Explanation: The class of languages known as the regular language has atleast four different descriptions: i) DFA ii) NFA iii) e-NFA iv) Regular Expressions

Explanation: We use the powerful technique called Pumping Lemma, for showing certain languages not to be regular. We use Ardens theorem to find out a regular expression out of a finite automaton.

Explanation: Here, i has limits i.e. the language is finite, contains few elements and can be graphed using a deterministic finite automata. Thus, it is regular. Others can be proved non regular using Pumping lemma.

Explanation: All of the given languages are regular and finite and thus, can be represented using respective deterministic finite automata. We can also use mealy or moore machine to represent remainders for option c.

Explanation: This is a simple example of a closure property: a property saying that the set of DFA-regular languages is closed under certain operations.

Explanation: Let L be a regular language. If ~L has k equivalent classes, then any DFA that recognizes L must have atleast k states.

Explanation: In automata theory, the Myphill Nerode theorem provides a necessary and sufficient condition for a language to be regular. The Myphill Nerode theorem can be used to show a language L is regular by proving that the number of equivalence classes of RL(relation) is finite.

Explanation: The myphill nerode theorem can be generalized to trees and an application of tree automata prove an algorithmic meta theorem about graphs.

Explanation: There is no regular expression that can parse HTML documents. Other options are also non-regular as they cannot be drawn into finite automaton.

Explanation: It is the disadvantage or lack of property of a DFA that it cannot remember an arbitrarily such large amount of data which makes it incapable of accepting such languages like palindrome, reversal, etc.