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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
+
+* Question One
+** Partition Refinement
+{ {q_0, q_1, q_3}, {q_2, q_4} }
+
+S_1 = {(q_0, q_1), (q_0, q_3), (q_1, q_3)}
+S_2 = {(q_2, q_4)}
+
+\delta(q_0, 1) = q_3 \in S_1
+\delta(q_1, 1) = q_4 \in S_2
+
+(q_0, q_1) need to be split
+
+\delta(q_0, 0) = q_1 \in S_1
+\delta(q_3, 0) = q_2 \in S_2
+
+(q_1, q_2) need to be split
+
+\forall x \in \Sigma, \delta(q_1, x) = \delta(q_3, x)
+so {q_1, q_3} does not need to be split
+
+In S_2, \delta(q_2, 0) \in S_1 and \delta(q_4, 0) \in S_2, thus need to be split
+
+Finally, the refined partitions are {{q_0}, {q_1, q_3}, {q_2}, {q_4}}
+
+** Minimization
+| a \in \Sigma | {q_0}     | {q_1, q_3} | {q_2}     | {q_4} |
+|     0 | {q_1, q_3} | {q_2}     | {q_1, q_3} | {q_4} |
+|     1 | {q_1, q_3} | {q_4}     | {q_4}     | {q_4} |
+
+with d_0 = {q_0}, d_1 = {q_1, q_3}, d_2 = {q_2} and d_3 = {q_4}
+
+#+attr_latex: :width 350px
+[[./img/min_dfa.png]]
+
+* Question Two
+See attached python