Finite Automata (FA) and Push Down Automata (PDA) both are used to express the languages. The Finite Automata is deterministic and Push Down Automata is deterministic and as well as non-deterministic. You are required to give comments on the following statements: • Whether the PDA accepts all the languages that have been accepted by the FA? Yes or No, explain in either case with an example. • Whether the FA accepts all the languages that have been accepted by the PDA? Yes or No, explain in either case with an example.

1. Yes, because FA is deterministic and PDA is both deterministic and as well as non-deterministic therefore PDA will accept all languages that would have accepted by FA. For example Regular Langrage r=(aa+bb+(ab+ba)(aa+bb)*(ab+ba))* would be accepted by both FA and PDA.
2. No, because although PDA is both non-deterministic as well as deterministic however FA is just deterministic. Therefore it is not possible for FA to accept all languages which are being accepted by PDA. PDA would accept non-regular languages which FA cannot. For example L = { ww | w ∈ {a, b }^* } 

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