diff --git a/content/chapters/part1/1.tex b/content/chapters/part1/1.tex
index 46a8710..c61eb28 100644
--- a/content/chapters/part1/1.tex
+++ b/content/chapters/part1/1.tex
@@ -279,11 +279,11 @@ An automaton is a tuple $\langle S, s_{0}, T, \Sigma,f\rangle$
 \paragraph{Example} Given the language $L$ on the alphabet $\Sigma = \{A, C, T\}$, $L = \{A^{*}, CTT, CA^{*}\}$
 
 \begin{definition}[Deterministic automaton]
-    An automaton is deterministic, if for each couple $(p, a) \in S \times \Sigma$ it exists at most a state $q$ such as $f(p, q) = q$
+    An automaton is deterministic, if for each couple $(p, a) \in S \times \Sigma$ it exists at most a state $q$ such as $f(p, a) = q$
 \end{definition}
 
 \begin{definition}[Complete automaton]
-    An automaton is complete, if for each couple $(p, a) \in S \times \Sigma$ it exists at least a state $q$ such as $f(p, q) = q$.
+    An automaton is complete, if for each couple $(p, a) \in S \times \Sigma$ it exists at least a state $q$ such as $f(p, a) = q$.
 \end{definition}
 
 \begin{algorithm}
@@ -439,4 +439,4 @@ each state to the initial state whenever we encounter an unknown letter.
         \EndIf
         \EndFunction
     \end{algorithmic}
-\end{algorithm}
\ No newline at end of file
+\end{algorithm}
diff --git a/main.pdf b/main.pdf
index 4149104..e652f38 100644
--- a/main.pdf
+++ b/main.pdf
@@ -1,3 +1,3 @@
 version https://git-lfs.github.com/spec/v1
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-size 323717
+oid sha256:a66d43104a9c0c15866ece32a8c10862c33c5789abd8139916348895439b7f16
+size 341884