
diff -r ca349cfe3474 -r c29853b672fb hws/hw02.tex
--- a/hws/hw02.tex	Sat Nov 01 15:06:41 2014 +0000
+++ b/hws/hw02.tex	Sat Nov 01 16:19:05 2014 +0000
@@ -69,6 +69,32 @@
 
 \item Do $(a + b)^* \cdot b^+$ and $(a^* \cdot b^+) + (b^*\cdot b^+)$ define 
   the same language?
+
+\item Define the function $zeroable$ by recursion over regular
+  expressions. This function should satisfy the property
+
+  \[
+  zeroable(r) \;\;\text{if and only if}\;\;L(r) = \varnothing\qquad(*)
+  \]
+
+  The function $nullable$ for the not-regular expressions can be defined
+  by 
+
+  \[
+  nullable(\sim r) \dn \neg(nullable(r))
+  \]
+
+  Unfortunately, a similar definition for $zeroable$ does not satisfy
+  the property in $(*)$:
+
+  \[
+  zeroable(\sim r) \dn \neg(zeroable(r))
+  \]
+
+  Find out why?
+
+\item Give a regular expressions that can recognise all strings from the 
+  language $\{a^n\;|\;\exists k. n = 3 k + 1 \}$.
 \end{enumerate}
 
 \end{document}




