Unformatted text preview: plement and concatenation. 4. The set BALANCED is context free but not regular. It is context free because there is PDA for it (We want to check whether k − l = n − m . This can be done as follows. Push all a s, pop an a for every input b , push remaining b s (if any). At this stage stack contains either k − l a s or l − k b s. There are two cases. (1) If stack contains a s then pop an a for every input c , when stack becomes empty push all remaining c s, pop a c for every input d , accept if stack is empty after last input d . (2) If stack contained b s then push all c on a stack, pop a symbol ( c or b ) for every d , accept if stack is empty after last input d . The set BALANCED is not regular because BALANCED ∩ a * b * = a n b n is not a regular language, and set of regular languages is closed under intersection. 1...
View
Full Document
 Spring '08
 Staff
 Empty set, Formal language, Regular expression, Regular language, Chomsky hierarchy, Free monoid

Click to edit the document details