--- a/hws/hw06.tex	Sat Nov 11 10:08:33 2023 +0000
+++ b/hws/hw06.tex	Fri Nov 17 20:06:43 2023 +0000
@@ -27,6 +27,11 @@
 Observe the maximal munch rule and priorities of your regular
 expressions that make the process of lexing unambiguous.)
 
+\solution{
+  a and b are ok; c is not matched because x4x is not an identifier according to the rules.
+}
+
+
 \item Suppose the grammar
 
 \begin{plstx}[margin=1cm]    
@@ -43,6 +48,38 @@
 of precedences of the operators?
 
 \solution{
+  \begin{tikzpicture}[level distance=10mm, black,sibling distance=10mm]
+  \node {\meta{E}}
+  child[sibling distance=20mm] {node {\meta{F}} 
+    child {node {\meta{T}}
+      child[sibling distance=5mm] {node {(}}
+      child[sibling distance=5mm]  {node {\meta{E}}
+        child {node {\meta{F}}
+          child {node {\meta{T}} child {node {3}}}
+          child {node {+}}
+          child {node {\meta{T}} child {node {3}}}
+        }  
+      }
+      child[sibling distance=5mm]  {node {)}}
+    }
+    child {node {+}}
+    child {node {\meta{T}}
+      child[sibling distance=5mm] {node {(}}
+      child[sibling distance=5mm] {node {\meta{E}}
+        child {node {\meta{F}}
+          child {node {\meta{T}} child {node {2}}}
+        }
+        child {node {*}}
+        child {node {\meta{F}}
+          child {node {\meta{T}} child {node {3}}}
+        }
+        }
+      child[sibling distance=5mm] {node {)}}
+    }
+    };
+\end{tikzpicture}
+
+  
   For the second part "1+2*3" will be parsed as (1+2)*3, meaning + and - bind
   tighter than * and $\backslash$
 }
@@ -76,7 +113,16 @@
 and (ii) give a sample string involving all rules given in 1.-4.~that 
 can be parsed by this grammar.
 
+\solution{
+The simplest grammar is
+  
+\begin{plstx}[margin=1cm]    
+  :\meta{B} ::= true \;|\; false \;|\;\meta{B} \cdot $\wedge$ \cdot \meta{B} \;|\; \meta{B} \cdot $\vee$ \cdot \meta{B}
+  \;|\; $\neg$\meta{B} \;|\; (\cdot\meta{B}\cdot)\\
+\end{plstx}
 
+This is unfortunately a left-recursive grammar. Giving a not left-recursive one is a bit more involved.
+  }
 
 \item Parsing combinators consist of atomic parsers, alternative
   parsers, sequence parsers and semantic actions.  What is the purpose