Question

Convert the CFG given in Exercise 2.3 to an equivalent PDA, using the procedure given in Theorem 2.20.

Short answer

Answer

The Equivalent PDA is as follows,

Step-by-step solution

Explain Pushdown Automata

Pushdown Automata is the computational model that have an stack as additional memory. Pushdown automata recognizes the regular languages and context-free languages.

Convert the CFG to an equivalent PDA

Consider the grammar G,

$$\begin{gathered} R\to XRX|S \\ S\to aTb|bTa \\ T\to XTX\left|X\right|\epsilon \\ X\to a|b \end{gathered}$$

The grammar can be converted into the equivalent PDA as follows,

The transition functions are the production rules of the grammar, that moves to state on matching the terminal symbols. The path of Push down Automata of a string can be accepted only if the string is accepted by the grammar

Therefore, The Equivalent PDA has been obtained for the grammar G.