a) Construct a phrase-structure grammar that generates all signed decimal numbers, consisting of a sign, either +

Question:

a) Construct a phrase-structure grammar that generates all signed decimal numbers, consisting of a sign, either + or −; a nonnegative integer; and a decimal fraction that is either the empty string or a decimal point followed by a positive integer, where initial zeros in an integer are allowed.
b) Give the Backus-Naur form of this grammar.
c) Construct a derivation tree for−31.4 in this grammar.