Approximating the smallest grammar: Kolmogorov complexity in natural models
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Application of Lempel-Ziv Factorization to the Approximation of Grammar-Based Compression
CPM '02 Proceedings of the 13th Annual Symposium on Combinatorial Pattern Matching
Algorithmic self-assembly of dna
Algorithmic self-assembly of dna
Approximation algorithms for grammar-based data compression
Approximation algorithms for grammar-based data compression
Staged self-assembly: nanomanufacture of arbitrary shapes with O(1) glues
Natural Computing: an international journal
Synthesizing minimal tile sets for patterned DNA self-assembly
DNA'10 Proceedings of the 16th international conference on DNA computing and molecular programming
Complexity of self-assembled shapes
DNA'04 Proceedings of the 10th international conference on DNA computing
Synthesis of Tile Sets for DNA Self-Assembly
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Theory of algorithmic self-assembly
Communications of the ACM
Synthesizing minimal tile sets for complex patterns in the framework of patterned DNA self-assembly
Theoretical Computer Science
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We introduce the problem of staged self-assembly of one-dimensional nanostructures, which becomes interesting when the elements are labeled (e.g., representing functional units that must be placed at specific locations). In a restricted model in which each operation has a single terminal assembly, we prove that assembling a given string of labels with the fewest stages is equivalent, up to constant factors, to compressing the string to be uniquely derived from the smallest possible context-free grammar (a well-studied O(log n)-approximable problem). Without this restriction, we show that the optimal assembly can be substantially smaller than the optimal context-free grammar, by a factor of Ω(√n/ log n) even for binary strings of length n. Fortunately, we can bound this separation in model power by a quadratic function in the number of distinct glues or tiles allowed in the assembly, which is typically small in practice.