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].
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Kuske, D., Weigel, P. (2004). The Role of the Complementarity Relation in Watson-Crick Automata and Sticker Systems. In: Calude, C.S., Calude, E., Dinneen, M.J. (eds) Developments in Language Theory. DLT 2004. Lecture Notes in Computer Science, vol 3340. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30550-7_23
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DOI: https://doi.org/10.1007/978-3-540-30550-7_23
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