q_4$

$\delta_D(q_5, 0) = q_5$

$\delta_D(q_5, 1} = q_4$

* Problem 3
See attached python