Abstract not found

The maximum number of strands used is an important measure of a molecular algorithm's complexity. This measure is also called the volume used by the algorithm. Every problem that can be solved by an NP Turing machine with b(n) binary nondeterministic choices can be solved by molecular computation in a polynomial number of steps, with four test tubes, in volume 2 b(n) . We identify a large class of recursive algorithms that can be implemented using bounded nondeterminism. This yields improved molecular algorithms for important problems like 3-SAT, independent set, and 3-colorability. 1. A model of molecular computing Molecular computation was first studied in [1, 20]. The models we define were inspired as well by the work of [3, 28]. A molecular sequence is a string over an alphabet \Sigma (we can use any alphabet we like, encoding characters of \Sigma by finite sequences of base pairs). A test tube is a multiset of molecular sequences. We describe the allowable operations below. Whe...

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.

Molecular computing is viewed here as a process of writing on molecules while they are dissolved in water. When DNA molecules are employed, they are used only in double stranded form and only as data registers. All computations are initialized with the same single molecular variety. Current progress toward laboratory prototyping of computations is reported. 1 Introduction A vision for the future of molecular computing is sketched here. It may be regarded as a more conventional approach to molecular computing than other approaches currently in progress: There is an identifiable computer. The computer, in its initial state, consists of a volume of water in which a vast number of identical molecules are dissolved. The molecular type selected for this initialization is chosen to contain specific distinguishable locations that can function as bistable devices, thus representing bits 0 or 1. We will call these locations stations. Every computation begins with each of these molecules havin...

The relationship between the family SH of simple splicing languages, which was recently introduced by A. Mateescu and coauthors, and the family SLT of strictly locally testable languages is clarified by establishing an ascending hierarchy of families fS i H : i \Gamma1g of splicing languages for which SH = S1H and the union of the families is the family SLT . A procedure is given which, for an arbitrary regular language L, determines whether L is in SLT and, when L is in SLT , specifies constructively the smallest family in the hierarchy to which L belongs. Examples are given of sets of restriction enzymes for which the action on DNA molecules is naturally represented by splicing systems of the types discussed. Key words. Splicing systems, H Systems, DNA Computing, local testability, regular languages, restriction enzymes 1 Introduction The splicing system concept was introduced in [6] as a formal device for the generation of languages and as a formal model of specific forms ...

The splicing system concept was created in 1987 to allow the convenient representation in formal language theoretic terms of recombinant actions of certain sets of enzymes on double stranded DNA molecules. Characterizations are given here for those regular languages that are generated by splicing systems having splicing rules that test context on only one side. An algorithm is given for deciding whether any arbitrary regular language can be generated by a splicing system in which all splicing rules test context on the same side. Schutzenberger's concept of a constant relative to a language provides the tool for constructing the required splicing rules. To provide a potential biochemical example, the formal generative capacity of the restriction enzyme BpmI in the company of a ligase is discussed. Experimental investigation is invited. Key words: Splicing systems, H-Systems, DNA-computing, biocomputing, bioinformatics, regular languages, finite automata. 1 Introduction The sp...

. The rapid developments in the field of DNA computing reflects two substantial questions: 1. Which models for DNA based computation are really universal? 2. Which model fulfills the requirements to a universal lab-practicable programmable DNA computer that is based on one of these models? This paper introduces the functional model DNA-Haskell focussing its lab-practicability. This aim could be reached by specifying the DNA based operations in accordiance to an analysis of molecular biological processes. The specification is determined by an abstraction level that includes nucleotides and strand end labels like 5'-phosphate. Our model is able to describe DNA algorithms for any NP-complete problem -- here exemplified by the knapsack problem -- as well as it is able to simulate some established mathematical models for computation. We point out the splicing operation as an example. The computational completeness of DNA-Haskell can be supposed. This paper is based on discussions about the ...

Insertions and deletions of small circular DNA strands into long linear DNA strands are phenomena that happen frequently in nature and thus constitute an attractive paradigm for biomolecular computing. This paper presents a new model for DNA-based computation that involves circular as well as linear molecules, and that uses the operations of insertion and deletion. After introducing the formal model we investigate its properties and prove in particular that the circular insertion/deletion systems are capable of universal computation. We also give the results of an experimental laboratory implementation of our model. This shows that rewriting systems of the circular insertion/deletion type are viable alternatives in DNA computation. 1 Introduction Early models of DNA recombination, the splicing systems, have already been defined by [4]. They aimed to describe the action of restriction enzymes and ligases on DNA molecules which resulted in cleavage and reassociation of DNA strands. Almo...

This article arose from a reading of the paper of Q.Ouyang, P.D.Kaplan, S.Liu and A.Libchaber

Length of DNA strands is an important resource in DNA computing. We show how to decrease strand lengths in known molecular algorithms for some NP-complete problems, such as like 3-SAT and Independent Set, without substantially increasing their running time or volume. 1. Introduction Since Adleman's pioneering experiment [1], many researchers have explored efficient molecular algorithms for NP-complete problems. The running time for a molecular algorithm is to the number of operations on test tubes. The volume is the maximum number of strings in all test tubes at any time, counting multiplicities. The strand-length complexity of a molecular algorithm is the length of the longest DNA strand used in the computation. Although time and volume complexity have been well studied [13, 6, 2, 14, 5, 9, 10, 8], strand length has received less attention. Yet Roweis et al [16], state that 2500-base sequences decay at a rate of 10% per hour, and Sambrook [17] states that DNA strands longer than 1000...