Reif, J.H.: Parallel molecular computation. In: Seventh Annual ACM Symposium on Parallel Algorithms and Architectures (1995) pp 213-223  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... only by the number of laboratory operations, include that of Reif, who showed that a nondeterministic Turing machine com putation with input size n, space , and time 2 can be executed in his PAM Model using O(s) PA Match steps and O(s log s) other PAM steps, employing aggregates of length O(s) [29]. Beaver showed that polynomial step molecular computers compute PSPACE [5] RooBand Wagner proved that the problems in pNP = AP can be solved in polynomial time using Lipton s model [30] As for the complexity of self assembly, Rothemund and Winfree proved that for any non decreasing unbounded ....

Reif, J.H.: Parallel molecular computation. In: Seventh Annual ACM Symposium on Parallel Algorithms and Architectures (1995) pp 213-223

....algorithm is an important measure of the algorithm s complexity. This measure is also called the volume used by the algorithm. The number of operations used in a molecular computation is called time. In [3, 15, 7, 14] efforts were made in optimize the volume of DNA solution. Various papers [19, 6, 17, 8] apply molecular computing to solve standard computational problems. Beaver [6] and Roos and Wagner [18] designed DNA algorithms to solve a PSPACEcomplete problem, but they used an operation that requires every strand of DNA in a test tube to anneal with its exact counterpart. This is biologically ....

J. Reif. Parallel molecular computation. In Proceedings of the 7th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 213--223, 1995.

....the product of the space used by the automata ( and the number of generations for which it is run (t) The attractive feature of this model is that computations are done in vitro. Unlike other models, no intervention of a lab technician is required. 8) This is the result of Beaver [5] Reif [14] and Papadimitriou [13] that it is possible to simulate PSPACE with DNA operations; denotes the space needed. This, too, is mainly a theoretical result. The problem is that these methods use biological operations that are likely to be impossible to implement in practice. Very roughly speaking, ....

J. Reif. Parallel Molecular Computation. In proceedings of 7th Annual ACM Symposium on Parallel Algorithms and Architectures SPAA'95, 1995, pp. 213-223.

....work as when the plain text was known. Finally, using chosen cipher text attack 1 it is possible to recover the key in one day of work using some preprocessing. This means that after the preprocessing work is done it is possible to break many DES systems for very little work. Several researchers [11, 2, 10] have come up with various methods for implementing non deterministic Turing Machines using molecular computers. Clearly a non deterministic Turing Machine can break any crypto system, including DES, by guessing the correct key. Though these results are very important theoretically, they are not ....

J. Reif, "Parallel Molecular Computation", To appear, SPAA 95.

....a state and a memory and of executing an indefinite number of transitions. In this section, we describe two of the proposals made in order to show how DNA computations can simulate the behavior of a Turing Machine. Other interesting realization of Turing Machines via DNA have been suggested in [Rei95] RW95] Rot96] 7 For example an oligonucleotide 15 base pair long with 10 fixed positions and 5 variable bases. 9 5.1 Beaver s realization of a nondeterministic Turing Machine In [Bea95] and [Bea96] Donald Beaver designed a deterministic Turing Machine consisting of a single DNA strand. ....

....number of Black symbols before halting. 14 increase the computational interest of DNA molecules, proving they are able of keeping a memory too. After Adleman s proposal, another author suggested the realization of a memory model. We will describe the PAM model (suggested by John Reif in [Rei95] in section 8.2. This high level model is characterized by the PA Match operation which added to other known biological operations allows to simulate a CREW PRAM with M memory cells, time bound D and processor bound P , using O(t) PA Match operations and O(s log s) of the other operations, ....

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John Reif. Parallel Molecular Computation. In 7th annual ACM Symposium on Parallel Algorithms and Architectures, Santa Barbara, USA, 1995.

....has been actively studied (for a survey see (Ogihara et al. 1997) One important issue in this field is to clarify how much power DNA based computation can have. A number of papers have studied this problem (Beaver 1995, Boneh et al. 1996, Fu and Beigel 1997, Hagiya 1998, Ogihara and Ray 1998b, Reif 1995, Roo and Wagner 1996, Winfree 1996) but the results are quite diverse. This is partly because DNA computation can be formulated in various ways. One can think of computation as working on a huge collection of library strands that have been generated prior to actual computation, as repeating ....

Reif, J. (1995). Parallel molecular computation. In: Proceedings of 7th ACM Symposium on Parallel Algorithms and Architecture. ACM Press. pp. 213--223.

....variables is set to true. 7) This result increases the efficiency of the two previous algorithms. Details about this algorithm can be found in [BDLS95] 8) The result we refer to is due to Donald Beaver ( Bea94] Bea96] It is only one of the proposals of realizing a Turing Machine via DNA ( Rei95] RW95] Rot96] We will see these kinds of result in section 5 and in section 7.2. 9) The most interesting aspect of this result is the constant number of required biological operation. The trick of this efficiency is the following: the cellular automata is encoded associating each rule of ....

....the value to a bit. The aim of this proposal was to increase the computational interest of DNA molecules, proving they are able of keeping a memory too. After Adleman s proposal, another author suggested the realization of a memory model. We will describe the PAM model (suggested by John Reif in [Rei95] in section 8.2. This high level model is characterized by the PAMatch operation which added to other known biological operations allows to simulate a CREW PRAM with M memory cells, time bound D and processor bound P , using O(t) PA Match operations and O(s log s) of the other operations, ....

[Article contains additional citation context not shown here]

John Reif. Parallel Molecular Computation. In 7th annual ACM Symposium on Parallel Algorithms and Architectures, Santa Barbara, USA, 1995.

....[40] propose models based on cutting DNA strands with restriction enzymes then reannealing and ligating them in new formats. Roweis et al. 39] proposes another very different model that creates an addressable memory by annealing or denaturing stickers to particular sites on a strand. Reif[35] proposes a hypothetical Parallel Associative Matching (PAM) operation, which given two strings, fffi and fi 0 fl, yields fffl if fi = fi 0 and nothing if fi 6= fi 0 . Reif also proposes an alternate model, based on recombinant DNA techniques, which adds a cleavage operation to cut ....

....2.2 Theory Many theoretical analyses have been conducted of Adleman s model and its variations. One key issue is demonstrating the general model capable of universal computation. This has been shown through Turing machine simulations under several varieties of manual molecular computation [11, 35, 38, 40] as well as through somewhat different simulations of boolean circuits [3, 32] There have also been many attempts to analyze the time and space complexity of important problems run on such models. This work has focused primarily on problem classes that cannot be solved in polynomial time by any ....

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J. H. Reif. Parallel molecular computation. In Proceedings of the Seventh ACM Symposium on Parallel Algorithms and Architectures, pages 213--223, 1995.

.... is, What is the computing power of a molecular computer Since the Turing machine model is the standard model of computation, the question can be put in this way, Is the class of molecular computers as powerful as the class of Turing machines Reif has affirmatively answered this question [4]. In particular, he proved that in his parallel associative memory model, a nondeterministic Turing machine computation with input size n and space s can be simulated by a molecular computation in O(s log s) lab steps. Similarly, a crew pram with time t, m memory cells, and p processors can be ....

J.H. Reif, "Parallel molecular computation," Proc. 7th ACM Symposium on Parallel Algorithms and Architectures, July 1995, 213--223.

....write to the global memory in parallel (at the same time) and depending on the outcome of the simultaneous read and the simultaneous write, various PRAM models are defined. The complexity of a PRAM algorithm is measured by the number of processors involved and the running time. Recently, Reif [Rei95] formulated an abstract parallel DNA computation model, the Parallel Associative Memory model (the PAM model, in short) The PAM model, in addition to the standard Recombinant DNA operations, assumes an operation called PA Match, which is a generalized form of ligation of long DNA strands. Reif ....

....the cost functions (the time and the space) of the DNA simulation algorithms expressed as the depth and the size of the circuits to be simulated; 3) the maximum size of the circuits that the DNA algorithms can simulate. The question on simulation efficiency was addressed in the past by Reif [Rei95] First, combined with the fact that Boolean circuits of size m and depth d can be simulated by CREW PRAM algorithms with O(m log m) processors in time O(d log m) see [SV84] the results of Reif [Rei95] indicate that the PAM model can simulate Boolean circuits of size m and depth d in time ....

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J. Reif. Parallel molecular computation. In Proceedings of 7th ACM Symposium on Parallel Algorithms and Architecture, pages 213--223. ACM Press, 1995.

....with all NAND gates presented in [5, 4] suffers from this limitation. One way to overcome this problem is to use the DeMorgan s law to push all the negation gates to the input level [32, 34] This conversion only doubles the size of the circuit. An alternative parallel computation model Reif [35] formulated an abstract parallel DNA computation model, the Parallel Associative Memory model (the PAM model, in short) The PAM model, in addition to the standard Recombinant DNA operations, assumes an operation called PA Match, which is a generalized form of ligation of long DNA strands. Reif ....

J. Reif. Parallel molecular computation. In Proc. 7th Symp. on Parallel Algorithms and Architechture, pages 213--223. ACM Press, 1995.

....by Adleman [Adl94] the potential of DNA as an alternative device for massively parallel computation has been actively studied (for a survey see [ORS97] One important issue in this field is to clarify how much power DNA based computation can have. A number of papers have studied this problem [Bea95,BDLS96,FB97,Hag98,OR98b,Rei95,RW96,Win96], but the results are quite diverse. This is partly because DNA computation can be formulated in various ways. One can think of computation as working on a huge collection of library strands that have been generated prior to actual computation, as repeating generation processes so that all members ....

J. Reif. Parallel molecular computation. In Proceedings of 7th ACM Symposium on Parallel Algorithms and Architecture, pages 213--223. ACM Press, 1995.

....is also called the volume used by the algorithm. The number of operations used in a molecular computation is called time. In (Bach et al. 1996, Ogihara 1996, Beigel and Fu 1997, Morimoto 1996) efforts were made in optimize the volume of DNA solution. Various papers (Roweis et al. 1996, Beaver 1995, Reif 1995, Boneh et al. 1995) apply molecular computing to solve standard computational problems. Beaver (Beaver 1995a) and Roos and Wagner (Roos and Wagner 1996) designed DNA algorithms to solve a PSPACE complete problem, but they used an operation that requires every strand of DNA in a test tube to anneal ....

Reif, J., 1995, Parallel molecular computation, In proceedings of the 7th annual ACM symposium on parallel algorithms and architectures, 213-223.

....the product of the space used by the automata (S) and the number of generations for which it is run (t) The attractive feature of this model is that computations are done in vitro. Unlike other models, no intervention of a lab technician is required. 8) This is the result of Beaver [5] Reif [14] and Papadimitriou [13] that it is possible to simulate PSPACE with DNA operations; S denotes the space needed. This, too, is mainly a theoretical result. The problem is that these methods use biological operations that are likely to be impossible to implement in practice. Very roughly speaking, ....

J. Reif. Parallel Molecular Computation. In proceedings of 7th Annual ACM Symposium on Parallel Algorithms and Architectures SPAA'95, 1995, pp. 213--223.

....3SAT algorithm with volume requirement 1:50 n , and a 1:23 n algorithm for Independent Set. In [Ogi96] an empirical result is shown that gradually extending partial assignments reduces the amount of DNA for 3SAT. How about simulation of existing parallel computer models In regards to PRAM, Rei95] presents a model that assumes ligation of long DNA strands. Under that model, a CREW PRAM algorithm running in time T on P processors can be simulate with the total memory size M , with O(T S) long strand ligation steps and O(S log S) other steps, and with the total volume polynomial in S, ....

J. Reif. Parallel molecular computation. In Proceedings of 7th ACM Symposium on Parallel Algorithms and Architecture, pages 213--223. ACM Press, 1995.

....algorithm is an important measure of the algorithm s complexity. This measure is also called the volume used by the algorithm. The number of operations used in a molecular computation is called time. In [3, 15, 7, 14] efforts were made in optimize the volume of DNA solution. Various papers [19, 6, 17, 8] apply molecular computing to solve standard computational problems. Beaver [6] and Roos and Wagner [18] designed DNA algorithms to solve a PSPACEcomplete problem, but they used an operation that requires every strand of DNA in a test tube to anneal with its exact counterpart. This is biologically ....

J. Reif. Parallel molecular computation. In Proceedings of the 7th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 213--223, 1995.

.... a splicing rule is applicable only when certain strings, called permitting contexts, are present in the terms of splicing (see [16] Constructions showing how to simulate the work of a Turing machine by a DNA model of computation have also been proposed in [40] 37] 2] 8] 6] 46] [36]. In an optimistic way, one may think of an analogy between these results and the work on finding models of computation carried out in the 30 s, which has laid the foundation for the design of the electronic computers. In a similar fashion, the results obtained about the models of DNA ....

J.Reif. Parallel Molecular Computation. To appear in SPAA'95, also at http://www.cs.duke.edu/~reif/HomePage.html.

....familiarity with those ideas. Fortunately, Adleman s paper is concise and well written. It should be easily accessible to any readers who have penetrated our discussion of molecular biology. Readers interested in subsequent developments within Adleman s framework should consult Reif s paper [Rei95] and the papers he cites. The computational models we have developed are strikingly different from Adleman s use of biotechnology to solve the Hamiltonian Path problem. The Hamiltonian Path problem is NP complete. Like all NP complete problems it has an exponentially large space of potential ....

J. Reif. Parallel molecular computation. In Proceedings of the 7th ACM Symposium on Parallel Algorithms and Architectures, pages 213--223, 1995.

....write to the global memory in parallel (at the same time) and depending on the outcome of the simultaneous read and the simultaneous write, various PRAM models are defined. The complexity of a PRAM algorithm is measured by the number of processors involved and the running time. Recently, Reif [Rei95] formulated an abstract parallel DNA computation model, the Parallel Associative Memory model, and showed that his parallel model can simulate the Concurrent Read, Exclusive Write PRAM model (CREW PRAM model) with a small time overhead. More precisely, a CREW PRAM algorithm running in time T on ....

....the answer for the following two reasons. First, direct simulations may result in a smaller overhead. Second, more importantly, concerns have been expressed about the use of extact for separation, as employed in Reif s method. There has been much discussion on the feasibility of extract [Adl95, Rei95, BL95, KKW96] because its error rate, even with the current best Recombinant DNA technique, is as large as 10 Gamma6 (see, ABL 94] which is high enough to fail the whole computation. We thus study the problem of simulating Boolean circuits by DNA computers without using extract. This ....

J. Reif. Parallel molecular computation. In Proceedings of the 7th ACM Symposium on Parallel Algorithms and Architecture, pages 213--223. ACM Press, 1995.

....some marker sequence M on all strings created. Extracting on M would get you a tube full of sequences coded in the positive . PCR and separation and extraction on M would get you a tube coded in the complement. You can mix these. Then one might hope that complementary strings might 2 Reif[13] and Beaver [2] proposed a solution to this problem. This solution, however, involves using enough DNA molecules to encode all pairs of virtual processors. If one might (optimistically) have 10 18 DNA molecules, then, this proposal would restrict one to 10 9 virtual processors. But since DNA ....

J. Reif, "Parallel Molecular Computation", Proceedings of SPAA 95.

....of traditional resource bounded complexity. Much work has been done in this regard. In particular, variations of the models by Adleman and Lipton, in which computations take place by applying operations to an exponential size set of strands created beforehand, are well studied in the literature [2, 4, 5, 6, 7, 12, 13, 18]. These papers show that the power of polynomial time computation in such models will become, depending on the choice of permissible biochemical operations (realistic or unrealistic) a) PBP (the polynomial size branching programs) 18] b) Delta p 2 [6] c) Delta p 3 [13] d) PH [5] or ....

.... show that the power of polynomial time computation in such models will become, depending on the choice of permissible biochemical operations (realistic or unrealistic) a) PBP (the polynomial size branching programs) 18] b) Delta p 2 [6] c) Delta p 3 [13] d) PH [5] or (e) PSPACE [4, 12]. Of all the variations that have been considered, the smallest is the model studied in (a) namely, the Restricted Model proposed by Adleman [2] a library based model assuming only Merge, Detect, and Separate. One may ask whether there are smaller DNA computational models, i.e. whether some of ....

J. Reif. Parallel molecular computation. In Proceedings of 7th ACM Symposium on Parallel Algorithms and Architecture, pages 213--223. ACM Press, 1995.

....can enable them to recognize that they are identical 2 . 4 Solving the knapsack problem The dynamic programming approach for solving the knapsack problem [4] can be easily stated as a graph connectivity problem. The diameter of the resulting graph is linear in the size of the knapsack 2 Reif[9] proposes a solution to this problem. His solution, however, involves using enough DNA molecules to encode all pairs of virtual processors. If one might (optimistically) have 10 18 DNA molecules, then, his proposal would restrict one to 10 9 virtual processors. But since DNA processors are at ....

J. Reif, "Parallel Molecular Computation", SPAA 95.

.... very different from each other, their computational capabilities are quite similar in the sense that one model can be simulated by the other model with a reasonably small overhead in resources (Fortune and Wyllie 1978) Regarding DNA based simulations of abstract parallel computation models, Reif (Reif 1995) introduced the PAM model, Supported in part by the National Science Foundation CAREER Award CCR 9701911 and the NSF Grant CCR 9725021. y Supported in part by the National Science Foundation Grant MCB9630402. which is capable of simulating PRAM with a small overhead. Ogihara and Ray ....

Reif, J. (1995). Parallel molecular computation. In: Proceedings of 7th ACM Symposium on Parallel Algorithms and Architecture. ACM Press. pp. 213--223.

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