1. Consider the following format for floating point literals. Assume a fraction part consisting of a string of one or more decimal digits with an optional decimal point (period) that can be added immediately before or after any of the digits. In addition, an optional exponent can be appended to the fraction part, consisting of an e or E, followed by an optional sign, followed by one or more decimal digits. A floating point literal must contain either a decimal point, or an exponent, or both. Examples: .0, 0., 0.1, .01e-01, 01E00 a. Give a regular expression for this construct. You may use . b. Use Thompson's construction to translate the regular expression into an NFA.