D0L System + Watson-Crick Complementarity = Universal Computation

Abstract

D0L systems consist of iterated letter-to-string morphism over a finite alphabet. Their descriptional power is rather limited and their length sequences can be expressed as sum of products of polynomial and exponential functions. There were several attempts to enrich their structure by various types of regulation, see e.g. [1], leading to more powerful mechanisms.

Due to increasing interest in biocomputing models, V. Mihalache and A. Salomaa suggested in 1997 Watson-Crick D0L systems with so called Watson-Crick morphism. This letter-to-letter morphism maps a letter to the complementary letter, similarly as a nucleotide is joined with the complementary one during transfer of genetic information. Moreover, this new morphism is triggered by a simple condition (called trigger), e.g. with majority of pyrimidines over purines in a string.

This paper deals with the expressive power of standard Watson-Crick D0L systems. A rather unexpected result is obtained: any Turing computable function can be computed by a Watson-Crick D0L system.

Acknowledgements

I am grateful to Arto Salomaa for inspiration, useful remarks and discussions about this paper, to Erzsebet Csuhaj-Varjú and Rudi Freund for invitation to their institutes, and to Alica Kelemenová and Jozef Kelemen for continuous support. Research was supported by the Grant Agency of Czech Republic, grants No. 201/98/P047 and 201/99/1086.