Answer:
Step-by-step explanation:
I'd be happy to help you with creating pushdown automata for these languages! Let's go through each language one by one:
1. L = a^n b^k
To create a pushdown automaton for this language, we can follow these steps:
- Start in the initial state.
- Read 'a' and push it onto the stack.
- Read 'b' and push it onto the stack.
- Repeat the previous step until you reach the end of the input.
- If the number of 'a's is odd or the number of 'b's is even, accept the input.
2. L = {w ∈ {a,b}* | w = w^R} (Use nondeterminism, w^R is the reverse of w)
To create a pushdown automaton for this language, we can use nondeterminism, which allows multiple paths to be taken simultaneously. Here are the steps:
- Start in the initial state.
- Read the first symbol of the input and push it onto the stack.
- Move to a new state.
- Read the next symbol of the input and push it onto the stack.
- Repeat the previous steps until you reach the end of the input.
- At this point, the stack should contain the reverse of the input.
- If the stack is empty, accept the input.
3. L = a^i b^j c^k
To create a pushdown automaton for this language, we can follow these steps:
- Start in the initial state.
- Read 'a' and push it onto the stack.
- Repeat the previous step until there are no more 'a's in the input.
- Read 'b' and push it onto the stack.
- Repeat the previous step until there are no more 'b's in the input.
- Read 'c' and pop 'a' and 'b' from the stack.
- Repeat the previous step until there are no more 'c's in the input.
- If the stack is empty, accept the input.
Remember, these are general steps to give you an idea of how to approach creating pushdown automata for these languages. You may need to adjust the steps based on the specific requirements of your assignment or the exact definition of the languages.
I hope this helps! Let me know if you have any further questions