Optimal Self-Assembly of Counters at Temperature Two
نویسندگان
چکیده
We present a tile system for assembling a counter of width K and height N = 2 on top of a seed-row in optimum time Θ(N). Our counter works at temperature 2. Earlier known constructions either took sub-optimal time or required temperature 3. Using existing techniques, our system for assembling a counter from a seed row can be extended into a system for assembling an N × N square in optimum time Θ(N) and with optimum program size Θ(log N/ log log N). We also present a general technique for analyzing the expected completion time of irreversible self-assemblies.
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