Edit this page Backlinks This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong. ====== Push down automata ====== **Exercise 1.** Write PDAs for the following languages: **1.1.** $ L = \{\: w \in \{A,B\}^* \ | \:w \text{ is a palindrome}\} $ **1.2.** $ L = \{\: w \in \{A,B\}^* \ | \: \text{#}A(w) \neq \: \text{#}B(w) \} $ **1.3.** $ L = \{ A^{n} B^{m+n} C^{n} \ | \: n, m \geq 0 \} $ **1.4.** $ L = \{ A^{n}B^{n}C^{m}D^{m} | \: \ n,m \geq 0 \} U \{ 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: (q0, w, Z0) |- (q,e,e) where q is any state from K Prove that a language is CF if it can be accepted by a PDA via the empty-stack definition. (**Hint**, you need to prove two parts)