Error detection and correction in the DNA computing based on the Adleman Lipton model
Subject Areas : Information Technology in Engineering Design (ITED) JournalFarzaneh Famoori 1 , امیر صباغ ملاحسینی 2 , Azadeh Alsadat Emrani Zarandi 3
1 - PHD student of Islamic Azad University, Kerman Branch- Faculty Member of Islamic Azad University, Zahedshahr Branch
2 - گروه مهندسی کامپیوتر - دانشگاه آزاد اسلامی واحد کرمان
3 - Department of Computer Engineering, Shahid Bahonar University of Kerman, Kerman, Iran
Keywords: DNA Arithmetic, Redundant Residue Number system (RRNS), error detection, error correction,
Abstract :
DNA computing is an area of natural computing based on the idea that molecular biology processs can be used to arithmetic and logical operations on information encoded as DNA strands. DNA is typically computed in test tubes that are prone to error, The RNS error detection and correction capabilities can be applied for error-prone DNA computing. In this work , we propose a DNA computing system based on Redundency Residue Number System (RRNS). While the system can detect two errors it is also able to correct an error. The Adleman-Lipton model is used to implement DNA operations with error detection and correction capability. The advantage of this proposed computing system is the ability to detect and correct errors. However, the proposed arithmetic operations work on larger numbers DNA-represented ,that RNS split these numbers into smaller numbers. Implementing of arithmetic operations on these small numbers reduces the possibility of errors in DNA operations.
[1] H. M. H. Babu. "Multiple-Valued Computing in Quantum Molecular Biology: Arithmetic and Combinational Circuits". CRC Press, 2023.
[2] S. Minocha, S. Namasudra. "Research challenges and future work directions in DNA computing." Advances in Computers 129 (2023): 363-387.
[3] C. Zhang, G. Lulu, Z. Yuchen, S. Ziyuan,Z. Zhiwei, Zaichen, Y. Xiaohu You. "DNA computing for combinational logic." Science China Information Sciences 62 (2019): 1-16.
[4] F. Hochella, M., "There’s plenty of room at the bottom: Nanoscience in geochemistry," Elsevier, 2001.
[5] L. M. Adleman. "Molecular computation of solutions to combinatorial problems. Science", 266(5187), 1021-1024, 1994
. [6] L. Sousa. "Nonconventional computer arithmetic circuits, systems and applications." IEEE Circuits and Systems Magazine 21, no. 1 (2021): 6-40
. [7] CH. Chang, A. Sabbagh Molahosseini, A. Emrani Zarandi, TF. Tay, "Residue Number Systems: A New Paradigm to Data path Optimization for Low-Power and High-Performance Digital Signal Processing Applications," IEEE Circuits and systems magazine, vol. 15, no. 4, pp. 26-44, 2015
. [8] B. Yurke, A. J. Turberfield, A.P. Mills Jr, F. C. Simmel, J. L. Neumann, "A DNA-fuelled molecular machine made of DNA," Nature, vol. 406, no. 6796, pp. 605-608, 2000
. [9] X. Zheng, B.Wang, C. Zhou, X. Wei, Q. Zhang, "Parallel DNA Arithmetic Operation With One Error Detection Based on 3-Moduli Set," IEEE transactions, vol. 15, no. 5, pp. 499-507, 14 June 2016
[10] X. Zheng, J. Xu, W. Li, "Parallel DNA arithmetic operation based on the n-moduli set," Applied Mathematics and Computation, vol. 212, no. 1, Jun 2009, pp. 177-184
. [11] F. Famoori, A. Sabbagh Molahosseini. A, and A. Alsadat Emrani Zarandi. "DNA Arithmetic With Error Correction." IEEE Transactions on NanoBioscience 22.2 (2022): 329-336
. [12] M. Sarkar, P Ghosal, SP Mohanty, "Exploring the Feasibility of a DNA Computer: Design of an ALU using Sticker Based DNA Model," IEEE Transactions on Nanobioscience, vol. 16, no. 20, pp. 383-399, 2017
. [13] A. Fujiwara, KI. Matsumoto, W. Chen, "Procedures for logic and arithmetic operations with DNA molecules," International Journal of Foundations of Computer Science, vol. 15, no. 3, 2004
. [14] A. Molahosseini, L. Sousa, C. Chang (Eds), “Embedded Systems Design with Special Arithmetic and Number Systems”, Springer, 2017
. [15] L Sousa, S Antao, P Martins, “Combining Residue Arithmetic to Design Efficient Cryptographic Circuits and Systems”, IEEE Circuits and Systems Magazine, 16 (4), pp. 6-32, 2016
. [16] F. J. Taylor, "Residue Arithmetic A Tutorial with Examples," IEEE Computer, vol. 17, no. 5, pp. 50–62, 1984
. [17] EB Olsen, "Introduction of the Residue Number Arithmetic Logic Unit with Brief Computational Complexity Analysis (Rez-9soft processor)," Whitepaper, Digital System Research 2015
. [18] Ds. Anderson, "Design and Implementation of an Instruction Set Architecture and an Instruction Execution Unit for the REZ9 Coprocessor System," M.S. Thesis, U of Nevada LV, 2014
. [19] K. Navi, A. Sabbagh Molahosseini. M. Esmaeildoust, "How to Teach Residue Number System to Computer Scientists and Engineers," IEEE Transactions on Education, vol. 54, no. 1, pp. 156-163, 2011
. [20] T. F. Tay and C. H. Chang, "A non-iterative Multiple Residue Digit Error Detection and Correction Algorithm in RRNS,” IEEE Transactions on Computers, vol. 65, no. 2, pp. 396-408, February 2016
[21] F. Guarnieri, M. F. Liss, C. Bancroft, "Making DNA add," Science, vol. 273, no. 5272, pp. 220-223, 1996
. [22] A. Fujiwara, S. Kamio," Procedures for Multiple Input Functions with DNA strands," Journal of Foundations of Computer Science 2005
. [23] W. Wang, M. N. S. Swamy, and M. Omair Ahmad. "Moduli selection in RNS for efficient VLSI implementation." 2003 IEEE International Symposium on Circuits and Systems (ISCAS). Vol. 4. IEEE, 2003
. [24] A. Sabbagh Molahosseini, K.Navi, C. Dadkhah, O. Kavehei, S. Trimarchi, "Efficient Reverse Converter Designs for the New 4-Moduli Sets {2n–1, 2n, 2n+1, 22n+1–1} and {2n–1, 2n+1, 22n, 22n+1} Based on New CRTs," IEEE Transactions on Circuits and Systems-I, vol. 57, no. 4, pp. 823-835, 2010
. [25] B. Deng, S. Srikanth, E. R. Hein, T. M. Conte, E. Debenedictis, Je. Cook, M.P. Frank, "Extending Moore’s Law via Computationally Error Tolerant Computing," ACM Transactions on Architecture and Code Optimization (TACO), vol. 15, no. 1, 2018
. [26]
https://www.xlnsresearch.com/sticker1.htm
