In my Computer Organisation module, the class was taught about how to use Karnaugh Map and Quine-McCluskey algorithm to implement some function in simpler form. The idea of using these methods to get the formula of check digit (for example, some IDs have the letter after the numbers which are used to check the validity of the ID) just popped into my head. For example, we could assign all numbers and letters with some binary digits (probably following ASCII or just make a new mapping of characters and numbers). Then, we will compute the simplified Boolean expression and make it into a function.
The problem here would be we need lots and lots of IDs before we could compute the whole thing, because for the methods mentioned above, we often take into account the don't care condition, in which smaller samples would lead to more don't care condition which are not necessarily true, thus leading to wrong check digit formula.
What's the use of this? Indeed, I could only think of negative use of this method. Getting such formula would only mean you are just curious or you want to create a new valid ID, in which case you would only fall into two categories: you are the authorized ID assigner (which means you would already have the formula thus such method is not needed) or you want to mess with some ID (and this would be illegal).
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