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
Complexities for Generalized Models of Self-Assembly
SIAM Journal on Computing
Computation with finite stochastic chemical reaction networks
Natural Computing: an international journal
Random Number Selection in Self-assembly
UC '09 Proceedings of the 8th International Conference on Unconventional Computation
Complexity of graph self-assembly in accretive systems and self-destructible systems
DNA'05 Proceedings of the 11th international conference on DNA Computing
Less haste, less waste: on recycling and its limits in strand displacement systems
DNA'11 Proceedings of the 17th international conference on DNA computing and molecular programming
Exact shapes and turing universality at temperature 1 with a single negative glue
DNA'11 Proceedings of the 17th international conference on DNA computing and molecular programming
The power of nondeterminism in self-assembly
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Natural Computing: an international journal
An introduction to tile-based self-assembly
UCNC'12 Proceedings of the 11th international conference on Unconventional Computation and Natural Computation
| Hi-index | 0.00 |
This paper explores the use of negative (i.e., repulsive) interactions in the abstract Tile Assembly Model defined by Winfree. Winfree in his Ph.D. thesis postulated negative interactions to be physically plausible, and Reif, Sahu, and Yin studied them in the context of reversible attachment operations. We investigate the power of negative interactions with irreversible attachments, and we achieve two main results. Our first result is an impossibility theorem: after t steps of assembly, Ω(t) tiles will be forever bound to an assembly, unable to detach. Thus negative glue strengths do not afford unlimited power to reuse tiles. Our second result is a positive one: we construct a set of tiles that can simulate an s-space-bounded, t-time-bounded Turing machine, while ensuring that no intermediate assembly grows larger than O(s), rather than O(s ċ t) as required by the standard Turing machine simulation with tiles.