# MadeEasy Test Series 2019: Thoery of Computation - Regular Languages

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Is the following language regular or not?

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yes. (modular counting is regular )
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Can u please elaborate how is it possible to construct a dfa/nfa  for this problem.

:)
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 state/inputs x y z A(final state) B B B B C C C C D D D D E E E E A A A

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What are the other options bro ??

It is general fact that modular counting is always regular
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Other options is to make a DFA or NFA for it or use pumping lemma to show that its not regular.

A language is said to be regular if you can draw a Finite Automata for it.

Every mod n counting has n states and the remainder that we want is the final state.

for example mod 3 counting will have 3 states and if we want remainder as 1 then the middle state will be the final state.

## 1 Answer

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 state/inputs x y z A B B B B C C C C D D D D E E E E A A A

A is the initial as well as final state.

since we can draw a finite automata for this language

=> the language is regular.

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Thanks for the solution.

I still have a doubt that while providing the loop back to state A from state E there will be strings out of the language and they also get accepted right?. Also x should be followed by y and then by z. Please clear this one.

Appreciate that :)
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yes.... you are correct. xzy will also be accepted. Here i only checked l+m+n mod 5 and forgot to check the order. :(
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Yeah. The one's who came up with this question are saying it as a regular language. Still now am confused of their statement . Is there a way to realize this?.

" Whenever we provide a feedback transition from a state then the language acts like kleen closure. "

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