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57
The programsize complexity of selfassembled squares
 In Proceedings of the thirtysecond annual ACM symposium on Theory of computing
, 2000
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Algorithmic SelfAssembly of DNA
, 1998
"... How can molecules compute? In his early studies of reversible computation, Bennett imagined an enzymatic Turing Machine which modified a heteropolymer (such as DNA) to perform computation with asymptotically low energy expenditures. Adleman's recent experimental demonstration of a DNA computation, ..."
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Cited by 104 (6 self)
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How can molecules compute? In his early studies of reversible computation, Bennett imagined an enzymatic Turing Machine which modified a heteropolymer (such as DNA) to perform computation with asymptotically low energy expenditures. Adleman's recent experimental demonstration of a DNA computation, using an entirely different approach, has led to a wealth of ideas for how to build DNAbased computers in the laboratory, whose energy efficiency, information density, and parallelism may have potential to surpass conventional electronic computers for some purposes. In this thesis, I examine one mechanism used in all designs for DNAbased computer  the selfassembly of DNA by hybridization and formation of the double helix  and show that this mechanism alone in theory can perform universal computation. To do so, I borrow an important result in the mathematical theory of tiling: Wang showed how jigsawshaped tiles can be designed to simulate the operation of any Turing Machine. I propose...
Computation at the onset of chaos
 The Santa Fe Institute, Westview
, 1988
"... Computation at levels beyond storage and transmission of information appears in physical systems at phase transitions. We investigate this phenomenon using minimal computational models of dynamical systems that undergo a transition to chaos as a function of a nonlinearity parameter. For perioddoubl ..."
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Cited by 83 (14 self)
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Computation at levels beyond storage and transmission of information appears in physical systems at phase transitions. We investigate this phenomenon using minimal computational models of dynamical systems that undergo a transition to chaos as a function of a nonlinearity parameter. For perioddoubling and bandmerging cascades, we derive expressions for the entropy, the interdependence ofmachine complexity and entropy, and the latent complexity of the transition to chaos. At the transition deterministic finite automaton models diverge in size. Although there is no regular or contextfree Chomsky grammar in this case, we give finite descriptions at the higher computational level of contextfree Lindenmayer systems. We construct a restricted indexed contextfree grammar and its associated oneway nondeterministic nested stack automaton for the cascade limit language. This analysis of a family of dynamical systems suggests a complexity theoretic description of phase transitions based on the informational diversity and computational complexity of observed data that is independent of particular system control parameters. The approach gives a much more refined picture of the architecture of critical states than is available via
On the Computational Power of DNA Annealing and Ligation
 DNA Based Computers, volume 27 of DIMACS
, 1995
"... In [Winfree] it was shown that the DNA primitives of Separate, Merge, and Amplify were not sufficiently powerful to invert functions defined by circuits in linear time. Dan Boneh et al [Boneh] show that the addition of a ligation primitive, Append, provides the missing power. The question becomes, " ..."
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Cited by 75 (19 self)
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In [Winfree] it was shown that the DNA primitives of Separate, Merge, and Amplify were not sufficiently powerful to invert functions defined by circuits in linear time. Dan Boneh et al [Boneh] show that the addition of a ligation primitive, Append, provides the missing power. The question becomes, "How powerful is ligation? Are Separate, Merge, and Amplify necessary at all?" This paper proposes to informally explore the power of annealing and ligation for DNA computation. We conclude, in fact, that annealing and ligation alone are theoretically capable of universal computation. 1 Introduction When Len Adleman introduced the paradigm of using DNA to solve combinatorial problems [Adleman], his computational scheme involved two distinct phases. To solve the directed Hamiltonian path problem, he first mixed together in a test tube a carefully designed set of DNA oligonucleotide "building blocks", which anneal to each other and are ligated to create long strands of DNA representing paths t...
Toward a Mathematical Theory of SelfAssembly (Extended Abstract)
, 1999
"... October, 1999 Leonard M. Adleman University of Southern California Abstract Selfassembly is the ubiquitous process by which objects autonomously assemble into complexes. Nature provides many examples: Atoms react to form molecules. Molecules react to form crystals and supramolecules. Cells some ..."
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Cited by 67 (6 self)
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October, 1999 Leonard M. Adleman University of Southern California Abstract Selfassembly is the ubiquitous process by which objects autonomously assemble into complexes. Nature provides many examples: Atoms react to form molecules. Molecules react to form crystals and supramolecules. Cells sometimes coalesce to form organisms. Even heavenly bodies selfassemble into astronomical systems. It has been suggested that selfassembly will ultimately become an important technology, enabling the fabrication of great quantities of small complex objects such as computer circuits. Recent developments in DNA computing have highlighted the intimate connection between selfassembly and computation. Despite its importance, selfassembly is poorly understood. In this paper, an attempt is made to provide a basis for a mathematical theory of self assembly. A simple mathematical model of selfassembly with 'step counting' is presented and used to investigate the time complexity of polymerization. It...
Optimal Ordered Problem Solver
, 2002
"... We present a novel, general, optimally fast, incremental way of searching for a universal algorithm that solves each task in a sequence of tasks. The Optimal Ordered Problem Solver (OOPS) continually organizes and exploits previously found solutions to earlier tasks, eciently searching not only the ..."
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Cited by 62 (20 self)
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We present a novel, general, optimally fast, incremental way of searching for a universal algorithm that solves each task in a sequence of tasks. The Optimal Ordered Problem Solver (OOPS) continually organizes and exploits previously found solutions to earlier tasks, eciently searching not only the space of domainspecific algorithms, but also the space of search algorithms. Essentially we extend the principles of optimal nonincremental universal search to build an incremental universal learner that is able to improve itself through experience.
Theory of molecular machines. II. Energy dissipation from molecular machines
 J. Theor. Biol
, 1991
"... Single molecules perform a variety of tasks in cells, from replicating, controlling and translating the genetic material to sensing the outside environment. These operations all require that specific actions take place. In a sense, each molecule must make tiny decisions. To make a decision, each “mo ..."
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Cited by 22 (15 self)
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Single molecules perform a variety of tasks in cells, from replicating, controlling and translating the genetic material to sensing the outside environment. These operations all require that specific actions take place. In a sense, each molecule must make tiny decisions. To make a decision, each “molecular machine ” must dissipate an energy Py in the presense of thermal noise Ny. The number of binary decisions that can be made by a machine which has dspace
Computation with finite stochastic chemical reaction networks
 Natural Computing
, 2008
"... Abstract. A highly desired part of the synthetic biology toolbox is an embedded chemical microcontroller, capable of autonomously following a logic program specified by a set of instructions, and interacting with its cellular environment. Strategies for incorporating logic in aqueous chemistry have ..."
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Cited by 19 (5 self)
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Abstract. A highly desired part of the synthetic biology toolbox is an embedded chemical microcontroller, capable of autonomously following a logic program specified by a set of instructions, and interacting with its cellular environment. Strategies for incorporating logic in aqueous chemistry have focused primarily on implementing components, such as logic gates, that are composed into larger circuits, with each logic gate in the circuit corresponding to one or more molecular species. With this paradigm, designing and producing new molecular species is necessary to perform larger computations. An alternative approach begins by noticing that chemical systems on the small scale are fundamentally discrete and stochastic. In particular, the exact molecular counts of each molecular species present, is an intrinsically available form of information. This might appear to be a very weak form of information, perhaps quite difficult for computations to utilize. Indeed, it has been shown that errorfree Turing universal computation is impossible in this setting. Nevertheless, we show a design of a chemical computer that achieves fast and reliable Turinguniversal computation using molecular counts. Our scheme uses only a small number of different molecular species to do computation of arbitrary complexity. The total probability of error of the computation can be made arbitrarily small (but not zero) by adjusting the initial molecular counts of certain species. While physical implementations would be difficult, these results demonstrate that molecular counts can be a useful form of information for small molecular systems such as those operating within cellular environments. Key words. stochastic chemical kinetics; molecular counts; Turinguniversal computation; probabilistic computation 1. Introduction. Many