Question

According to the given language, which among the following expressions does it corresponds to? Language L={xϵ{0,1}|x is of length 4 or less}

(a) (0+1+0+1+0+1+0+1)^4

(b) (0+1)^4

(c) (01)^4

(d) (0+1+ε)^4

I had been asked this question in examination.

The above asked question is from Regular Expression-Introduction in section Regular Expressions and Languages of Automata Theory

Answer 1

The correct answer is (d) (0+1+ε)^4

To elaborate: The extended notation would be (0+1)^4 but however, we may allow some or all the factors to be ε. Thus ε needs to be included in the given regular expression.