Abstract
Systems based on the splicing operation are computationally complete. Usually demonstrations of this are based on simulations of type-0 grammars. We propose a different way to reach this result by solving Diophantine equations using extended H system with permitting context. Completeness then follows from Matiyasevichâs theorem stating that the class of Diophantine sets is identical to the class of recursive enumerable sets.
Solutions to a Diophantine equation are found in parallel. The numbers are coded in base one.
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Frisco, P. (2001). Diophantine equations and splicing: A new demonstration of the generative capability of H systems. In: Condon, A., Rozenberg, G. (eds) DNA Computing. DNA 2000. Lecture Notes in Computer Science, vol 2054. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44992-2_4
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DOI: https://doi.org/10.1007/3-540-44992-2_4
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