Create DFA for the regular expression of a real number?

Question

I'm trying to construct the Definite Finite Automata(DFA) of a real number, that is defined as:

• A string leading with an optional '+' or '-'.
• Followed by a single zero or non-empty sequence of digits that doesn't start with a zero.
• Followed by a decimal point.
• Followed by a non-empty sequence of digits

And its finish depends on digits if its real or not.

I constructed the regular expression: /[+ | -]?(O | ([1-9][0-9]*)).[0-9]+/ /[+ | -]?(O | ([1-9][0-9]*)).[0-9]+/

Answer 1

See regex in use here

^[+-]?(?:0|[1-9]\d*)(?:\.\d+)?$

• ^ Assert position at the start of the line
• [+-]? Optionally match either + or -
• (?:0|[1-9]\\d*) Match either 0 or a number beginning with a digit in the range of 1-9 , followed by any number of any digit
• (?:\\.\\d+)? Optionally match a decimal point number (a dot . , followed by one or more digits)
• $ Assert position at the end of the line

Answer 2

Here, start state is q0 .

Final state is q5 .

DFA enters state q1 if sign is provided.

State q2 is reached if the first digit is 0.

State q3 if the first digit is not 0 and remains in that state for further numbers till a decimal point is seen.

State q4 reached on decimal point from where there is transition to state q5 if a digit is seen.

Dead state is not shown.