To understand and demonstrate the fundamental equivalence between Pushdown Automata and Context-Free Grammars by exploring how these two distinct computational models recognize identical languages through different mechanisms. Students will learn to trace step-by-step PDA transitions using stack operations while simultaneously following CFG derivation processes, observing how both approaches accept the same strings through parallel execution. Through interactive experimentation with bidirectional language recognition, students will gain practical experience in understanding how state-based stack machines and grammar-based production rules represent dual paradigms for context-free language processing, reinforcing the theoretical foundation that PDAs and CFGs are equivalent in computational power.