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A Clause String DNA Algorithm for SAT [chapter]

Vincenzo Manca, Claudio Zandron
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.  ... 
doi:10.1007/3-540-48017-x_16 fatcat:hpq72vefsbajhjsmrfse6fbggy

Molecular Computation by DNA Hairpin Formation

K. Sakamoto
2000 Science  
The infrared reflectance measurements were conducted using 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  ... 
doi:10.1126/science.288.5469.1223 pmid:10817993 fatcat:o4dz4sf35ndc3jnnzh4ekvjtzu

DNA computing on a chip

Mitsunori Ogihara, Animesh Ray
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) .  ... 
doi:10.1038/35003071 pmid:10646580 fatcat:nhzje5w74bghjbfrh2l4ik2yxe

An Improved Parallel DNA Algorithm of 3-SAT

Wei Liu, Shou Xia Sun, Ying Guo
2007 Data Science Journal  
This paper proposes 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.  ... 
doi:10.2481/dsj.6.s566 fatcat:oxlqsg6pavgsla6dytaeabdbwi

Genetic Algorithm for Restricted Maximum k-Satisfiability in the Hopfield Network

Mohd Shareduwan Bin Mohd Kasihmuddin, Mohd Asyraf Bin Mansor, Saratha Sathasivam
2016 International Journal of Interactive Multimedia and Artificial Intelligence  
Furthermore, the outcome had provided 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  ... 
doi:10.9781/ijimai.2016.429 fatcat:xawv63b4qncxrknj3fgvfgyoeu

DNA computing by blocking

G. Rozenberg, H. Spaink
2003 Theoretical Computer Science  
The method is explained by presenting 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.  ... 
doi:10.1016/s0304-3975(01)00194-3 fatcat:2vt7rwqnoner5ldcnq3li6uuw4

A DNA solution of SAT problem by a modified sticker model

Chia-Ning Yang, Chang-Biau Yang
2005 Biosystems (Amsterdam. Print)  
In this theoretical work, we modify 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  ... 
doi:10.1016/j.biosystems.2005.01.001 pmid:15917122 fatcat:6x2s4m3jirdf3gxnqvwr3ncalq

Finding the Anticover of a String

Mai Alzamel, Alessio Conte, Shuhei Denzumi, Roberto Grossi, Costas S. Iliopoulos, Kazuhiro Kurita, Kunihiro Wasa, Oren Weimann, Inge Li Gørtz
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.  ... 
doi:10.4230/lipics.cpm.2020.2 dblp:conf/cpm/AlzamelCDGIKW20 fatcat:k5stzny64naefeckmv42bg2l2m

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 stringalgorithms are compared and a new formulation of these algorithms is given in terms of membrane systems.  ... 

On the Power of DNA-Computing

Diana Rooß, Klaus W. Wagner
1996 Information and Computation  
In [Adl94] Adleman used biological manipulations with 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.  ... 
doi:10.1006/inco.1996.0094 fatcat:pc2co7xu55ewfdndhmt35vykrq

Solving satisfiability problems using a novel microarray-based DNA computer

Che-Hsin Lin, Hsiao-Ping Cheng, Chang-Biau Yang, Chia-Ning Yang
2007 Biosystems (Amsterdam. Print)  
An 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.  ... 
doi:10.1016/j.biosystems.2006.08.009 pmid:17029765 fatcat:sosbehog5bfezlaubtk64je5hm

Consequences of Faster Alignment of Sequences [chapter]

Amir Abboud, Virginia Vassilevska Williams, Oren Weimann
2014 Lecture Notes in Computer Science  
The best 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.  ... 
doi:10.1007/978-3-662-43948-7_4 fatcat:yehmne24lfhanleikcc6fekrcu

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)

Karl Bringmann, Michael Wagner
2019 Symposium on Theoretical Aspects of Computer Science  
We can keep searching 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] .  ... 
doi:10.4230/lipics.stacs.2019.4 dblp:conf/stacs/Bringmann19 fatcat:ulgtwbxw3jctdkuh37lliq3jjy

Exact and Approximation Algorithms for DNA Tag Set Design [chapter]

Ion I. Măndoiu, Dragoş Trincă
2005 Lecture Notes in Computer Science  
In this paper we propose new solution methods 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.  ... 
doi:10.1007/11496656_33 fatcat:bbga4lg7zzgtjh6siywcigbsum
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