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+#+TITLE: Assignment Two
+#+AUTHOR: Logan Hunt
+#+STARTUP: entitiespretty fold inlineimages
+#+LATEX_HEADER: \notindent \notga \usepackage{ dsfont } \usepackage{amsmath}
+#+LATEX: \setlength\parindent{0pt}
+#+OPTIONS: toc:nil
+
+* Question One
+** a
+There are four productions.
+** b
+The terminals of this grammar are:
+
+\begin{verbatim}
+a b c d
+\end{verbatim}
+** c
+N_1, N_2, N_3, N_4 are all nonterminals.
+** d
+The start symbol is N_1.
+** e
+The symbols N_1, N_2, N_3, N_4 are present in the production heads.
+** f
+N_2, N_3, N_4, "a", "b", "c", "d" are present in the production bodies.
+* Question Two
+** a
+There are fifteen productions.
+** b
+The terminals of this grammar are:
+\begin{verbatim}
+0 1 2 3 4 5 6 7 8 9 + -
+\end{verbatim}
+** c
+The nonterminals are "list" and "digit".
+** d
+The start symbol is "list".
+** e
+"list" and "digit" are present in the production heads.
+** f
+"list", "digit", 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, $+$, $-$ are present in the production bodies.
+* Question Three
+\begin{verbatim}
+x -> A (3)
+x -> A (3)
+xx* -> AA* (2)
+(xx*)x+ -> AA+ (1)
+((xx*)x+)x+ -> AA+ (1)
+\end{verbatim}
+* Question Four
+** a
+Examples:
+1. "xy"
+2. "xxyy"
+3. "xxxyyy"
+4. "xxxxyyyy"
+
+This grammar generates a string of x's prepended to a string of y's with the same amount of characters.
+
+The grammar is unambiguous.
+
+** b
+Example:
+1. "x"
+2. "-xx"
+3. "+-xx-xx"
+4. "-x-xx"
+
+This grammar generates addition and subtraction prefix expressions on "x" or chains of "x".
+
+The grammar is unambiguous.
+
+** c
+Example:
+1. ""
+2. "()"
+3. "()()"
+4. "(())"
+
+This grammar generates balanced sets of potentially nested parentheses.
+
+The grammar is ambiguous. For example, the string "()()" can be parsed multiple ways:
+
+#+attr_latex: :width 250px
+[[./4c.png]]
+
+** d
+1. ""
+2. "xyyx"
+3. "xyxy"
+4. "xy"
+
+This grammar generates jumbled combinations of the same number of x's and y's.
+
+The grammar is ambiguous.
+
+For example, the string "xyxy" has two parse trees:
+
+#+attr_latex: :width 250px
+[[./4d.png]]
+
+** e
+1. "(x)**"
+2. "x+x"
+3. "x*"
+4. "xx"
+
+This grammar generates combinations of + / * expressions on x in any nested amount of balanced parentheses.
+
+This grammar is unambiguous.
+
+* Question Five
+** a
+#+attr_latex: :width 250px
+[[./5a.png]]
+
+** b
+#+attr_latex: :width 250px
+[[./5b.png]]
+
+* Question Six
+\begin{verbatim}
+expr -> expr expr op
+expr -> factor
+op -> + | - | / | *
+factor -> 0
+factor -> 1
+factor ... 9
+\end{verbatim}
+* Question Seven
+\begin{verbatim}
+sentence -> character
+sentence -> character,sentence
+character -> a
+character -> b
+character -> ...
+\end{verbatim}
+* Question Eight
+\begin{verbatim}
+expr -> expr - term
+expr -> expr + term
+expr -> expr * term
+expr -> expr / term
+expr -> term
+term -> +num
+term -> -num
+term -> num
+num -> Integer
+num -> Ident
+\end{verbatim}
+* Question Nine
+#+attr_latex: :width 250px
+[[./9.png]]
+* Question Ten
+\begin{verbatim}
+expr -> {print '+'} expr + term
+expr -> {print '-'} expr - term
+expr -> term                     
+term -> 0 {print '0'}
+term -> 1 {print '1'}          
+term -> ... {print ...}
+\end{verbatim}
+* Question Eleven
+** 3-1+2
+#+attr_latex: :width 250px
+[[./11-1.png]]
+** 2+3-1
+#+attr_latex: :width 250px
+[[./11-2.png]]
+
+* Question Twelve
+Predictive parsing is a special kind of recursive descent parsing where the "lookahead unambiguously determines the flow of control".
+* Question Thirteen
+None of the productions have the same start symbol (disjoint ~FIRST~ sets), and it is not left-recursive.
+* Question Fourteen
+See ~Infix.java~.
+* Question Fifteen
+\begin{verbatim}
+A -> w R
+R -> x y z R | \epsilon
+\end{verbatim}
+* Question Sixteen
+\begin{verbatim}
+S -> w R
+R -> x y z R
+R -> g h R
+R -> \epsilon
+\end{verbatim}
+* Question Seventeen
+[[./17.png]]
+* Question Eighteen
+#+attr_latex: :width 250px
+[[./18.png]]