Test: The Language of DFA - Computer Science Engineering (CSE) MCQ

A language over an alphabet R is a set of strings over A which is uncountable and infinite.

Q is the Finite set of states, whose elements i.e. the states constitute the finite automata.

 δ or the Transition function describes the best, how a DFA behaves on a string where to transit next, which direction to take.

As the question has dot operation, ε will not be a part of the concatenated set. Had it been a union operation, ε would be a part of the operated set.

All the decimal numbers on division would lead to only 4 remainders i.e. 0,1,2,3 (Property of Decimal division).

Correct Answer :- d

Explanation : The given DFA accepts all the binary strings such that they are divisible by 3 and 2.Thus, it can be said that it also accepts all the strings which is divisible by 6.

The maximum number of transitions which a DFA allows for a language is the number of elements the transitions constitute.

The out degree for a DFA I fixed while the in degree depends on the number of states in the DFA and that cannot be determined without the dependence over the Language.

 The maximum number of final states for a DFA can be total number of states itself and minimum would always be 1, as no DFA exits without a final state. Therefore, the solution is n+1.