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lfa:lab08-push-down-automata [2020/11/21 22:49] ruxandrarusu |
lfa:lab08-push-down-automata [2020/12/04 22:08] (current) dmihai |
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| **1.2.** $ L = \{\: w \in \{A,B\}^* \ | \: \text{#}A(w) \neq \: \text{#}B(w) \} $ | **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 \} $ | + | **1.3.** $ 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 \} U \{ A^nB^mC^mD^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} \} $ | **1.5.** $ L = \{ A^{i}B^{j}C^{k} | \: \text{ i=j or j=k} \} $ | ||
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| 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 if it can be accepted by a PDA via the empty-stack definition. | 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) | (**Hint**, you need to prove two parts) | ||