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58
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 53 (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
Towards parallel evaluation and learning of boolean µformulas with molecules
 Proc. of DNA 3 (H.Rubin, D.Wood, Eds.) DIMACS 48
, 1997
"... A {formula is a Boolean formula in which each variable occurs at most once. The paper treats its molecular representation including its queries using techniques in molecular biology. The novelty is that this method can evaluate a Boolean formula in a single tube within a short time. The preliminary ..."
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Cited by 35 (3 self)
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A {formula is a Boolean formula in which each variable occurs at most once. The paper treats its molecular representation including its queries using techniques in molecular biology. The novelty is that this method can evaluate a Boolean formula in a single tube within a short time. The preliminary experimental result suggests the possibility of parallel evaluation and learning of general {formulas. This method is essentially a simulation of state transitions and can be used to simulate a decision tree or a state machine. 1
Arithmetic and Logic Operations with DNA
, 1997
"... A lot of current research in DNA computing has been directed towards solving difficult combinatorial search problems. However, for DNA computing to be applicable on a wider range of problems, support for basic computational operations such as logic operations like AND, OR and NOT and arithmetic oper ..."
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Cited by 29 (1 self)
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A lot of current research in DNA computing has been directed towards solving difficult combinatorial search problems. However, for DNA computing to be applicable on a wider range of problems, support for basic computational operations such as logic operations like AND, OR and NOT and arithmetic operations like addition and subtraction is necessary. Unlike search problems, which can be solved by generating all possible combinations and extracting the correct output, these operations mandate that only a unique output be generated by specific inputs. The question of suitability of DNA for such simple operations has so far largely been unaddressed. In this paper we describe a novel method for using DNA molecules to solve the basic arithmetic and logic operations. We also show that multiple rounds of operations can be performed in a single test tube, utilizing the output of an operation as an input for the next. Furthermore, the operations can be performed in a linear series or a seriesparallel fashion and operators can be mixed to form any operation sequence.
DNA Simulation of Boolean Circuits
 Proceedings of 3rd Annual Genetic Programming Conference
, 1997
"... In this paper we describe a simulation of Boolean circuits using standard biomolecular techniques. Previously proposed simulations have been shown to run in time proportional to the size of the circuit. The simulation we present here runs in time proportional to the depth of the circuit. We describ ..."
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Cited by 28 (1 self)
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In this paper we describe a simulation of Boolean circuits using standard biomolecular techniques. Previously proposed simulations have been shown to run in time proportional to the size of the circuit. The simulation we present here runs in time proportional to the depth of the circuit. We describe the abstract model and its laboratory implementation, before concluding with a brief analysis.
DNAbased parallel computation of simple arithmetic
 In Proceedings of the 7th International Meeting on DNA Based Computers
, 2001
"... We propose a model for representing and manipulating binary numbers on a DNA chip which allows parallel execution of simple arithmetic. As an example we describe how addition of large binary numbers can be done by using a DNA chip. The number of steps is independent of the size (bits) of the numb ..."
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Cited by 23 (0 self)
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We propose a model for representing and manipulating binary numbers on a DNA chip which allows parallel execution of simple arithmetic. As an example we describe how addition of large binary numbers can be done by using a DNA chip. The number of steps is independent of the size (bits) of the numbers. However, the time for some biochemical reactions is still large, and increases with the size of the sequences to be assembled.
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 16 (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.
DNA Computation: Theory, Practice, and Prospects
 Evolutionary Computation
, 1999
"... Adleman launched the field of DNA computing with a demonstration in 1994 that strands of DNA could be used to solve the Hamiltonian Path Problem for a simple graph. He also identified three broad categories of open questions for the field. First, is DNA capable of universal computation? Second, what ..."
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Cited by 14 (0 self)
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Adleman launched the field of DNA computing with a demonstration in 1994 that strands of DNA could be used to solve the Hamiltonian Path Problem for a simple graph. He also identified three broad categories of open questions for the field. First, is DNA capable of universal computation? Second, what kinds of algorithms can DNA implement? Third, can the error rates in the manipulations of the DNA be controlled enough to allow for useful computation? In the two years that have followed, theoretical work has shown that DNA is in fact capable of universal computation. Furthermore, algorithms for solving interesting questions, like breaking the Data Encryption Standard, have been described using currently available technology and methods. Finally, a few algorithms have been proposed to handle some of the apparently crippling error rates in a few of the common processes used to manipulate DNA. It is thus unlikely that DNA computation is doomed to be only a passing curiosity. However,...
The Complexity and Viability of DNA Computations
, 1997
"... In this paper we examine complexity issues in DNA computation. We believe that these issues are paramount in the search for socalled "killer applications", that is, applications of DNA computation that would establish the superiority of this paradigm over others in particular domains. An ..."
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Cited by 14 (4 self)
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In this paper we examine complexity issues in DNA computation. We believe that these issues are paramount in the search for socalled "killer applications", that is, applications of DNA computation that would establish the superiority of this paradigm over others in particular domains. An assured future for DNA computation can only be established through the discovery of such applications. We demonstrate that current measures of complexity fall short of reality. Consequently, we define a more realistic model, a socalled strong model of computation which provides better estimates of the resources required by DNA algorithms. We also compare the complexities of published algorithms within this new model and the weaker, extant model which is commonly (often implicitly) assumed. 1 Introduction Following the inital promise and enthusiastic response to Adleman's seminal work [1] in DNA computation, progress towards the realisation of worthwhile computations in the laboratory has become st...
Micro Flow BioMolecular Computation
 BioSystems
, 1999
"... In this paper we provide a model for microflow based biomolecular computation (MFBMC). It provides an abstraction for the design of algorithms which account for the constraints of the model. Our MFBMC model uses abstractions of both the recombinant DNA (RDNA) technology as well as of the microf ..."
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Cited by 13 (0 self)
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In this paper we provide a model for microflow based biomolecular computation (MFBMC). It provides an abstraction for the design of algorithms which account for the constraints of the model. Our MFBMC model uses abstractions of both the recombinant DNA (RDNA) technology as well as of the microflow technology and takes into account both of their limitations. For example, when considering the efficiency of the recombinant DNA operation of annealing, we take into account the limitation imposed by the concentration of the reactants. The fabrication technology used to construct MEMS is limited to constructing relatively thin 3D structures. We abstract this by limiting the model to a small constant number of layers (as is done with VLSI models). Besides our contribution of the MFBMC model, the paper contains two other classes of results. The main result is the volume and time efficient algorithm for message routing in the MFBMC model, specifically useful for PAMatch [Rei98a]. We will show that routing of strands between chambers will occur in time O ( N·D m·n), where N is the number of strands in the MFBMC, n is the number of chambers where RDNA operations are occurring, D is the diameter of the topology of the layout of the chambers, and m is proportional to the channel width. Operations that need annealing, such as PAMatch, are shown feasible in O ( N 2 log N