DCFL s and CFL s
We now show that class of languages accepted by DPDA s is properly included in the CFLS .
First, note that, every DCFL is a CFL since every DPDA is a special case of a PDA .
Now, there are two ways to prove the proper inclusion- direct method or indirect method.
In the direct method we need to show that there exists a language which is CFL but not DCFL . We have already argued intuitively that the language 
is a CFL but not a DCFL . We will show later that there is a CFL which is not a DCFL .
The indirect method follows the following steps to prove the fact-
First, prove the fact that DCFL s are closed under complement. |