Let Σ = {0,1}, L = Σ* and R = {0ⁿ1ⁿ such that n >0} then the languages L ∪ R and R are respectively

Which of the following definitions below generates the same language as L, where L = {xⁿyⁿ such that n >= 1}?

 I. E → xEy|xy
 II. xy|(x+xyy+)
 III. x+y+ 

Consider the following statements.

I. If L₁ ∪ L₂ is regular, then both L₁ and L₂ must be regular.
II. The class of regular languages is closed under infinite union.

Which of the above statements is/are TRUE?

For Σ = {a,b}, let us consider the regular language L = {x|x = a^2+3k or x = b^10+12k, k ≥ 0}. Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for L?

If L is a regular language over Σ = {a,b}, which one of the following languages is NOT regular?

Which of the following statements is false?

(a) Given that A is regular and A∪B is regular, does it follow that B is necessarily regular? Justify your answer.
(b) Given two finite automata M1, M2, outline an algorithm to decide if L(M1)⊆L(M2). (note: strict subset)

Consider the following languages:

L1 = {ww|w ∈ {a,b}*}
L2 = {ww^R|w ∈ {a,b}*, w^R is the reverse of w}
L3 = {0²ⁱ|i is an integer}
L3 = {0ⁱ²|i is an integer}

Which of the languages are regular?

Consider the following two statements:

S1: {0²ⁿ|n≥1|} is a regular language
S2: {0^m1ⁿ0^m+n|m≥1 and n≥1|} is a regular language

Which of the following statements is correct?

• Consider the following two statements about regular languages:
  S₁: Every infinite regular language contains an undecidable language as a subset.
  S₂: Every finite language is regular.
  Which one of the following choices is correct.?

Consider the context-free grammar

E → E + E 
E → (E * E) 
E → id 

Consider the non-deterministic finite automaton (NFA) shown in the figure.

State X is the starting state of the automaton. Let the language accepted by the NFA with Y as the only accepting state be L1. Similarly, let the language accepted by the NFA with Z as the only accepting state be L2. Which of the following statements about L1 and L2 is TRUE? Correction in Question: There is an edge from Z->Y labeled 0 and another edge from Y->Z labeled 1 - in place of double arrowed and no arrowed edges.

The language {0ⁿ 1ⁿ 2ⁿ | 1 ≤ n ≤ 10⁶} is

Let L be a regular language and M be a context-free language, both over the alphabet Σ. Let L^c and M^c denote the complements of L and M respectively. Which of the following statements about the language if L^c ∪ M^c is TRUE?

Which of the following statements is TRUE about the regular expression 01*0?

Let L be a regular language. Consider the constructions on L below:
I. repeat (L) = {ww | w ∊ L}
II. prefix (L) = {u | ∃v : uv ∊ L}
III. suffix (L) = {v | ∃u : uv ∊ L}
IV. half (L) = {u | ∃v : | v | = | u | and uv ∊ L}
Which of the constructions could lead to a non-regular language?

Let L be a regular language. Consider the constructions on L below:
(I) repeat (L) = {ww | w ∊ L}
(II) prefix (L) = {u | ∃v : uv ∊ L}
(III) suffix (L) = {v | ∃u uv ∊ L}
(IV) half (L) = {u | ∃v : | v | = | u | and uv ∊ L}
Which choice of L is best suited to support your answer above?

Which of the following statements about regular languages is NOT true?

Regularity is preserved under the operation of string reversal.

All subsets of regular sets are regular.