Problem 9 Find a regular expression that defines the language consisting of all strings of a's and b's in which the third character from the end is a b Problem 10 Let V = {S, A, B, a, b} and T = {a, b). Find the language generated by the grammar (V , T , S, P) for each set P of productions below. Which are regular languages? a, S AB, S aA, A a, B ba. Problem 11 a. Construct a grammar that generates all signed decimal numbers, consisting of a sign, either + or -; a non-negative integer; and a decimal fraction that is either the empty string ora decimal point followed by a positive integer, where initial zeros in an integer are allowed. The grammar should be specified using the Backus-Naur form b. Show the derivation for -31.4 in this grammar Problem 12 Give production rules in Backus-Naur form that generate all identifiers in the C programming language. In C an identifier starts with a letter or an underscore () that is followed by one or more lowercase letters, uppercase letters, underscores, and digits