A Survey of Combinatorial Gray Codes
SIAM Review
The program-size complexity of self-assembled squares (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Algorithmic self-assembly of dna
Algorithmic self-assembly of dna
Negative interactions in irreversible self-assembly
DNA'10 Proceedings of the 16th international conference on DNA computing and molecular programming
Efficient turing-universal computation with DNA polymers
DNA'10 Proceedings of the 16th international conference on DNA computing and molecular programming
Strand algebras for DNA computing
Natural Computing: an international journal
Complexity of graph self-assembly in accretive systems and self-destructible systems
DNA'05 Proceedings of the 11th international conference on DNA Computing
Asymptotically good codes correcting insertions, deletions, and transpositions
IEEE Transactions on Information Theory
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We study the potential for molecule recycling in chemical reaction systems and their DNA strand displacement realizations. Recycling happens when a product of one reaction is a reactant in a later reaction. Recycling has the benefits of reducing consumption, or waste, of molecules and of avoiding fuel depletion. We present a binary counter that recycles molecules efficiently while incurring just a moderate slowdown compared to alternative counters that do not recycle strands. This counter is an n-bit binary reflecting Gray code counter that advances through 2n states. In the strand displacement realization of this counter, the waste--total number of nucleotides of the DNA strands consumed-- is O(n3), while alternative counters have Ω(2n) waste. We also show that our n-bit counter fails to work correctly when Θ(n) copies of the species that represent the state (bits) of the counter are present initially. The proof applies more generally to show that a class of chemical reaction systems, in which all but one reactant of each reaction are catalysts, are not capable of computations longer than 1/2 n2 steps when there are at least n copies.