From 24fadf347a12b656f7e3cbc914e6d24f2863e49f Mon Sep 17 00:00:00 2001
From: Mark <mark@betalupi.com>
Date: Mon, 7 Aug 2023 08:53:27 -0700
Subject: [PATCH] Minor edits

---
 Advanced/DFAs/parts/0 DFA.tex | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/Advanced/DFAs/parts/0 DFA.tex b/Advanced/DFAs/parts/0 DFA.tex
index 5d2677f..5e9a9a2 100644
--- a/Advanced/DFAs/parts/0 DFA.tex	
+++ b/Advanced/DFAs/parts/0 DFA.tex	
@@ -41,7 +41,7 @@ $A$ will go through the states $a - b - c - b - b$ while processing this string.
 
 
 \problem{}
-Which of the following strings are accepted by $A$? \\
+Which of the following strings are accepted by $A$? \par
 \begin{itemize}
 	\item \texttt{1}
 	\item \texttt{1010}
@@ -99,7 +99,7 @@ It starts in the state $s$ and has two accepting states $a_1$ and $b_1$.
 \end{center}
 
 \problem{}
-Which of the following strings are accepted by $B$:
+Which of the following strings are accepted by $B$?
 \begin{itemize}
 	\item \texttt{aa}
 	\item \texttt{abba}
@@ -171,7 +171,7 @@ For example, $\{\texttt{0}, \texttt{1}\}^*$ is the set $\{\varepsilon, \texttt{0
 Note that this set contains the empty string.
 
 \definition{}
-A \textit{language} over an alphabet $Q$ is a subset of $Q^*$. \\
+A \textit{language} over an alphabet $Q$ is a subset of $Q^*$. \par
 For example, the language \say{strings of length 2} over $\{\texttt{0}, \texttt{1}\}$ is $\{\texttt{00}, \texttt{01}, \texttt{10}, \texttt{11}\}$
 
 \definition{}
@@ -432,7 +432,7 @@ Draw a DFA over an alphabet $\{\texttt{a}, \texttt{b}, \texttt{@}, \texttt{.}\}$
 \pagebreak
 
 \problem{}
-Draw a state diagram for a DFA over an alphabet of your choice that accepts exactly $f(n)$ strings of length $n$ if \\
+Draw a state diagram for a DFA over an alphabet of your choice that accepts exactly $f(n)$ strings of length $n$ if \par
 \begin{itemize}
 	\item $f(n) = n$
 	\item $f(n) = n+1$
@@ -441,7 +441,7 @@ Draw a state diagram for a DFA over an alphabet of your choice that accepts exac
 	\item $f(n)$ is a Tribonacci number. \par
 	Tribonacci numbers are defined by the sequence $f(0) = 0$, $f(1) = 1$, $f(2) = 1$,
 	and $f(n) = f(n-1)+f(n-2)+f(n-3)$ for $n \ge 3$ \par
-	\hint{Fibonacci numbers are given by the automaton prohibiting two \texttt{'a'}s in a row.}
+	\hint{Fibonacci numbers are given by the automaton prohibiting two \texttt{`a'}s in a row.}
 \end{itemize}