So, when's your homework due?

Have you read perlre ? Did you understand the section about character classes?

One way to "allow only" is to check for the characters which are not allowed. This can be done by checking the inverse set of the allowed characters. [^...] will do that.

if ($str =~ /[^[:alpha:][:digit:].]/) {
   die("Bad data\n");
}
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The other way is to use [...] to check for allowed characters. But you need to make sure every character in the string is checked by anchoring the regexp with ^ and \z.

if (!($str =~ /^[[:alpha:][:digit:].]*\z/)) {
   die("Bad data\n");
}
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Everything used here is documented in perlre.

Update: Switched to character classes. Original code in HTML comment.