For each of the following decision problem¹ P: i. Describe a way to represent the inputs as strings (the alphabet doesn't have to be binary). ii. Describe a regular expression that represents the language L := {w | P(w) = 1} and briefly explain why the regular expression is correct. Note: You don't have to provide the exact regular expression for part (ii). Describing how you would formulate the regular expression is sufficient, given that the exact regular expression could indeed be obtained by following your solution.

For each of the following decision problem¹ P: i. Describe a way to represent the inputs as strings (the alphabet doesn't have to be binary). ii. Describe a regular expression that represents the language L := {w | P(w) = 1} and briefly explain why the regular expression is correct. Note: You don't have to provide the exact regular expression for part (ii). Describing how you would formulate the regular expression is sufficient, given that the exact regular expression could indeed be obtained by following your solution.