Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Next revision 		Previous revision
lfa:lab08-push-down-automata [2020/11/21 22:30]
ruxandrarusu created 		lfa:lab08-push-down-automata [2020/12/04 22:08] (current)
dmihai
Line 2: Line 2:
  
 **Exercise 1.** Write PDAs for the following languages: **Exercise 1.** Write PDAs for the following languages:
-1.1. $ L = \{\: w \in \{A,B\}^* \| w is a palindrome\} $ + 
-1.2. L = {w in {A,​B}* ​. #A(w) =/= #B(w)} +**1.1.** $ L = \{\: w \in \{A,B\}^* \ | \:w \text{ ​is a palindrome}\} $ 
-1.3. L = {A^nB^{m+n}C^n ​. n,m >= 0} + 
-1.4. L = {A^nB^nC^mD^m . n,m >= 0} U {A^nB^mC^mD^n ​. n,m >= 0} +**1.2.** $ L = \{\: w \in \{A,B\}^* \ | \: \text{#}A(w) \neq \: \text{#}B(w) \} $ 
-1.5. L = {A^iB^jC^k . i = j or j = k} + 
-2. Acceptance by empty stack.+**1.3.** $ L = \{ A^{m} B^{m+n} C^{n} \ | \: n, m \geq 0 \} $ 
 + 
 +**1.4.** $ L = \{ A^{n}B^{n}C^{m}D^{m} | \: \ n,m \geq 0 \}  ​\cup ​ \{ A^nB^mC^mD^n ​| \: \ n,m \geq 0 \} $ 
 + 
 +**1.5.** $ L = \{ A^{i}B^{j}C^{k} | \: \text{ ​i=j or j=k} \} $ 
 + 
 +**Exercise ​2.** Acceptance by empty stack. 
 Consider the following definition for an accepted word, by a PDA: Consider the following definition for an accepted word, by a PDA:
- (q0, w, Z0) |- (q,e,e) where q is any state from K + $(q_{0}, w, Z_{0}) \vdash ​(q,e,e)$ where $ q $ is any state from K. 
-Prove that a language is CF iff it can be accepted by a PDA via the empty-stack definition. + 
-(Hint, you need to prove two parts) +Prove that a language is CF if it can be accepted by a PDA via the empty-stack definition. 
-Collapse+ 
 +(**Hint**, you need to prove two parts)