Question

Construct a pushdown automata for the following languages (in

all parts the alphabet is Σ = {0,1}).
L = {ww^r | w ∈ {0,1}∗and w contains 010 as a substring}

Answer 1

To construct a pushdown automata (PDA) for the given language, we need to consider two main parts: recognizing the substring '010' and checking if the input is a palindrome.

Step-by-step explanation:

To construct a pushdown automata (PDA) for the given language, we need to consider two main parts: recognizing the substring '010' and checking if the input is a palindrome. Here is an example of how we can construct the PDA:

1. Create an initial state and push a symbol (let's say 'Z') onto the stack.
2. When reading '0', transition to a new state and push '0' onto the stack.
3. If the next symbol is '1', transition to another state. If it is '0', stay in the same state. If it is '1', transition to a different state and pop '0' from the stack.
4. Continue this process, transitioning between states based on the input symbols and stack operations.
5. If the PDA reaches an accepting state and the stack is empty, the input is in the language. Otherwise, it is not.

This is a simplified example, but it represents the basic idea of how to construct a PDA for the given language.