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On the Power of Circular Splicing Systems and DNA Computability
 Proc. of IEEE Intern. Conf. on Evol. Comput. (ICEC'97
, 1997
"... From a biological motivation of interactions between linear and circular DNA sequences, we propose a new type of splicing models called circular H systems and show that they have the same computational power as Turing machines. It is also shown that there effectively exists a universal circular H sy ..."
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Cited by 22 (5 self)
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From a biological motivation of interactions between linear and circular DNA sequences, we propose a new type of splicing models called circular H systems and show that they have the same computational power as Turing machines. It is also shown that there effectively exists a universal circular H system which can simulate any circular H system with the same terminal alphabet, which strongly suggests a feasible design for a DNA computer based on circular splicing. 1 Introduction Since Adleman's breathtaking paper on molecular (DNA) computing ([1]), there have already been quite a few papers on this challenging topic : [10] shows how to solve NPcomplete problems using DNA, while [3] discusses a design method for simulating a Turing machine by molecular biological techniques and shows how to compute PSPACE, and [4]) gives a methodology for breaking the DES using techniques in genetic engineering. In response to the rapid stream of experimental research on this new computation paradigm...
DNA Computing Based on Splicing: Universality Results
 FIRST ANNUAL PACIFIC SYMPOSIUM ON BIOCOMPUTING
, 1996
"... The paper extends some of the most recently obtained results on the computational universality of specific variants of H systems (e. g. with regular sets of rules) and proves that we can construct universal computers based on various types of H systems with a finite set of splicing rules as well as ..."
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Cited by 20 (6 self)
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The paper extends some of the most recently obtained results on the computational universality of specific variants of H systems (e. g. with regular sets of rules) and proves that we can construct universal computers based on various types of H systems with a finite set of splicing rules as well as a finite set of axioms, i. e. we show the theoretical possibility to design programmable universal DNA computers based on the splicing operation. For H systems working in the multiset style (where the numbers of copies of all available strings are counted) we elaborate how a Turing machine computing a partial recursive function can be simulated by an equivalent H system computing the same function; in that way, from a universal Turing machine we obtain a universal H system. Considering H systems as language generating devices we have to add various simple control mechanisms (checking the presence/absence of certain symbols in the spliced strings) to systems with a finite set of splicing ru...
DNA Computing Based on Splicing: The Existence of Universal Computers
 THEORY OF COMPUTING SYSTEMS
, 1995
"... Splicing systems are generative mechanisms based on the splicing operation introduced by Tom Head as a model of DNA recombination. We prove that the generative power of finite extended splicing systems equals that of Turing machines, provided we consider multisets or provided a control mechanism is ..."
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Cited by 19 (3 self)
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Splicing systems are generative mechanisms based on the splicing operation introduced by Tom Head as a model of DNA recombination. We prove that the generative power of finite extended splicing systems equals that of Turing machines, provided we consider multisets or provided a control mechanism is added. We also show that there exist universal splicing systems with the properties above, i. e. there exists a universal splicing system with fixed components which can simulate the behaviour of any given splicing system, when an encoding of the particular splicing system is added to its set of axioms. In this way the possibility of designing programmable DNA computers based on the splicing operation is proved.
Test Tube Distributed Systems Based on Splicing
 COMPUTERS AND AI
, 1996
"... We define a symbol processing mechanism with the components (test tubes) working as splicing schemes in the sense of T. Head and communicating by redistributing the contents of tubes (in a similar way to the separate operation of LiptonAdleman). (These systems are similar to the distributed generat ..."
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Cited by 19 (1 self)
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We define a symbol processing mechanism with the components (test tubes) working as splicing schemes in the sense of T. Head and communicating by redistributing the contents of tubes (in a similar way to the separate operation of LiptonAdleman). (These systems are similar to the distributed generative mechanisms called Parallel Communicating Grammar Systems.) Systems with finite initial contents of tubes and finite sets of splicing rules associated to each component are computationally complete, they characterize the family of recursively enumerable languages. The existence of universal test tube distributed systems is obtained on this basis, hence the theoretical proof of the possibility to design universal programmable computers with the structure of such a system.
DNA Computing, Sticker Systems, and Universality
 ACTA INFORMATICA
, 1998
"... We introduce the sticker systems, a computability model, which is an abstraction of the computations using the WatsonCrick complementarity as in Adleman's DNA computing experiment, [1]. Several types of sticker systems are shown to characterize (modulo a weak coding) the regular languages, hen ..."
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Cited by 12 (3 self)
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We introduce the sticker systems, a computability model, which is an abstraction of the computations using the WatsonCrick complementarity as in Adleman's DNA computing experiment, [1]. Several types of sticker systems are shown to characterize (modulo a weak coding) the regular languages, hence the power of finite automata. One variant is proven to be equivalent to Turing machines. Another one is found to have a strictly intermediate power.
DNA Computing Based on Splicing: Universality Results
, 1997
"... First, we recall some characterizations of recursively enumerable languages by means of finite H systems with certain regulations on the splicing operation. Then, we consider a variant of the splicing operation where the splicing proceeds always in couples of steps: the two strings obtained after a ..."
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Cited by 10 (0 self)
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First, we recall some characterizations of recursively enumerable languages by means of finite H systems with certain regulations on the splicing operation. Then, we consider a variant of the splicing operation where the splicing proceeds always in couples of steps: the two strings obtained after a splicing enter immediately a second splicing (the rules used in the two steps are not prescribed). Somewhat surprising if we take into account the loose control on the performed operations, extended H systems with finite sets of axioms and of splicing rules, using this double splicing operation, can again characterize the recursively enumerable languages. Finally, we consider twotypes of distributed H systems: communicating distributed H systems and timevarying distributed H systems. For the first type of devices, we give a new proof of the recent result of [24] that (in the extended case) such systems with three components characterize the recursively enumerable languages. In what...
DNA Computing: Models and Implementations
, 2002
"... As the fabrication of integrated circuits continues to take place on increasingly smaller scales, we grow closer to several fundamental limitations on electronic computers. For many classes of problems, computing devices based on biochemical reactions present an attractive alternative to conventiona ..."
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Cited by 8 (0 self)
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As the fabrication of integrated circuits continues to take place on increasingly smaller scales, we grow closer to several fundamental limitations on electronic computers. For many classes of problems, computing devices based on biochemical reactions present an attractive alternative to conventional computing paradigms. We present here a survey of the theory and implementation of biologically and biochemically based computers.
DNA Implementation of Simple Horn Clause Computation
, 1997
"... In this paper, we propose a method for biologically implementing simple Boolean formulae. This method enables us to compute logical consequences of a given set of simple Horn clauses in parallel and takes advantage of potentially huge number of molecular CPUs of DNA computers. Further, we show that ..."
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Cited by 7 (0 self)
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In this paper, we propose a method for biologically implementing simple Boolean formulae. This method enables us to compute logical consequences of a given set of simple Horn clauses in parallel and takes advantage of potentially huge number of molecular CPUs of DNA computers. Further, we show that the method is nicely applied to the parallel implementation of a grammatical recognition algorithm which is based on `dynamic programming. ' 1 Introduction Adleman's work on the DNA implementation of computing a given instance of directed Hamiltonian path problem, which is known to be NPComplete, opens the door to the highly parallel computation using `molecules'([Adl94]). His study was followed by many researches: generalizing his technique([Lip95a][Lip95b]), providing abstract DNA computer models with Turing computability([Adl95] [Bea95][WR95]), and so forth. In spite of those efforts on pursuing possible implementation of DNA computers with Turing computability using a finite set of bio...
Simulating Boolean circuits by finite splicing
, 1999
"... As a computational model to be simulated in a DNA computing context, Boolean circuits are especially interesting because of their parallelism. Simulations in concrete biochemical computing settings have been given by [OR96] and [AD97]. In this paper, we show how to simulate Boolean circuits by finit ..."
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Cited by 6 (0 self)
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As a computational model to be simulated in a DNA computing context, Boolean circuits are especially interesting because of their parallelism. Simulations in concrete biochemical computing settings have been given by [OR96] and [AD97]. In this paper, we show how to simulate Boolean circuits by finite splicing systems, an abstract model of enzymatic recombination ([Hea87], [Gat94], [P au96a]). We argue that using an abstract model of DNA computation as a basis leads to simulations of greater clarity and generality. In our construction, the running time of the simulating system is proportional to the depth, and the use of material is proportional to the size of the Boolean circuit simulated. However, the rules of the simulating splicing system depend on the size of the Boolean circuit, but not on the connectives used.
Test tube systems with cutting/recombination operations
 In Pacific Symposium on Biocomputing
, 1997
"... We introduce test tube systems 1;2;3;9 based on operations that are closely related to the splicing operation8, i.e. we consider the operations of cutting a string at a speci c site into two pieces with marking them at the cut ends and of recombining two strings with speci cly marked endings 7. Wher ..."
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Cited by 5 (0 self)
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We introduce test tube systems 1;2;3;9 based on operations that are closely related to the splicing operation8, i.e. we consider the operations of cutting a string at a speci c site into two pieces with marking them at the cut ends and of recombining two strings with speci cly marked endings 7. Whereas in the splicing of two strings these strings are cut at speci c sites and the cut pieces are recombined immediately in a crosswise way, inCR(cutting/recombination)schemes cutting can happen independently from recombining the cut pieces. Test tube systems based on these operations of cutting and recombinationturn out to have maximal generativepower even if only very restricted types of input lters for the test tubes are used for the redistribution of the contents of the test tubes after a period of cuttings and recombinations in the test tubes. 1