By David M. Burton
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Extra resources for An introduction to abstract mathematical systems
J. Patitz bit=1 1 msb 0 int 0 int 1 lsb 1 new 0 grow 0 int 0 lsb 1 msb 1 int 1 lsb 1 msb 1 int 0 lsb 1 msb 0 int 1 lsb 1 new 0 grow 0 lsb 1 msb 1 lsb 1 msb 0 lsb 0 msbseed 1 lsbseed bit=0 grow lsb bit=(0,1) carry=(0,1) ,1) interior bit=1 bit=0 bit=(0,1) bit=1 =1 msbseed carry=(0,1) =(0 rry ca msb carry=(0,1) bit new carry=1 lsbseed (a) Schematic diagram depicting the tile templates and joins which are used to generate a tile set that selfassembles a log-width binary counter. All east-west joins pass the carry signal and south-north joins pass the bit signal (although some of them are restricted to subsets of the allowable values (0, 1)).
However, weak self-assembly is a more general notion. For example, Winfree’s above mentioned result shows that the discrete Sierpinski triangle weakly self-assembles at temperature 2 , yet this shape Limitations of Self-assembly at Temperature One 37 does not strictly self-assemble at any temperature . Hence weak self-assembly allows for a more relaxed notion of set building, in which intermediate space can be used for computation, without requiring that the space ﬁlled to carry out the computation also represent the ﬁnal result of the computation.
In either case the major objective is to express “commands” in the DSL that more closely model the way one thinks about the domain than the “host” language in which the project is written. If the syntax and semantics of the DSL are precisely deﬁned, this facilitates the creation of a semantic editor (text-based or visual), in which programs in the DSL may be produced using a tool that can visually show semantically meaningful information such as compilation or even logical errors, and can help the programmer directly edit the abstract components of the DSL, instead of editing the source code directly.