Regular Expressions And Finite Automata

Match LIST-I with LIST-II $%5Cbegin%7Barray%7D%7B%7Cc%7Cc%7Cc%7C%7D%5Chline%20%5Ctext%7B%20%7D%20%26%20%5Ctext%7BLIST-I%7D%20%26%20%5Ctext%7BLIST-II%7D%20%5C%5C%20%5Chline%20%5Ctext%7BA.%7D%20%26%20%5Ctext%7BA%20Language%20L%20can%20be%20accepted%20by%20a%20Finite%20Automata%2C%20if%20and%20only%20if%2C%20the%20set%20of%20equivalence%20classes%20of%20%5C(L%5C)%20is%20finite.%7D%20%26%20%5Ctext%7BIII.%20Myhill-Nerode%20Theorem%7D%20%5C%5C%20%5Chline%20%5Ctext%7BB.%7D%20%26%20%5Ctext%7BFor%20every%20finite%20automaton%20M%20%3D%20%5C((Q%2C%20%5CSigma%2C%20q_0%2C%20A%2C%20%5Cdelta)%5C)%20%2C%20the%20language%20L(M)%20is%20regular.%7D%20%26%20%5Ctext%7BII.%20Regular%20Expression%20Equivalence%7D%20%5C%5C%20%5Chline%20%5Ctext%7BC.%7D%20%26%20%5Ctext%7BLet%2C%20X%20and%20Y%20be%20two%20regular%20expressions%20over%20%5C(%5CSigma%5C)%20.%20If%20X%20does%20not%20contain%20null%2C%20then%20the%20equation%20%5C(R%20%3D%20Y%20%2B%20RX%5C)%20in%20R%2C%20has%20a%20unique%20solution%20(i.e.%20one%20and%20only%20one%20solution)%20given%20by%20%5C(R%20%3D%20YX%5E*%5C)%20.%7D%20%26%20%5Ctext%7BI.%20Arden's%20Theorem%7D%20%5C%5C%20%5Chline%20%5Ctext%7BD.%7D%20%26%20%5Ctext%7BThe%20regular%20expressions%20X%20and%20Y%20are%20equivalent%20if%20the%20corresponding%20finite%20automata%20are%20equivalent.%7D%20%26%20%5Ctext%7BIV.%20Kleen's%20Theorem%7D%20%5C%5C%20%5Chline%20%5Cend%7Barray%7D$

$%5Ctext%7BMatching%20List-I%20with%20List-II%7D$

Choose the correct answer from the options given below:

Step 1: Matching the Concepts.
- $A$ : The statement is related to **Arden's Theorem**, which deals with regular expressions and finite automata, so the correct match is $A$ - I.

- $B$ : This is related to the fact that the language of a finite automaton is regular, which is part of the **Myhill-Nerode Theorem**, so the correct match is $B$ - III.

- $C$ : This matches with **Regular Expression Equivalence**, where the equation $R%20%3D%20Y%20%2B%20RX$ has a unique solution, which is described by the regular expression equivalence theory, so the correct match is $C$ - II.

- $D$ : The equivalence of regular expressions $X$ and $Y$ when their corresponding finite automata are equivalent is given by **Kleen's Theorem**, so the correct match is $D$ - IV.

Step 2: Conclusion.
Thus, the correct matching is $A%20-%20I%2C%20B%20-%20III%2C%20C%20-%20II%2C%20D%20-%20IV$ , which corresponds to answer (3).

High-Yield Trend

Chapter Questions
1 MCQs

Official Solution

Regular Expressions And Finite Automata

High-Yield Trend

Chapter Questions 1 MCQs

Official Solution

Chapter Questions
1 MCQs