diff --git a/content/chapters/include.tex b/content/chapters/include.tex
index 173bbbf..b59250b 100755
--- a/content/chapters/include.tex
+++ b/content/chapters/include.tex
@@ -11,7 +11,7 @@
 		}
 }
 
-\includechapters{part1}{2}
+\includechapters{part1}{3}
 
 % \includechapters{part2}{2}
 
diff --git a/content/chapters/part1/0.tex b/content/chapters/part1/0.tex
index 9e69b2a..8a6fa1d 100755
--- a/content/chapters/part1/0.tex
+++ b/content/chapters/part1/0.tex
@@ -58,6 +58,6 @@
 				\EndIf
 			\EndFor 
 			\State \Return $c$ 
-		\EndFunction
+			\EndFunction
     \end{algorithmic}
 \end{algorithm}
diff --git a/content/chapters/part1/2.tex b/content/chapters/part1/2.tex
index de516cc..f4f558d 100644
--- a/content/chapters/part1/2.tex
+++ b/content/chapters/part1/2.tex
@@ -51,8 +51,8 @@ Let $S = $ ACGUUACGUU. Let's write the comparison matrix.
         \State \Return $M$
         \EndFunction
     \end{algorithmic}
-
 \end{algorithm}
+
 \begin{algorithm}
     \caption{Construct the top half of a comparison matrix}
     \begin{algorithmic}[1]
@@ -259,7 +259,7 @@ The suffix language of $S$ is $\{S, ACTACT, CTACT, TACT, ACT, CT, T\}$.
 \end{figure}
 
     \begin{algorithm}
-        \caption{Check if a sequences matches a motif, from a suffix automaton $\mathcal{O}(m)$}
+        \caption{Check if a sequences matches a motif, from a suffix automaton $\mathcal{O}(m)$, built from the automaton}
         \begin{algorithmic}[1]
             \Function{CheckMotifInSuffixAutomaton}{$W$: Array($m$), $A$: $\langle S, s_{0}, T, \Sigma,f \rangle$}
             \Returns{Boolean valued to \True{} if the motif is in the sequence}
diff --git a/content/chapters/part1/3.tex b/content/chapters/part1/3.tex
new file mode 100644
index 0000000..1bd7525
--- /dev/null
+++ b/content/chapters/part1/3.tex
@@ -0,0 +1,84 @@
+\chapter{Automata for motif search}
+
+Let $M$ be a motif $M = $ ACAT.
+
+\begin{figure}
+    \centering
+    \includegraphics{figures/part1/motif_search_automaton.pdf}
+    \caption{Motif search automaton for $M = $ ACAT}
+\end{figure}
+
+The alphabet of motif is the same as the alphabet of the sequence.
+The search automaton is complete.
+If the there exists a letter $c$ in the sequence that is not
+in the motif alphabet, we can make a virtual transition from 
+each state to the initial state whenever we encounter an unknown letter.
+
+\begin{algorithm}
+    \caption{Search a motif in a sequence with an automaton}
+    \begin{algorithmic}[1]
+        \Function{SearchMotif}{$S$: Array($n$), $A$: $\langle S, s_{0}, T, \Sigma, f \rangle$, $P$: Array($m$)}
+            \Returns{A set of positions where the motif has been found}
+            \State $s \gets s_0$
+            \State $i \gets 0$
+            \State $pos \gets \{\}$
+            \While {$i < n$} % $\exists f(s, S[i])$  We assume $S$ and $P$ are formed on the same alphabet, so we could remove the second check, as $A$ is complete
+                \If {$s \in T$}
+                    \State $pos \gets pos \cup \{ i - m \}$
+                \EndIf
+                \State $s \gets f(s, S[i])$
+                \State $i++$
+            \EndWhile
+            \State \Return $pos$
+        \EndFunction
+    \end{algorithmic}
+\end{algorithm}
+
+\begin{algorithm}
+    \caption{Check if the a motif automaton recognizes only the prefix of size $m-1$ of a motif $P$ of size $m$ }
+    \begin{algorithmic}[1]
+        \Function{SearchMotifLastPrefix}{$S$: Array($n$), $A$: $\langle S, s_{0}, T, \Sigma, f \rangle$, $P$: Array($m$)}
+            \Returns{A set of positions where the motif has been found}
+            \State $s \gets s_0$
+            \State $i \gets 0$
+            \State $T_{new} \gets \{\}$
+            \For {$s \in S$}
+                \For {$a \in \Sigma$}
+                    \For {$t \in T$}
+                        \If {$\exists f(s, a)$ and $f(s, a) = t$}
+                            \State $T_{new} \gets T_{new} \cup s$
+                        \EndIf
+                    \EndFor
+                \EndFor
+            \EndFor
+            \While {$i < n$}
+                \If {$s \in T_{new}$}
+                    \State \Return \True
+                \EndIf
+                \State $s \gets f(s, S[i])$
+                \State $i++$
+            \EndWhile
+            \State \Return \False 
+        \EndFunction
+    \end{algorithmic}
+\end{algorithm}
+
+\begin{algorithm}
+    \caption{Check if the a motif automaton recognizes only the prefix of size $m-1$ of a motif $P$ of size $m$, knowing the sequence of the motif}
+    \begin{algorithmic}[1]
+        \Function{SearchMotifLastPrefix}{$S$: Array($n$), $A$: $\langle S, s_{0}, T, \Sigma, f \rangle$, $P$: Array($m$)}
+        \Returns{A set of positions where the motif has been found}
+        \State $s \gets s_0$
+        \State $i \gets 0$
+        \While {$i < n$ and $f(s, P[m-1]) \notin T$}
+        \State $s \gets f(s, S[i])$
+        \State $i++$
+        \EndWhile
+        \If{$f(s, P[m-1]) \in T$} 
+        \State \Return \True
+        \Else
+        \State \Return \False 
+        \EndIf
+        \EndFunction
+    \end{algorithmic}
+\end{algorithm}
\ No newline at end of file
diff --git a/main.pdf b/main.pdf
index c2428f1..37a5a01 100644
--- a/main.pdf
+++ b/main.pdf
@@ -1,3 +1,3 @@
 version https://git-lfs.github.com/spec/v1
-oid sha256:05a8df7c52c74678b9c1749d55d444d80a68fa2e4f53ac83721990eb2896e064
-size 250664
+oid sha256:f7d399a14f4887c141303c27212572571690acfe832b36202fb3758bf5f76992
+size 279254
diff --git a/tmp.pdf b/tmp.pdf
index 130f8e5..1f58660 100644
--- a/tmp.pdf
+++ b/tmp.pdf
@@ -1,3 +1,3 @@
 version https://git-lfs.github.com/spec/v1
-oid sha256:94c2912fea2b02c615c3534646b4496fc2f622a9af88a4f87602c7e6c772ad2e
-size 49570
+oid sha256:a4ca0430df97538f18dd19ee77273b26e99f7e1ef07cc5b353cba53d88994dff
+size 63306
diff --git a/tmp.tex b/tmp.tex
index 0907187..47a449a 100644
--- a/tmp.tex
+++ b/tmp.tex
@@ -14,3 +14,5 @@
 
 
 \end{document}
+
+\end{document}
\ No newline at end of file