Convert the following CFGs to PDA:

S → aA
A → aABC | bB | a
B → b
C → c

To convert a Context-Free Grammar (CFG) into a Pushdown Automaton (PDA), we can follow a systematic approach where we simulate the CFG using a stack in the PDA.
Let's take the provided CFG:

S → aA
A → aABC | bB | a
B → b
C → c

We want to construct a PDA that recognizes the same language generated by this CFG. Here’s how to do it step by step:

Initialize the PDA : Start the PDA with a stack containing the start symbol of the CFG, which is 'S' in this case.

Construct Transitions : The PDA will have transitions that mimic the production rules of the CFG:

For the production S → aA , create a transition that replaces 'S' on the stack with 'aA' and reads 'a' from the input.
For A → aABC , have a transition replacing 'A' with 'aABC' and reading 'a'.
For A → bB , replace 'A' with 'bB' while reading 'b'.
For A → a , replace 'A' with 'a' while reading 'a'.
For B → b , replace 'B' with 'b' while reading 'b'.
For C → c , replace 'C' with 'c' while reading 'c'.


Reading Input and Manipulating the Stack : The PDA uses the stack to keep track of what it expects next based on the grammar rules.

For any input symbol, if the top of the stack matches an expected terminal, the PDA pops the stack and moves to the next input symbol.


Acceptance : The PDA accepts a string if it can fully read the input string and empty the stack by following the transitions built upon the CFG's production rules.


Constructing a PDA from a CFG is a way to dynamically recognize strings generated by the grammar using stack operations, which is fundamental in the study of computational theory, especially in the context of formal languages and automata.

Answered by RyanHarmon181 | 2025-07-06