This works well, except that it also accepts space(' ') as a valid character.

This is because of array interpolation, which uses the contents of $" to separate array elements when joining them together. You can use this to your advantage by doing something like

@a = ( 'a', 'x', 'z' ); # simplified array
while(<>)
{
   local $" = "";
   print if(/^[@a]{3}$/);
}
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Note that this re-localizes $" within a loop, which isn't the most effecient approach, but then again you might not notice the performance difference without a microsocope.