Fixed errors in formulas and document now compiles to latex

Formal Languages and Compilers/lesson_03.md

@@ -69,8 +69,8 @@ $$ e_N = (a_1\cup (b_2b_3))^*(c_4^+ \cup (a_5 \cup (b_6b_7)))$$
 3. Isolate the subexpressions and put them into evidence
 $$ (a_1\cup (b_2b_3))^*\;\;\;\;c_4^+ \cup (a_5 \cup (b_6b_7))$$
 $$ a_1\cup (b_2b_3)\;\;\;\;\;\;c_4^+\;\;\;\;a_5 \cup (b_6b_7)$$
-$$ a_1\;\;\;\;b_2b_3\;\;\;\;\;\;c_4^\;\;\;\;a_5 \;\;(b_6b_7)$$
-$$ a_1\;\;\;\;b_2\;\;\;b_3\;\;\;\;\;\;c_4^\;\;\;\;a_5 \;\;\;b_6\;\;\;b_7$$
+$$ a_1\;\;\;\;b_2\;\;b_3\;\;\;\;\;\;c_4^+\;\;\;\;a_5 \;\;(b_6b_7)$$
+$$ a_1\;\;\;\;b_2\;\;\;b_3\;\;\;\;\;\;c_4^+\;\;\;\;a_5 \;\;\;b_6\;\;\;b_7$$
 <!--*-->
 
 ### Different parenthesization
@@ -89,8 +89,8 @@ If the two regexp $e'$ and $e''$ can be factored as
 $$e'=\alpha\beta\gamma \;\;\; e''=\alpha\delta\gamma$$
 With
 - $\beta$ subexpression of $e'$
-- $\gamma$ subexpression of $e''$
-- $\gamma$ is a *choice* of $\beta$
+- $\delta$ subexpression of $e''$
+- $\delta$ is a *choice* of $\beta$
 
 ##### examples
 - one step derivation
@@ -174,6 +174,10 @@ An __element__ can be a __terminal__ (alphabetic symbol) or a __compound object_
 ##### example:
 List with separators and start-marker of end-marker
 $$ie(se)^*f\;\;\;i[e(se)^*]f$$
+i: inizio
+e: elemento
+s: separatore
+f:fine
 
 ### Substitution
 Operation that replaces the terminal characters of the source language with the phrases of the destination languages