Discussion
Which of the following pairs of regular expressions are equivalent ?
Answer: D
The answer is All of the above: every pair is equivalent.
- \(1(01)^{*}\) and \((10)^{*}1\) both give 1, 101, 10101, ...: alternating strings that begin and end with 1.
- \(x(xx)^{*}\) and \((xx)^{*}x\) both give the strings of x of odd length: x, xxx, xxxxx, ...
- \(x^{+}\) and \(x^{+}x^{*+}\): since \((x^{*})^{+} = x^{*}\), the second is \(x^{+}x^{*} = x^{+}\), one or more x's.
Because each of the three pairs describes the same language, no single pair is the whole answer.
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