Difference between revisions of "Cooperation"

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(Overview)
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==Overview==
 
==Overview==
  
Cooperation is a property of systems that can take information from two different places in order to determine which tiles to place in a third location. Cooperation is important because it enables tile assembly systems to simulate Turing machines and, by extension, perform universal computations. This is traditionally a property of temperature 2 or higher systems, since this enables single tiles to have certain glues that allow them to attach in place based off of the exposed glues nearby. However, temperature 1 systems have been known to "fake" cooperation using geometry in certain augmentations of the model.
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In tile assembly models, cooperation is the process by which two or more glues on nearby tiles contribute enough strength to allow a tile to attach when one of the glues would not have been sufficient. Most interesting tile systems in the aTAM (such as Turing machine simulations, binary counters, and efficient shape builders) seem to require cooperation, which has lead to the long standing conjecture that non-cooperative tile assembly systems cannot perform arbitrary computation.
  
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==Weak-Cooperation
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Cooperation normally requires a binding threshold parameter (temperature) of 2 or more; however, in a variety of tile assembly models, this sort of behavior can be simulated through mechanisms other than glue binding, such as geometric hindrance or negative glues. Models in which this occurs are called *weakly-cooperative* and are often capable of universal computation even at temperature 1.
  
 
[[Category:Self-assembly]]
 
[[Category:Self-assembly]]
 
[[Category:Terminology]]
 
[[Category:Terminology]]

Revision as of 12:10, 8 July 2019

Overview

In tile assembly models, cooperation is the process by which two or more glues on nearby tiles contribute enough strength to allow a tile to attach when one of the glues would not have been sufficient. Most interesting tile systems in the aTAM (such as Turing machine simulations, binary counters, and efficient shape builders) seem to require cooperation, which has lead to the long standing conjecture that non-cooperative tile assembly systems cannot perform arbitrary computation.

==Weak-Cooperation Cooperation normally requires a binding threshold parameter (temperature) of 2 or more; however, in a variety of tile assembly models, this sort of behavior can be simulated through mechanisms other than glue binding, such as geometric hindrance or negative glues. Models in which this occurs are called *weakly-cooperative* and are often capable of universal computation even at temperature 1.