# Regular languages and finite automata

Question 1 |

Consider the languages L1 = and L2 = {a}. Which one of the following represents L1 L2^{*} U L1^{*}

{[Tex]epsilon [/Tex]} | |

[Tex]phi [/Tex] | |

a | |

{[Tex]epsilon [/Tex],a} |

**GATE CS 2013**

**Regular languages and finite automata**

**Discuss it**

L1 L2* U L1* Result of L1 L2* is . {} indicates an empty language. Concatenation of with any other language is . It works as 0 in multiplication. L1* = * which is {}. Union of and {} is {}

Question 2 |

Consider the DFA given.

Which of the following are FALSE?

Complement of L(A) is context-free. | |

L(A) = L((11*0+0)(0 + 1)*0*1*). | |

For the language accepted by A, A is the minimal DFA. | |

A accepts all strings over {0, 1} of length at least 2. |

**GATE CS 2013**

**Regular languages and finite automata**

**Discuss it**

1 is true. L(A) is regular, its complement would also be regular. A regular language is also context free. 2 is true. 3 is false, the DFA can be minimized to two states. Where the second state is final state and we reach second state after a 0. 4 is clearly false as the DFA accepts a single 0.

Question 3 |

Given the language L = {ab, aa, baa}, which of the following strings are in L*?

abaabaaabaa | |

aaaabaaaa | |

baaaaabaaaab | |

baaaaabaa |

**Regular languages and finite automata**

**Regular languages and finite automata**

**Discuss it**

See question 2 of http://www.geeksforgeeks.org/automata-theory-set-2/

Question 4 |

Given the language L = {ab, aa, baa}, which of the following strings are in L*?

abaabaaabaa | |

aaaabaaaa | |

baaaaabaaaab | |

baaaaabaa |

**Regular languages and finite automata**

**Regular languages and finite automata**

**Discuss it**

See question 2 of http://www.geeksforgeeks.org/automata-theory-set-2/

Question 5 |

Consider the set of strings on {0,1} in which, every substring of 3 symbols has at most two zeros. For example, 001110 and 011001 are in the language, but 100010 is not. All strings of length less than 3 are also in the language. A partially completed DFA that accepts this language is shown below.

The missing arcs in the DFA are

**GATE CS 2012**

**Regular languages and finite automata**

**Discuss it**

Question 6 |

Definition of a language L with alphabet {*a*} is given as following.

L={|a^{nk}|k>0, and n is a positive integer constant}

What is the minimum number of states needed in DFA to recognize L?

k+1 | |

n+1 | |

2 | |

2[Tex](k+1)[/Tex] |

**GATE CS 2011**

**Regular languages and finite automata**

**Discuss it**

See Question 3 of http://www.geeksforgeeks.org/automata-theory-set-4/

Question 7 |

A | |

B | |

C | |

D |

**GATE CS 2011**

**Regular languages and finite automata**

**Discuss it**

Question 8 |

n-1 | |

n | |

n+1 | |

2n-1 |

**GATE CS 2010**

**Regular languages and finite automata**

**Discuss it**

Question 9 |

The set of all strings containing the substring 00. | |

The set of all strings containing at most two 0’s. | |

The set of all strings containing at least two 0’s. | |

The set of all strings that begin and end with either 0 or 1. |

**GATE-CS-2009**

**Regular languages and finite automata**

**Discuss it**

Question 10 |

There is unique minimal DFA for every regular language | |

Every NFA can be converted to an equivalent PDA. | |

Complement of every context-free language is recursive. | |

Every nondeterministic PDA can be converted to an equivalent deterministic PDA. |

**GATE-CS-2009**

**Regular languages and finite automata**

**Discuss it**