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Local parallel biomolecular computing
 DNA Based Computers III, volume 48 of DIMACS
, 1999
"... Biomolecular Computation(BMC) is computation at the molecular scale, using biotechnology engineering techniques. Most proposed methods for BMC used distributed (molecular) parallelism (DP); where operations are executed in parallel on large numbers of distinct molecules. BMC done exclusively by DP r ..."
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Cited by 56 (16 self)
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Biomolecular Computation(BMC) is computation at the molecular scale, using biotechnology engineering techniques. Most proposed methods for BMC used distributed (molecular) parallelism (DP); where operations are executed in parallel on large numbers of distinct molecules. BMC done exclusively by DP requires that the computation execute sequentially within any given molecule (though done in parallel for multiple molecules). In contrast, local parallelism (LP) allows operations to be executed in parallel on each given molecule. Winfree, et al [W96, WYS96]) proposed an innovative method for LPBMC, that of computation by unmediated selfassembly of � arrays of DNA molecules, applying known domino tiling techniques (see Buchi [B62], Berger [B66], Robinson [R71], and Lewis and Papadimitriou [LP81]) in combination with the DNA selfassembly techniques of Seeman et al [SZC94]. The likelihood for successful unmediated selfassembly of computations has not been determined (we discuss a simple model of assembly where there may be blockages in selfassembly, but more sophisticated models may have a higher likelihood of success). We develop improved techniques to more fully exploit the potential power of LPBMC. To increase
Beyond Turing Machines
"... In this paper we describe and analyze models of problem solving and computation going beyond Turing Machines. Three principles of extending the Turing Machine's expressiveness are identified, namely, by interaction, evolution and infinity. Several models utilizing the above principles are pr ..."
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Cited by 40 (6 self)
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In this paper we describe and analyze models of problem solving and computation going beyond Turing Machines. Three principles of extending the Turing Machine's expressiveness are identified, namely, by interaction, evolution and infinity. Several models utilizing the above principles are presented. Other
Emergent Computation by Catalytic Reactions
, 1996
"... Recently, biochemical systems have been shown to possess interesting computational properties. In a parallel development, the chemical computation metaphor is becoming more and more frequently used as part of the emergent computation paradigm in Computer Science. We review in this contribution the i ..."
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Cited by 23 (14 self)
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Recently, biochemical systems have been shown to possess interesting computational properties. In a parallel development, the chemical computation metaphor is becoming more and more frequently used as part of the emergent computation paradigm in Computer Science. We review in this contribution the idea behind the chemical computational metaphor and outline its relevance for nanotechnology. We set up a simulated reaction system of mathematical objects and examine its dynamics by computer experiments. Typical problems of computer science, like sorting, parity checking or prime number computation are placed within this context. The implications of this approach for nanotechnology, parallel computers based on molecular devices and DNARNAprotein information processing are discussed. 1 Introduction The idea of using natural systems for computational purposes has long been pondered. Haken, for instance, has proposed to use laser mode competition as a way to recognize patterns [1]. Others h...
Parallel Biomolecular Computation: Models and Simulations
 Algorithmica
, 1995
"... This paper is concerned with the development of techniques for massively parallel computation at the molecular scale, which we refer to as molecular parallelism. While this may at first appear to be purely science fiction, already Adleman [A 94] has employed molecular parallelism in the solution ..."
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Cited by 18 (0 self)
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This paper is concerned with the development of techniques for massively parallel computation at the molecular scale, which we refer to as molecular parallelism. While this may at first appear to be purely science fiction, already Adleman [A 94] has employed molecular parallelism in the solution of the Hamiltonian path problem, and successfully tested his techniques in a lab experiment on DNA for a small graph. Lipton [L 94] showed that finding the satisfying inputs to a Boolean expression of size n can be done in O(n) lab steps using DNA of length O(n log n) base pairs. This recent work by Adleman and Lipton in molecular parallelism considered only the solution of NP search problems, and provided no way of quickly executing lengthy computations by purely molecular means; the number of lab steps depended linearly on the size of the simulated expression. See Reif [R97a] for further recent work on molecular parallelism and see Reif [R97] for an extensive survey of molecular pa...
Paradigms for Biomolecular Computation
 UNCONVENTIONAL MODELS OF COMPUTATION
, 1998
"... Biomolecular Computation (BMC) is computation done at the molecular scale, using Biotechnological techniques. This paper discusses the underlying biotechnology that BMC may utilize, and surveys a number of distinct paradigms for doing BMC. We also identify a number of key future experimental mile ..."
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Cited by 17 (7 self)
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Biomolecular Computation (BMC) is computation done at the molecular scale, using Biotechnological techniques. This paper discusses the underlying biotechnology that BMC may utilize, and surveys a number of distinct paradigms for doing BMC. We also identify a number of key future experimental milestones for the field of BMC.
On the Integrality Ratio for the Asymmetric Traveling Salesman Problem
 Mathematics of Operations Research
, 2006
"... informs ® doi 10.1287/moor.1060.0191 ..."
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Solid Phase DNA Solution to the Hamiltonian Path Problem
, 1997
"... . A solidphase method for solving the Hamiltonian path problem (HPP) is described. The method employs only fast and simple DNA operations amenable to full automation. Singlestranded DNA molecules representing paths with no city visited twice are synthesized citybycity from the start city on the ..."
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Cited by 14 (0 self)
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. A solidphase method for solving the Hamiltonian path problem (HPP) is described. The method employs only fast and simple DNA operations amenable to full automation. Singlestranded DNA molecules representing paths with no city visited twice are synthesized citybycity from the start city on the surface of a solid support. The solution can thus be found in the computation time proportional to the number of cities. As well as the stepwise path synthesis, a pruning technique developed for the removal of looping paths helps the reduction of DNA molecules necessary for the computation; thus definitely increasing the size of problems solvable on a DNAbased computer. Experiments using Adleman's sevencity instance of the HPP showed that the path extension cycle was very accurate and took only about 45 min. Our solidphase method has originally been developed for solving the HPP, but it could also be applied to other problems requiring a massive parallelism in computation. 1. Introduction...
Challenges and applications for selfassembled DNAnanostructures
 In: Proceedings of the Sixth DIMACS Workshop on DNA Based Computers (meeting at
, 2000
"... Abstract. DNA selfassembly is a methodology for the construction of molecular scale structures. In this method, arti cially synthesized single stranded DNA selfassemble into DNA crossover molecules (tiles). These DNA tiles have sticky ends that preferentially match the sticky ends of certain other ..."
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Cited by 14 (4 self)
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Abstract. DNA selfassembly is a methodology for the construction of molecular scale structures. In this method, arti cially synthesized single stranded DNA selfassemble into DNA crossover molecules (tiles). These DNA tiles have sticky ends that preferentially match the sticky ends of certain other DNA tiles, facilitating the further assembly into tiling lattices. We discuss key theoretical and practical challenges of DNA selfassembly, aswell as numerous potential applications. The selfassembly of large 2D lattices consisting of up to thousands of tiles have been recently demonstrated, and 3D DNA lattices maysoonbe feasible to construct. We describe various novel DNA tiles with properties that facilitate selfassembly and their visualization by imaging devices such as atomic force microscope. We discuss bounds on the speed and error rates of the various types of selfassembly reactions, as well as methods that may minimize errors in selfassembly. We brie y discuss the ongoing development of attachment chemistry from DNA lattices
Molecular assembly and computation: From theory to experimental demonstrations
 In 29th International Colloquium on Automata, Languages, and Programming(ICALP), Mlaga
, 2002
"... Abstract. While the topic of Molecular Computation would have appeared even a half dozen years ago to be purely conjectural, it now is an emerging subeld of computer science with the development of its theoretical basis and a number of moderate to largescale experimental demonstrations. This paper ..."
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Cited by 10 (0 self)
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Abstract. While the topic of Molecular Computation would have appeared even a half dozen years ago to be purely conjectural, it now is an emerging subeld of computer science with the development of its theoretical basis and a number of moderate to largescale experimental demonstrations. This paper focuses on a subarea of Molecular Computation known as DNA selfassembly. Selfassembly is the spontaneous selfordering of substructures into superstructures driven by the selective aÆnity of the substructures. DNA provides a molecular scale material for eecting this programmable selfassembly, using the selective aÆnity of pairs of DNA strands to form DNA nanostructures. DNA selfassembly is the most advanced and versatile system known for programmable construction of patterned systems on the molecular scale. The methodology of DNA selfassembly begins with the synthesis of singlestrand DNA molecules that selfassemble into macromolecular building blocks called DNA tiles. These tiles have sticky ends that match the
In Some Curved Spaces, One Can Solve NPHard Problems in Polynomial Time
"... In the late 1970s and the early 1980s, Yuri Matiyasevich actively used his knowledge of engineering and physical phenomena to come up with parallelized schemes for solving NPhard problems in polynomial time. In this paper, we describe one such scheme in which we use parallel computation in curved s ..."
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In the late 1970s and the early 1980s, Yuri Matiyasevich actively used his knowledge of engineering and physical phenomena to come up with parallelized schemes for solving NPhard problems in polynomial time. In this paper, we describe one such scheme in which we use parallel computation in curved spaces. 1 Introduction and Formulation of the Problem Many practical problems are NPhard. It is well known that many important practical problems are NPhard; see, e.g., [11, 14, 27]. Under the usual hypothesis that P̸=NP, NPhardness has the following intuitive meaning: every algorithm which solves all instances of the corresponding problem requires, for