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+#+TITLE: Assignment Three
+#+AUTHOR: Lizzy Hunt
+#+STARTUP: entitiespretty fold inlineimages
+#+LATEX_HEADER: \notindent \notga \usepackage{ dsfont } \usepackage{amsmath} \usepackage[a4paper,margin=1in,landscape]{geometry}
+#+LATEX: \setlength\parindent{0pt}
+#+OPTIONS: toc:nil
+
+* Question One
+** a
+#+attr_latex: :width 250px
+[[./1a.excalidraw.png]]
+** b
+#+attr_latex: :width 250px
+[[./1b.excalidraw.png]]
+** c
+#+attr_latex: :width 250px
+[[./1c.excalidraw.png]]
+** d
+#+attr_latex: :width 250px
+[[./1d.excalidraw.png]]
+** e
+#+attr_latex: :width 250px
+[[./1e.excalidraw.png]]
+** f
+#+attr_latex: :width 200px
+[[./1f.excalidraw.png]]
+
+* Question Two
+| State | a      | b   | e      |
+|     0 | \phi      | \phi   | {1, 3} |
+|     1 | {2, 4} | {4} | \phi      |
+|     2 | {2}    | \phi   | \phi      |
+|     3 | \phi      | {4} | \phi      |
+|     4 | \phi      | {4} | \phi      |
+
+* Question Three
+| State | a | b |
+|     0 | 1 | 0 |
+|     1 | 1 | 2 |
+|     2 | 1 | 3 |
+|     3 | 1 | 0 |
+
+* Question Four
+** a
+#+attr_latex: :width 350px
+[[./4a.excalidraw.png]]
+** b
+| DFA State | NFA States               | a             | b                             | c                             |
+| d_0        | {s_0, s_1, s_2, s_5, s_9}     | {s_3, s_6} (d_1) | s_e                            | s_e                            |
+| d_1        | {s_3, s_6}                 | s_e            | {s_4, s_8, s_9, s_1, s_2, s_5} (d_2) | {s_7, s_8, s_9, s_1, s_2, s_5} (d_3) |
+| d_2        | {s_4, s_8, s_9, s_1, s_2, s_5} | {s_3, s_6} (d_1) | s_e                            | s_e                            |
+| d_3        | {s_7, s_8, s_9, s_1, s_2, s_5} | {s_3, s_6} (d_1) | s_e                            | s_e                            |
+
+#+attr_latex: :width 200px
+[[./4b.excalidraw.png]]
+** c
+| partition            | a                           | b                        | c                        |
+| {d_1}, {d_0, d_2, d_3}   | {d_0, d_2, d_3} \Rightarrow {d_1, d_0, d_0} | {d_0, d_2, d_3} \Rightarrow {-, -, -} | {d_0, d_2, d_3} \Rightarrow {-, -, -} |
+| {d_1}, {d_0}, {d_2, d_3} | {d_2, d_3} \Rightarrow {d_0, d_0}         | {d_2, d_3} \Rightarrow {-, -}        | {d_2, d_3} \Rightarrow {-, -}        |
+
+#+attr_latex: :width 200px
+[[./4c.excalidraw.png]]
+
+* Question Five
+** regex 1
+*** NFA
+#+attr_latex: :width 350px
+[[./51a.excalidraw.png]]
+
+*** DFA
+| DFA State | NFA States               | 1                             | 0                             |
+| d_0        | {s_0, s_1, s_2, s_4, s_7}     | {s_1, s_2, s_3, s_4, s_6, s_7} (d_1) | {s_1, s_2, s_4, s_5, s_6, s_7} (d_2) |
+| d_1        | {s_1, s_2, s_3, s_4, s_6, s_7} | d_1                            | d_2                            |
+| d_2        | {s_1, s_2, s_4, s_5, s_6, s_7} | d_1                            | d_2                            |
+
+#+attr_latex: :width 200px
+[[./51b.excalidraw.png]]
+
+*** Minimization
+| partition    |                           1 |                           0 |
+| {d_0, d_1, d_2} | {d_0, d_1, d_2} \Rightarrow {d_1, d_1, d_1} | {d_0, d_1, d_2} \Rightarrow {d_2, d_2, d_2} |
+
+#+attr_latex: :width 75px
+[[./51c.excalidraw.png]]
+
+** regex 2
+*** NFA
+#+attr_latex: :width 350px
+[[./52a.excalidraw.png]]
+*** DFA
+| DFA State | NFA States                                  | 1                                                | 0                                           |
+| d_0        | {s_0, s_1, s_2, s_3, s_5, s_11, s_6, s_12 }         | {s_1, s_2, s_3, s_5, s_6, s_7, s_8, s_10, s_11, s_12} (d_1) | {s_1, s_2, s_3, s_4, s_5, s_11, s_6, s_12} (d_2)     |
+| d_1        | {s_1, s_2, s_3, s_5, s_6, s_7, s_8, s_10, s_11, s_12} | d_1                                               | {s_1, s_2, s_3, s_4, s_5, s_9, s_11, s_6, s_12} (d_3) |
+| d_2        | {s_1, s_2, s_3, s_4, s_5, s_11, s_6}               | d_1                                               | d_2                                          |
+| d_3        | {s_1, s_2, s_3, s_4, s_5, s_9, s_11, s_6, s_12}      | d_1                                               | d_2                                          |
+
+#+attr_latex: :width 150px
+[[./52b.excalidraw.png]]
+
+*** Minimization
+| partition        |                                   1 |                                   0 |
+| {d_0, d_1, d_2, d_3} | {d_0, d_1, d_2, d_3} \Rightarrow {d_1, d_1, d_1, d_1} | {d_0, d_1, d_2, d_3} \Rightarrow {d_2, d_3, d_2, d_2} |
+
+#+attr_latex: :width 100px
+[[./52c.excalidraw.png]]
+
+* Question Six
+** a
+*** DFA
+#+attr_latex: :width 350px
+[[./6a.excalidraw.png]]
+
+*** catMap
+#+BEGIN_SRC json
+{
+  '-': 'sign',
+  '+': 'sign',
+  [0-9]: 'digit',
+  'e': 'scntfc'
+}
+#+END_SRC
+
+*** transMap
+#+BEGIN_SRC json
+{
+  's0': {
+    'sign': 's1',
+    'digit': 's2',
+  },
+  's1': {
+    'digit': 's2',
+  },
+  's2': {
+    'digit': 's2',
+    'scntfc': 's3',
+  },
+  's3': {
+    'sign': 's4',
+    'digit': 's5',
+  },
+  's4': {
+    'digit': 's6',
+  },
+  's5': {
+    'digit': 's6',
+  },
+  's6': {
+    'digit': 's6',
+  },
+}
+#+END_SRC
+
+*** tokenTypes
+#+BEGIN_SRC json
+{
+  's2': 'integer',
+  's6': 'integer,
+}
+#+END_SRC
+** b
+*** DFA
+#+attr_latex: :width 200px
+[[./6b.excalidraw.png]]
+
+*** catMap
+#+BEGIN_SRC json
+{
+  [a-zA-Z]: 'letter',
+  '_': 'letter',
+  [0-9]: 'digit',
+}
+#+END_SRC
+
+*** transMap
+#+BEGIN_SRC json
+{
+  's1': {
+    'letter': 's2'
+  },
+  's2': {
+    'letter': 's2',
+    'digit': 's2',
+  },
+}
+#+END_SRC
+
+** c
+*** DFA
+#+attr_latex: :width 400px
+[[./6c.excalidraw.png]]
+
+*** catMap
+#+BEGIN_SRC json
+{
+  [^(\n)*/]: 'nonc',
+  '\n': 'newline',
+  'eof': 'eof',
+  '/': 'slash',
+  '*': 'star'
+}
+#+END_SRC
+*** transMap
+#+BEGIN_SRC json
+{
+  's0': {
+    'slash': 's1',
+  },
+  's1': {
+    'slash': 's2',
+    'star': 's4',
+  },
+  's2': {
+    'nonc': 's2',
+    'newline': 's3',
+    'eof': 's3'
+  },
+  's4': {
+    'nonc': 's4',
+    'star': 's5',
+  },
+  's5': {
+    'nonc': 's4',
+    'newline': 's4',
+    'slash': 's6'
+  }
+}
+#+END_SRC
+
+*** tokenType
+#+BEGIN_SRC json
+{
+  's3': 'singleLineComment',
+  's6': 'multiLineComment',
+}
+#+END_SRC
+