Topic: Formal Language, Grammar and Automata Please do it both (#1 and 2)

1. Let be(0,1). Describe the following regular sets with set operations. Describe them with regular expressions as well. a. The set of all strings in which a pair of adjacent 0's procedes a pair of adjacent I's b. The set of all strings not containing 101 as a substring. 2. Suppose that an alphabet is the set of digits and a decimal point, ie., = {,0,1,2,3,4,5,6,7,8,9). Give a regular grammar and a regular expression for the following language over For example, L includes 04035 and 0.0096601 L= { x | x is a decimal representation of a real number between 0 and 1 exclusive