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A Clause String DNA Algorithm for SAT
[chapter]

2002
*
Lecture Notes in Computer Science
*

*A*

*DNA*

*algorithm*

*for*

*SAT*, the satisfiability of propositional formulae, is presented where the number of separation steps is given by the number of

*clauses*of the instance. ... This represents

*a*computational improvement

*for*

*DNA*

*algorithms*based on Adleman and Lipton's extraction model, where the number of separations equates the number of literals of the instance. ... In conclusion, in the class of

*DNA*

*algorithms*

*for*

*SAT*based on Adleman and Lipton's extract model the

*clause*

*strings*approach implies

*a*direct scaleup in the size of

*DNA*solvable instances. ...

##
###
Molecular Computation by DNA Hairpin Formation

2000
*
Science
*

The infrared reflectance measurements were conducted using

doi:10.1126/science.288.5469.1223
pmid:10817993
fatcat:o4dz4sf35ndc3jnnzh4ekvjtzu
*a*Bruker IFS-66v interferometer with attached microscope; the apparatus was equipped with*a*globar source, KBr beamsplitter and liquid-nitrogen ... Spectra are reported with*a*resolution of 4 cm -1 and were collected from spot sizes ranging between 40 and 90 m in diameter; typical collection times were 3 to 10 min. ... could reduce the required*DNA*amount, together with use of the "breadth-first" search proposed*for*large*SAT*problems (6, 24) , where our*algorithm*must be repeated by the number of the*clauses*, although ...##
###
DNA computing on a chip

2000
*
Nature
*

*For*example,

*a*3-

*SAT*problem with 30

*clauses*and 50 variables could be solved in approximately 1.6 million steps by an ordinary computer

*algorithm*, but in only 91 steps by Liu and colleagues'

*DNA*computer ... The goal is to identify those

*strings*out of

*a*library of eight that satisfy all the

*clauses*of

*a*particular 3-

*SAT*formula (Fig. 1b) . ...

##
###
An Improved Parallel DNA Algorithm of 3-SAT

2007
*
Data Science Journal
*

This paper proposes

doi:10.2481/dsj.6.s566
fatcat:oxlqsg6pavgsla6dytaeabdbwi
*a*parallel*algorithm*model*for*the universal 3-*SAT*problem based on the Adleman-Lipton model and applies biological operations to handling the mass of data in solution space. ...*DNA*computing is*a*means of solving*a*class of intractable computational problems in which the computing time grows exponentially with problem size. ...*DNA*computing solves computational problems by employing molecular biology-based techniques to manipulate*DNA**strings*, so that the*strings*code information of the related*algorithm*. ...##
###
Genetic Algorithm for Restricted Maximum k-Satisfiability in the Hopfield Network

2016
*
International Journal of Interactive Multimedia and Artificial Intelligence
*

Furthermore, the outcome had provided

doi:10.9781/ijimai.2016.429
fatcat:xawv63b4qncxrknj3fgvfgyoeu
*a*solid evidence of the robustness of our proposed*algorithms*to be used in other satisfiability problem. ... Genetic*algorithm*will be integrated with Hopfield network as*a*single network. The proposed method will be compared with the conventional Hopfield network. ... AcknowledgMenT The authors fully acknowledged Ministry of Higher Education (MOHE) and School of Mathematical Sciences, Universiti Sains Malaysia*for*the support which makes this important research viable ...##
###
DNA computing by blocking

2003
*
Theoretical Computer Science
*

The method is explained by presenting

doi:10.1016/s0304-3975(01)00194-3
fatcat:2vt7rwqnoner5ldcnq3li6uuw4
*a**DNA*based*algorithm**for*solving (albeit in the theoretical sense only!) the satisÿability problem. ... We present*a*method*for*molecular computing which relies on blocking (inactivating) this part of the total library of molecules that does not contribute to (ÿnding)*a*solution-this happens essentially ... Schmidt*for*useful comments on the ÿrst version of this paper. They are also indebted to Marloes van der Nat*for*the expert typing of the paper. ...##
###
A DNA solution of SAT problem by a modified sticker model

2005
*
Biosystems (Amsterdam. Print)
*

In this theoretical work, we modify

doi:10.1016/j.biosystems.2005.01.001
pmid:15917122
fatcat:6x2s4m3jirdf3gxnqvwr3ncalq
*a*well-known sticker model to design an*algorithm*that does not require an initial data pool*for**SAT*problem. ... The proposed*algorithm*is expected to provide*a*solution to*SAT*problem and become practical as the problem size scales up. ... Introduction*DNA*computing is to solve computational problems by employing molecular biology laboratory techniques to manipulate*DNA**strings*so that the*strings*encode information of the related*algorithm*...##
###
Finding the Anticover of a String

2020
*
Annual Symposium on Combinatorial Pattern Matching
*

*For*unbounded k, we provide an exact exponential

*algorithm*to find

*a*k-anticover of

*a*

*string*of length n (or determine that none exists), which runs in O*(min {3^{(n-k)/3)}, ((k(k+1))/2)^{n/(k+1)) time ... In this paper we address the complexity of the problem of finding

*a*k-anticover of

*a*

*string*x if it exists, showing that the decision problem is NP-complete on general

*strings*

*for*k ≥ 3. ... by an application in the

*DNA*compositions,

*a*short

*DNA*fragment can be obtained that can be self-united into the desired

*DNA*structure. ...

##
###
Page 7268 of Mathematical Reviews Vol. , Issue 2004i
[page]

2004
*
Mathematical Reviews
*

Summary: “Some

*DNA**algorithms*proposed in the literature*for*propositional satisfiability (*SAT*) are analyzed. ... In the class of ‘extract model’ the two sub-classes of ‘literal*string*’ and ‘*clause**string*’*algorithms*are compared and*a*new formulation of these*algorithms*is given in terms of membrane systems. ...##
###
On the Power of DNA-Computing

1996
*
Information and Computation
*

In [Adl94] Adleman used biological manipulations with

doi:10.1006/inco.1996.0094
fatcat:pc2co7xu55ewfdndhmt35vykrq
*DNA**strings*to solve some instances of the Directed Hamiltonian Path Problem. ... Various modifications of Lipton's model, based on other*DNA*manipulations, are investigated systematically, and it is proved that their computational power in polynomial time can be characterized by one ... Acknowledgement We are grateful to an anonymous referee*for**a*lot of very valuable hints, and to Heribert Vollmer and Gundula Niemann*for*interesting discussions. ...##
###
Solving satisfiability problems using a novel microarray-based DNA computer

2007
*
Biosystems (Amsterdam. Print)
*

An

doi:10.1016/j.biosystems.2006.08.009
pmid:17029765
fatcat:sosbehog5bfezlaubtk64je5hm
*algorithm*based on*a*modified sticker model accompanied with an advanced MEMS-based microarray technology is demonstrated to solve*SAT*problem, which has long served as*a*benchmark in*DNA*computing. ... Unlike conventional*DNA*computing*algorithms*needing an initial data pool to cover correct and incorrect answers and further executing*a*series of separation procedures to destroy the unwanted ones, we ... problem has emerged as*a*useful benchmark*for*exploring the feasibility of*DNA*-based*algorithms*and experiments. ...##
###
Consequences of Faster Alignment of Sequences
[chapter]

2014
*
Lecture Notes in Computer Science
*

The best

doi:10.1007/978-3-662-43948-7_4
fatcat:yehmne24lfhanleikcc6fekrcu
*algorithms**for*Local Alignment run in time that is roughly quadratic in the*string*length. It is*a*big open problem whether substantially subquadratic*algorithms*exist. ... Our result*for*CNF-*SAT*also applies to the easier problem of finding the longest common substring of binary*strings*with don't cares. ... We would like to thank Kevin Lewi, Ryan Williams and the anonymous reviewers*for*helpful discussions and comments. ...##
###
Page 5204 of Mathematical Reviews Vol. , Issue 2002G
[page]

2002
*
Mathematical Reviews
*

E (3) 56 (1997), no. 2, 1357-1370; MR 98g:82022] pro- posed the random (2+ p)-

*SAT*model:*for**a*given p € [0,1],*a*random (2+ p)-*SAT*formula, F2,)(n,m), has m randomly cho- sen*clauses*over n variables, ... Consider first-order logic on finite*strings*, in*a*language that also includes predicates*for*arithmetic operations on the positions of letters in the*string*. ...##
###
Fine-Grained Complexity Theory (Tutorial)

2019
*
Symposium on Theoretical Aspects of Computer Science
*

We can keep searching

doi:10.4230/lipics.stacs.2019.4
dblp:conf/stacs/Bringmann19
fatcat:ulgtwbxw3jctdkuh37lliq3jjy
*for**a*faster*algorithm*, but maybe none exists. Is there any reasoning that provides evidence against significantly faster*algorithms*, and thus allows us to stop searching? ... Suppose the fastest*algorithm*that we can design*for*some problem runs in time O(n 2 ). However, we want to solve the problem on big data inputs,*for*which quadratic time is impractically slow. ... More formally,*for*any δ > 0 there is*a*k ≥ 3 such that k-*SAT*has no O(2 (1−δ)n )-time*algorithm*[31] . ...##
###
Exact and Approximation Algorithms for DNA Tag Set Design
[chapter]

2005
*
Lecture Notes in Computer Science
*

In this paper we propose new solution methods

doi:10.1007/11496656_33
fatcat:bbga4lg7zzgtjh6siywcigbsum
*for*designing tag sets*for*use in universal*DNA*arrays. ... We show that combining*a*simple greedy cycle packing*algorithm*with*a*previously proposed alphabetic tree search strategy yields an increase of over 40% in the number of tags compared to previous methods ... We solved Conclusions In this paper we proposed new solution methods*for*designing tag sets*for*universal*DNA*arrays. ...
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