The role of the complementarity relation in Watson-Crick automata and sticker systems

Abstract

In [4, page166], it is asked what influence the complementarity relation plays as far as the expressiveness of sticker systems and Watson-Crick automata are concerned. Here, we give the answer: (almost) none! More precisely, we show that every language L of a sticker system or a Watson-Crick automaton is the language of such a system with a one-to-one complementarity relation. Our second group of results shows that L is the inverse block coding of a language from the same family over any nontrivial fixed complementarity relation. Finally, we prove that any Watson-Crick automaton can be transformed into an equivalent simple and all-final one. This implies the collapse of parts of the hierarchy introduced in [4]. © Springer-Verlag Berlin Heidelberg 2004.