Question

Construct a pushdown automata that recognizes w | w is an element of a, b, c, d* such that the number of a's in w the number of b's .

a) Pushdown automata cannot recognize this language.
b) Pushdown automata can recognize this language.
c) The language is regular, not requiring a pushdown automata.
d) None of the above.

Answer 1

The pushdown automata can recognize this language. The PDA can recognize strings where the number of a's is equal to the number of b's.

Step-by-step explanation:

The correct answer is b) Pushdown automata can recognize this language.

A pushdown automata (PDA) is a type of automaton that uses a stack to remember information. In this case, the PDA can use the stack to keep track of the number of a's and b's seen so far.

Here is a possible construction for the PDA:

1. Start in the initial state with an empty stack.
2. For each character in the input string:

• If it's an 'a', push it onto the stack.
• If it's a 'b', pop an 'a' from the stack if there is one.

After processing all the characters:

• If the stack is empty, accept the string.
• If the stack still has 'a's, reject the string.

By following this construction, the PDA can recognize strings where the number of a's is equal to the number of b's.