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+#+TITLE: HW 02
+#+AUTHOR: Elizabeth Hunt
+#+STARTUP: entitiespretty fold inlineimages
+#+LATEX_HEADER: \notindent \notag  \usepackage{amsmath} \usepackage[a4paper,margin=1in,portrait]{geometry}
+#+LATEX: \setlength\parindent{0pt}
+#+OPTIONS: toc:nil
+
+* Problem 1
+** Part 1
+$L(M) = \{ x | x \in \{ a \}^{*} \} \cup \{ x | x \in \{ b \}^{*} \} \cup \{ x | x \in \{ c \}^{*} \}$
+
+** Part 2
+
+#+attr_latex: :width 300px
+[[./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
+#+attr_latex: :width 300px
+[[./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