Question

Convert the following CFG into PDA using empty stack

S→aABB
A→aB/a
B→bA/b
​Convert the following CFG into PDA using empty stack
S→aSb| BC B→bB|b C→cC|ε

Answer 1

To convert the given CFG into a PDA, we create transitions for each production rule, handle the input symbols with transitions, and add transitions for the empty stack scenario.

Step-by-step explanation:

In order to convert the given context-free grammar (CFG) into a pushdown automaton (PDA), we need to follow a few steps. First, we create a transition for each production rule in the CFG. Second, we create transitions to handle the input symbols. Finally, we add transitions to handle the empty stack scenario. Let's go through the steps:

1. Create a transition for each production rule in the CFG:

• S → aABB : For each nonterminal, create a transition that pops S and pushes a, A, B, and B onto the stack in that order.
• A → aB/a : For each production, create a transition that pops A and pushes a, B onto the stack.
• B → bA/b : For each production, create a transition that pops B and pushes b, A onto the stack.

Create transitions to handle the input symbols:

• a: Create a transition that pops a from the input and pushes it onto the stack.
• b: Create a transition that pops b from the input and pushes it onto the stack.
• c: Create a transition that pops c from the input and pushes it onto the stack.

Add transitions to handle the empty stack scenario:

• Create a transition that pops the stack when it is empty and does not push anything onto the stack. This transition should lead to an accepting state.

By following these steps, we can convert the given CFG into a PDA.