regular expression for the language L = { w ∈ {0,1}* | w has no pair of…

To construct a regular expression for binary strings without consecutive zeros, consider valid blocks. Every zero must be followed by a one unless it is the last character. This allows repeating patterns of '1' or '01'. The expression (1 + 01)* covers these internal blocks. Finally, allow an optional trailing zero with (0 + ε). Thus, the regex is (1 + 01)*(0 + ε).