Given a word, how to tell whether it is a Roman numeral?

Question

If I have a word that consists of letters I, V, X, L, C, D, M, how can I tell whether it is a valid roman numeral? For example, how do I tell that IXXL is not valid?

Answer 1

To ease the description you can consider the pairs "IV", "IX", "XL", "XC", "CD" and "CM" as single symbols.

That is, the roman numerals are sequences made of these symbols: I, IV, V, IX, X, XL, L, XC, C, CD, D, CM, M.

The sequences must hold these rules:

• The symbols I, X, C, M can be repeated up to three consecutive times. Other symbols must not be repeated.
• In each sequence, the symbols appear in decreasing order.
• If a symbol with two letters occurs, none of these two letters occur after it, with the followinf exceptions: after XL and XC there can be IX; and after CD and CM there can be XC.

This way, your example is not legal because IX < XL, or because after IX there must not be any letter X.