Question

Construct a PDA that recognizes the following language. Please draw the PDA by hand.

Explain how the PDA works: write the algorithm it follows, and label the specific portions of the machine with the task performed.

Answer 1

To construct a PDA that recognizes a given language, define the states, transitions, alphabet, stack, and accepting states. For example, for a language with equal number of 'a' and 'b', push 'a' and pop 'a' for each input of 'a' and 'b' respectively. Accept if the stack is empty at the accepting state.

Step-by-step explanation:

To construct a PDA that recognizes a given language, you need to define the states, transitions, alphabet, stack, and accepting states of the PDA.

For example, let's consider a language where words have an equal number of 'a' and 'b' characters. The PDA can have two states: q0 and q1. The alphabet consists of 'a' and 'b'. Starting from state q0, if the input is 'a', push 'a' onto the stack and transition to state q1.

If the input is 'b', pop 'a' from the stack and stay in state q0. The machine accepts if it reaches state q1 and the stack is empty.

This PDA recognizes the language by pushing 'a' onto the stack for every 'a' inputted. Then, it pops 'a' from the stack for every 'b' inputted. If it reaches the accepting state with an empty stack, it means it has an equal number of 'a' and 'b' characters.