The program-size complexity of self-assembled squares (extended abstract)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Running time and program size for self-assembled squares
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Combinatorial optimization problems in self-assembly
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
DNA8 Revised Papers from the 8th International Workshop on DNA Based Computers: DNA Computing
Computation by Self-assembly of DNA Graphs
Genetic Programming and Evolvable Machines
Complexities for generalized models of self-assembly
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Invadable self-assembly: combining robustness with efficiency
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Reducing tile complexity for self-assembly through temperature programming
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A self-assembly model of time-dependent glue strength
DNA'05 Proceedings of the 11th international conference on DNA Computing
Complexity of compact proofreading for self-assembled patterns
DNA'05 Proceedings of the 11th international conference on DNA Computing
A computational model for self-assembling flexible tiles
UC'05 Proceedings of the 4th international conference on Unconventional Computation
Self-replication and evolution of DNA crystals
ECAL'05 Proceedings of the 8th European conference on Advances in Artificial Life
Compact error-resilient computational DNA tiling assemblies
DNA'04 Proceedings of the 10th international conference on DNA computing
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Self-assembly is a process in which small objects autonomously associate with each other to form larger complexes. It is ubiquitous in biological constructions at the cellular and molecular scale and has also been identified by nanoscientists as a fundamental method for building nano-scale structures. Recent years have seen convergent interest and efforts in studying self-assembly from mathematicians, computer scientists, physicists, chemists, and biologists. However most complexity theoretical studies of self-assembly utilize mathematical models with two limitations: (1) only attraction, while no repulsion, is studied; (2) only assembled structures of two dimensional square grids are studied. In this paper, we study the complexity of the assemblies resulting from the cooperative effect of repulsion and attraction in a more general setting of graphs. This allows for the study of a more general class of self-assembled structures than the previous tiling model. We define two novel assembly models, namely the accretive graph assembly model and the self-destructible graph assembly model, and identify a fundamental problem in them: the sequential construction of a given graph. We refer to it as the Accretive Graph Assembly Problem (AGAP) and the Self-Destructible Graph Assembly Problem (DGAP), in the respective models. Our main results are: (i) AGAP is NP-complete even if the maximum degree of the graph is restricted to 4 or the graph is restricted to be planar with maximum degree 5; (ii) counting the number of sequential assembly orderings that result in a target graph (#AGAP) is #P-complete; and (iii) DGAP is PSPACE-complete even if the maximum degree of the graph is restricted to 6 (this is the first PSPACE-complete result in self-assembly). We also extend the accretive graph assembly model to a stochastic model, and prove that determining the probability of a given assembly in this model is #P-complete.