5-Symbol 8-State and 5-Symbol 6-State Universal Turing Machines
Journal of the ACM (JACM)
A Machine-Independent Theory of the Complexity of Recursive Functions
Journal of the ACM (JACM)
The program-size complexity of self-assembled squares (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Open problems in artificial life
Artificial Life - Special issue on the Artificial Life VII: looking backward, looking forward
Introduction to the Theory of Computation
Introduction to the Theory of Computation
Self-replication and evolution of DNA crystals
ECAL'05 Proceedings of the 8th European conference on Advances in Artificial Life
Error free self-assembly using error prone tiles
DNA'04 Proceedings of the 10th international conference on DNA computing
Compact error-resilient computational DNA tiling assemblies
DNA'04 Proceedings of the 10th international conference on DNA computing
Complexity of self-assembled shapes
DNA'04 Proceedings of the 10th international conference on DNA computing
Simple evolution of complex crystal species
DNA'10 Proceedings of the 16th international conference on DNA computing and molecular programming
Programmable Control of Nucleation for Algorithmic Self-Assembly
SIAM Journal on Computing
Beyond biology: designing a new mechanism for self-replication and evolution at the nanoscale
Proceedings of the 13th annual conference on Genetic and evolutionary computation
Simple evolution of complex crystal species
Natural Computing: an international journal
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An enduring mystery in biology is how a physical entity simple enough to have arisen spontaneously could have evolved into the complex life seen on Earth today. Cairns-Smith has proposed that life might have originated in clays which stored genomes consisting of an arrangement of crystal monomers that was replicated during growth. While a clay genome is simple enough to have conceivably arisen spontaneously, it is not obvious how it might have produced more complex forms as a result of evolution. Here, we examine this possibility in the tile assembly model, a generalized model of crystal growth that has been used to study the self-assembly of DNA tiles. We describe hypothetical crystals for which evolution of complex crystal sequences is driven by the scarceness of resources required for growth. We show how, under certain circumstances, crystal growth that performs computation can predict which resources are abundant. In such cases, crystals executing programs that make these predictions most accurately will grow fastest. Since crystals can perform universal computation, the complexity of computation that can be used to optimize growth is unbounded. To the extent that lessons derived from the tile assembly model might be applicable to mineral crystals, our results suggest that resource scarcity could conceivably have provided the evolutionary pressures necessary to produce complex clay genomes that sense and respond to changes in their environment.