I am using python and would like a simple api or regex to check for a domain name's validity. By validity I am the syntactical validity and not whether the domain name actually exists on the Internet or not.
Any domain name is (syntactically) valid if it's a dot-separated list of identifiers, each no longer than 63 characters, and made up of letters, digits and dashes (no underscores).
would be a start. Of course, these days some non-Ascii characters may be allowed (a very recent development) which changes the parameters a lot -- do you need to deal with that?