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# CS402 GDB Spring 2019 Solution & Discussion

CS402 GDB Spring 2019 Solution & Discussion

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(PDA is more powerful than FA also use 7 tuples so it can accept all languages that can be accepted by FA.

FA is weak than DFA also it use 5 tuples so it cannot accept all languages tha DFA can accept).  according to me this is right but not sure.

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.
Yes:
As we know that FA`s deterministic and PDA`s are deterministic and non-deterministic as well. So it is very clear that languages which are accepted by FA`s will also be accepted by PDA`s. you can give examples of any regular language like language starting with and ending with different letters, language containing bb or aa

•           Whether the FA accepts all the languages that have been accepted by the PDA? Yes or No, explain in either case with an example.
No:
As PDA`s are non-deterministic also but FA`s are not. so it is not possible for FA to accept all the languages which are accepted by PDA`s.there are non-regular languages which will be accepted by PDA`s e.g.Language of double factorial which can’t be accepted by FA. Hence statement is false.

CS402 GDB Solution Spring 2019

CS402 GDB Solution Spring 2019

Cs402 gdb
a) Yes, as we know that FA’s are deterministic and PDA’s are deterministic and non-deterministic as well. So it is clear that languages which are accepted by FA’s will also be accepted by PDA’s. You can give examples of any regular language starting with and ending with different letters, languages containing bb or aa.

b) No, as PDA’s are non-deterministic also but FA’s are not. So it is not possible for FA to accept all the languages which are accepted by PDA’s. There are non-regular languages which will be accepted by PDA’s e.g. language of double factorial which cannot accepted by FA. Hence statement is false.

Cs402 gdb solution 2019
1st point yes 2nd point no

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