Finite H-systems with 3 test tubes are not predictable

Finite H-systems with n test tubes are splicing systems of n test tubes over a common molecular alphabet, sigma, with a filter Fi [symbol: see text] sigma for each test tube. Initially, arbitrary many copies of molecules and enzymes (splicing rules) from a finite set of molecules and enzymes are given to the test tubes that produce new molecules by splicing and filtering. It is known that any formal language can be generated by a finite H-system with 9 test tubes and that the results of finite H-systems with 6 test tubes are unpredictable. Here we present a rather simple proof that the results of finite H-systems with only 3 test tubes are unpredictable and that 4 test tubes suffices to generate any formal language.