Figure 2.

Elementary reduction rules of the DSD language. For each rule, the graphical representation below is equivalent to the program code above. We let S^∼ denote the migration rate of a domain concatenation S, and we let N⁺ and N⁻ denote the binding and unbinding rates, respectively, of a toehold N^. We let fst(S) and lst(S) denote the first and last domains in a concatenation S, respectively, and we assume that fst(R2) ≠ fst(S2) for rule (RM). This ensures that branch migration is maximal along a given domain concatenation and that rules (RM) and (RD) are mutually exclusive.