SAT問題是指對於一組任意給定的布林方程式，決定其是否存在一組或一組以上之 『給定真值（truth value assignment）』，使得該布林方程式之輸出值為真。由於此類問題並不滿足多項式求解之條件，而不具有特定解，因此對於電腦計算而言，其為一難題。而DNA電腦具有平行化運算能力之特性，便成為解SAT問題之利器。傳統之DNA計算方式多需仰賴複雜之樣本製備程序，才能解出一具有多變數之SAT問題，因此並不實用。
本研究利用微機電製程技術，將DNA電腦的概念在微陣列晶片上來執行，並將此技術應用於SAT問題之求解。有別於一般微影程序，本實驗以空白光罩為基板，利用一創新之背後曝光法取代一般曝光，其可於曝光時容許較大的對位誤差，使得在多次黃光微影製程中輕易定義出良好的光刻圖形，以利DNA電腦之運算。此外，利用空白光罩做為微陣列DNA電腦晶片之計算平台，除了可得到解析度較佳的圖形之外，同時亦可避免自體螢光現象的發生，而可得到高品質的螢光激發影像。
本研究將微機電製程運用於微陣列技術，以自行設計之單股DNA分子進行DNA電腦之平行運算，並成功解出一含有三個變數（x、y、z）及三個子句之簡化布林方程式。論文中並利用該簡化之布林方程式，詳細解說本DNA電腦之運算模式。最後，本研究並運用此一技術，成功解決一具有四個變數（w、x、y、z）及五個子句之複雜3-SAT問題。

This paper presents a novel MEMS based DNA computer for solving SAT problems. No time-consuming sample preparation procedures and delicate sample applying equipment were required for the computing process. Moreover, experimental results show the bound DNA sequences can sustain the chemical solutions during computing processes such that the proposed method shall be useful in dealing with large scale problems. An algorithm based on a modified sticker model accompanied with a state-of-the-art MEMS-based microarray experiment is demonstrated to solve SAT problem which has long served as a benchmark in DNA computing. Unlike conventional DNA computing algorithms need an initial data pool to cover all correct and incorrect answers and further execute a series of separation procedures to destroy the unwanted ones, we built solutions in parts to satisfy one clause in one step, and eventually solve the entire Boolean formula through steps. Accordingly this algorithm greatly reduces the formation of unnecessary candidate solutions and shall be very practical as problem size grows.
In this study, a novel MEMS-based technology including utilizing blank mask as the microarray substrate to prevent the self-fluorescent effect, a twin-mask back-side exposure process to improve the computing speed and a low-temperature backing process to prevent DNA damage during computing procedure. In addition, the minimal time requirement for DNA hybridization was also evaluated experimentally.
The paper reports a novel computing method for solving SAT problem utilizing a state-of-art MEMS-based microarray. The advantage of this method is as the problem size scales up, it only needs to linearly increase the variety of sequences standing for variables and augment the array size. Therefore, while solving a complicated SAT problem, the numbers of DNA sample and the time for the computing process can be dramatically reduced with this approach.

目錄
目錄....................................................................................................................Ⅰ
表目錄................................................................................................................Ⅳ
圖目錄................................................................................................................Ⅴ
中文摘要............................................................................................................Ⅷ
英文摘要............................................................................................................Ⅸ

第一章 緒論
1.1 前言.....................................................................................................1
1.2 生物晶片及微陣列技術.....................................................................3
1.2.1 接觸式點樣法........................................................................6
1.2.2 噴墨頭噴射法........................................................................8
1.2.3 光學微影法............................................................................9
1.3 微陣列技術應用於DNA電腦..........................................................11
1.3.1 DNA的特性..........................................................................12
1.3.2 DNA電腦的特性..................................................................13
1.4 研究動機與目的................................................................................14
1.5 研究架構............................................................................................15

第二章 DNA電腦之發展及其應用於SAT問題求解
2.1 DNA電腦之發展..............................................................................17
2.2 DNA電腦應用於SAT問題..............................................................23
2.3 DNA電腦求解SAT問題之運算原理與邏輯規則..........................25
2.3.1改良式標籤模型...................................................................26
2.3.2 DNA電腦求解SAT問題之邏輯規則................................27

第三章 微陣列DNA電腦晶片之設計與製作
3.1 選擇方程式與規劃運算步驟...........................................................33
3.2 光罩製作...........................................................................................35
3.3 微陣列DNA電腦晶片製作與運算流程..........................................35
3.3.1 微陣列DNA電腦晶片製作................................................36
3.3.2 晶片表面修飾及寡核

[1] Schena, M., Shalon, D., Davis, R. W., and Brown, P. O., "Quantitative Monitoring of Gene Expression Patterns with a Complementary DNA Microarray," Science, 1995, vol. 270, p. 467-470.
[2] Schena, M., Shalon, D., Heller, R., Chai, A., Brown, P. O., and Davis, R. W., "Parallel human genome analysis: microarray-based expression monitoring of 1000 genes," Proceedings of the National Academy of Sciences of the United States of America, 1996, vol. 93, p. 10614-10619.
[3] Shalon, D., Smith, S. J., and Brown, P. O., "A DNA microarray system for analyzing complex DNA samples using two-color fluorescent probe hybridization," Genome Research, 1996, vol. 6, p. 639-645.
[4] MacBeath, G. and Schreiber, S. L., "Printing proteins as microarrays for high-throughput function determination," Science, 2000, vol. 289, p. 1760-1763.
[5] Kononen, J., Bubendorf, L., Kallioniemi, A., Barlund, M., Schraml, P., Leighton, S., Torhorst, J., Mihatsch, M. J., Sauter, G., and Kallioniemi, O. P., "Tissue microarrays for high-throughput molecular profiling of tumor specimens," Nature Medicine, 1998, vol. 4, p. 844-847.
[6] Manz, A., Graber, N., and Widmer, H. M., "Miniaturized total chemical analysis systems: A novel concept for chemical sensing," Sensors and Actuators, 1990, vol. 1, p. 244-248.
[7] "The Chipping Forecast," Nature Genetics, 1999, vol. 21.
[8] Xiang, C. C. and Chen, Y., "cDNA microarray technology and its applications," Biotechnology Advances, 2000, vol. 18, p. 35-46.
[9] Hegde, P., Qi, R., Abernathy, K., Gay, C., Dharap, S., Gaspard, R., Hughes, J. E., Snesrud, E., Lee, N., and Quackenbush, J., "A concise guide to cDNA microarray analysis," Biotechniques, 2000, vol. 29, p. 548-550, 552-544, 556 passim.
[10] Zammatteo, N., Jeanmart, L., Hamels, S., Courtois, S., Louette, P., Hevesi, L., and Remacle, J., "Comparison between different strategies of covalent attachment of DNA to glass surfaces to build DNA microarrays," Analytical Biochemistry, 2000, vol. 280, p. 143-150.
[11] Kane, M. D., Jatkoe, T. A., Stumpf, C. R., Lu, J., Thomas, J. D., and Madore, S. J., "Assessment of the sensitivity and specificity of oligonucleotide (50mer) microarrays," Nucleic Acids Research, 2000, vol. 28, p. 4552-4557.
[12] Stillman, B. A. and Tonkinson, J. L., "Expression microarray hybridization kinetics depend on length of the immobilized DNA but are independent of immobilization substrate," Analytical Biochemistry, 2001, vol. 295, p. 149-157.
[13] Naef, F., Lim, D. A., Patil, N., and Magnasco, M., "DNA hybridization to mismatched templates: a chip study," Phys Rev E Stat Nonlin Soft Matter Phys, 2002, vol. 65, p. 040902.
[14] Diehl, F., Grahlmann, S., Berier, M., and Hoheisel, J. D., "Manufacturing DNA microarrays of high spot homogeneity and reduced background signal.," Nucleic Acids Research, 2001, vol. 29, p. e38.
[15] Evertsz, E. M., Au-Young, J., Ruvolo, M. V., Lim, A. C., and Reynolds, M. A., "Hybridization cross-reactivity within homologous gene families on glass cDNA microarrays," Biotechniques, 2001, vol. 31, p. 1182, 1184, 1186 passim.
[16] Mendoza, L. G., McQuary, P., Mongan, A., Gangadharan, R., Brignac, S., and Eggers, M., "High-throughput microarray-based enzyme-linked immunosorbent assay (ELISA)," Biotechniques, 1999, vol. 27, p. 778-788.
[17] Lueking, A., Horn, M., Eickhoff, H., Bussow, K., Lehrach, H., and Walter, G., "Protein microarrays for gene expression and antibody screening," Analytical Biochemistry, 1999, vol. 270, p. 103-111.
[18] Blanchard, A. P., Kaiser, R. J., and Hood, L. E., "High-Density Oligonucleotide Arrays," biosensors and bioelectronics, 1996, vol. 11, p. 687-690.
[19] Nilsson, S., Catharina, L., Laurell, T., and Bimbaum, S., "Thin-Layer Immunoaffinity Chromatography with Bar Code Quantitation of C-Reactive Protein," Analytical Chemistry, 1995, vol. 67, p. 3051-3056.
[20] Hughes, T. R., Mao, M., Jones, A. R., Burchard, J., Marton, M. J., Shannon, K. W., Lefkowitz, S. M., Ziman, M., Schelter, J. M., Meyer, M. R., Kobayashi, S., Davis, C., Dai, H. Y., He, Y. D. D., Stephaniants, S. B., Cavet, G., Walker, W. L., West, A., Coffey, E., Shoemaker, D. D., Stoughton, R., Blanchard, A. P., Friend, S. H., and Linsley, P. S., "Expression profiling using microarrays fabricated by an ink-jet oligonucleotide synthesizer," Nature Biotechnology, 2001, vol. 19, p. 342-347.
[21] Okamoto, T., Suzuki, T., and Yamamoto, N., "Microarray fabrication with covalent attachment of DNA using Bubble Jet technology," Nature Biotechnology, 2000, vol. 18, p. 438-441.
[22] Britland, S., Perez-Arnaud, E., Clark, P., McGinn, B., Connolly, P., and Moored, G., "Micropatterning proteins and synthetic peptides on solid supports: a novel application for microelectronics fabrication technology," Biotechnology Progress, 1992, vol. 8, p. 155-160.
[23] Blawas, A. S. and Reichert, W. M., "Protein patterning," Biomaterials, 1998, vol. 19, p. 595-609.
[24] Dontha, N., Nowall, W. B., and Kuhr, W. G., "Generation of biotin/avidin/enzyme nanostructures with maskless photolithography," Analytical Chemistry, 1997, vol. 69, p. 2619-2625.
[25] Adleman, L., "Molecular Computation of Solutions to Combinatorial Problems," Science, 1994, vol. 266, p. 1021-1024.
[26] Lipton, R. J., "DNA Solution of Hard Computational Problems," Science, 1995, vol. 268, p. 542-545.
[27] Cormen, T. H., Leiserson, C. E., Rivest, R. L., and Stein, C., "Introduction to Algorithms," The MIT Press, 2001.
[28] Sakamoto, K., Gouzu, H., Komiya, K., Kiga, D., Yokoyama, S., Yokomori, T., and Hagiya, M., "Molecular computation by DNA hairpin formation," Science, 2000, vol. 288, p. 1223-1226.
[29] Liu, Q. H., Wang, L. M., Frutos, A. G., Condon, A. E., Corn, R. M., and Smith, L. M., "DNA computing on surfaces," Nature, 2000, vol. 403, p. 175-179.
[30] Braich, R. S., Chelyapov, N., Johnson, C., Rothemund, P. W. K., and Adleman, L., "Solution of a 20-variable 3-SAT problem on a DNA computer," Science, 2002, vol. 296, p. 499-502.
[31] Rozenberg, G. and Spaink, H., "DNA computing by blocking," Theoretical Computer Science, 2003, vol. 292, p. 653-665.
[32] Wang, L. M., Liu, Q. H., Corn, R. M., Condon, A. E., and Smith, L. M., "Multiple word DNA computing on surfaces," Journal of the American Chemical Society, 2000, vol. 122, p. 7435-7440.
[33] Diaz, S., Esteban, J. L., and Ogihara, M., "A DNA-Based Random Walk Method for Solving k-SAT," Springer-Verlag, 2001, 209-219.
[34] Chen, K. and Ramachandran, V., "A Space-Efficient Randomized DNA Algorithm for k-SAT," Springer-Verlag, 2001, 199-208.
[35] Pirrung, M. C., Connors, R. V., Odenbaugh, A. L., Montague-Smith, M. P., Walcott, N. G., and Tollett, J. J., "The arrayed primer extension method for DNA microchip analysis. molecular computation of satisfaction problems," Journal of the American Chemical Society, 2000, vol. 122, p. 1873-1882.
[36] Paun, G. and Rozenberg, G., "Sticker systems," Theoretical Computer Science, 1998, vol. 204, p. 183-203.
[37] Yang, C. N. and Yang, C. B., "A DNA solution of SAT problem by a modified sticker model," Biosystems, 2005, vol. 81, p. 1-9.
[38] Guo, Z., Guilfoyle, R. A., Thiel, A. J., Wang, R., and Smith, L. M., "Direct fluorescence analysis of genetic polymorphisms by hybridization with oligonucleotide arrays on glass supports," Nucleic Acids Research, 1994, vol. 22, p. 5456-5465.
[39] Graham, C. R., Leslie, D., and Squirrel, D. J., "Gene probe assays on a fiber-optic evanescent wave biosensor," biosensors and bioelectronics, 1992, vol. 7, p. 487-493.