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lfa:2024:lab09 [2024/12/01 14:22] stefan.sterea |
lfa:2024:lab09 [2024/12/02 11:33] (current) pdmatei |
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| ===== 9.2. Equivalence of the definitions ===== | ===== 9.2. Equivalence of the definitions ===== | ||
| - | **9.2.1.** Prove that PDAs that accept by empty stack and PDAs that accept by final state are equivalent. Find a transformation from a PDA accepting by empty stack to one accepting by final state and a transformation from a PDA accepting by final state to one accepting by empty stack. | + | **9.2.1.** Prove that PDAs that accept by empty stack and PDAs that accept by final state are equivalent. More concretely: |
| + | * starting from a PDA $math[A] which accepts by empty stack, **create** a PDA $math[A'] which accepts by final state, such that $math[L(A) = L(A')]. | ||
| + | * perform the same task - vice-versa. | ||
| + | |||
| + | **9.2.2.** Prove that the language $math[L(A)] where $math[A] is a PDA which uses only a fixed number of $math[k] stack cells, is **regular**. | ||