Can a regex match valid credit card numbers?
a day ago
- The question of whether a regex can validate credit card numbers using the Luhn algorithm is explored in depth.
- Credit card numbers have a specific format: a prefix (Issuer Identification Number), an account ID, and a check digit calculated via the Luhn algorithm.
- The Luhn algorithm involves a right-to-left walk over digits, alternating between adding the digit and its 'Luhn double', with the final sum checked for divisibility by 10.
- A left-to-right equivalent is presented, based on the parity of the number of digits.
- The construction of a DFA recognizes the language of Luhn-valid strings, with states representing partial sums for even and odd-length strings.
- The DFA has 100 states and 1000 transitions, and the transition function is defined mathematically.
- The DFA is converted to a regex using the greenery library, resulting in two massive regexes (over 32 million and 48 million characters for even and odd lengths, respectively).
- The construction demonstrates that DFAs can handle computations like modulo arithmetic, and the union of even and odd DFA regexes provides a complete solution.
- The post plans future updates including visualizations, proofs of correctness and minimality, and additional code examples.