Two naming relations
Tester (comprehensive/analysis): a binary decision procedure (TM) – 1(0) if the input string is (not) in .
Generator (productive/generation): a TM generating a string in given an input integer.
A tester exists to test a recursive language, a generator exists to generate RE language.
It is possible to translate from testers to generators, but not vice versa if testers are identifiable than so are the corresponding generators, but not vice versa, e.g., anomalous text.