The program-size complexity of self-assembled squares (extended abstract)
STOC '00 Proceedings of the thirty-second 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
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the Decidability of Self-Assembly of Infinite Ribbons
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
DNA Self-Assembly For Constructing 3D Boxes
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Computation by Self-assembly of DNA Graphs
Genetic Programming and Evolvable Machines
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Complexity of Self-Assembled Shapes
SIAM Journal on Computing
Expectation and variance of self-assembled graph structures
DNA'05 Proceedings of the 11th international conference on DNA Computing
Complexity of graph self-assembly in accretive systems and self-destructible systems
DNA'05 Proceedings of the 11th international conference on DNA Computing
Multiset-Based Self-Assembly of Graphs
Fundamenta Informaticae - New Frontiers in Scientific Discovery - Commemorating the Life and Work of Zdzislaw Pawlak
On the complexity of graph self-assembly in accretive systems
Natural Computing: an international journal
Complexity classes for self-assembling flexible tiles
Theoretical Computer Science
Complexity of graph self-assembly in accretive systems and self-destructible systems
Theoretical Computer Science
On aggregation in multiset-based self-assembly of graphs
Natural Computing: an international journal
On stoichiometry for the assembly of flexible tile DNA complexes
Natural Computing: an international journal
Flexible versus rigid tile assembly
UC'06 Proceedings of the 5th 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
Spectrum of a pot for DNA complexes
DNA'06 Proceedings of the 12th international conference on DNA Computing
On the complexity of graph self-assembly in accretive systems
DNA'06 Proceedings of the 12th international conference on DNA Computing
Multiset-Based Self-Assembly of Graphs
Fundamenta Informaticae - New Frontiers in Scientific Discovery - Commemorating the Life and Work of Zdzislaw Pawlak
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We present a theoretical model for self-assembling tiles with flexible branches motivated by DNA branched junction molecules. We encode an instance of a “problem” as a pot of such tiles, and a “solution” as an assembled complete complex without any free sticky ends (called ports), whose number of tiles is within predefined bounds. We develop an algebraic representation of this self-assembly process and use it to prove that this model of self-assembly precisely captures NP-computability when the number of tiles in the minimal complete complexes is bounded by a polynomial.