fix: Definition on automata

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}
+\end{algorithm}