Abstract
Recently there has been a growing interest in the applicability of reversible circuits. Reversible circuits are designed using reversible gates, which can efficiently reconstruct the previous state of the computation from the current state. These circuits may find potential applications to the future generation of optical and quantum computers. To ensure the reliability of these circuits, testing is a mandatory phase of the design cycle. Several fault models have been introduced for reversible circuits among which some of them have been taken from the conventional circuits. In this paper, we consider the problem of testing bridging faults (such as single and multiple input bridging faults, single and multiple intra-level bridging faults) in a reversible circuit designed with the NOT, CNOT, Toffoli gates (NCT library) and generalized (n-bit) Toffoli gates (GT library). We propose an Automatic Test Pattern Generation (ATPG) method using the Path-Level expression for generating the minimal complete test set to detect the faults mentioned above. The analysis of the experimental results shows that the proposed method has 100% fault coverage, and test set size is smaller than the existing methods.
Similar content being viewed by others
References
Abramovici M, Breuer MA, Friedman AD (1995) Digital Systems Testing and Testable Design. IEEE Press, Piscataway
Bennett CH (1973) Logical reversibility of computation. IBM J Res Dev 17(6):525–532
Bubna M, Goyal N, Sengupta I (2007) A DFT methodology for detecting bridging faults in reversible logic circuits. In: Proceedings of IEEE region 10 (TENCON), pp 1–4
Chakraborty A (2005) Synthesis of Reversible Circuits for Testing with Universal Test Set and C-Testability of Reversible Iterative Logic Arrays. In: Proceedings of 18th International Conference on VLSI Design. IEEE, pp 249–254
Fang-ying X, Han-wu C, Wen-jie L, Zhi-giang L (2008) Fault Detection for Single and Multiple Missing-gate Faults in Reversible circuits. In: Proceedings of IEEE Congress on Evolutionary Computation, (IEEE World Congress on Computational Intelligence), CEC 2008, pp 131–135
Feynman RP (1986) Quantum mechanical computers. Found Phys 16(6):507–531
Frank MP (2017) Throwing computing into reverse. IEEE Spectr 54(9):32–37
Frank MP (2018) Back to the Future: The Case for Reversible Computing. arXiv:1803.02789
Fredkin E, Toffoli T (1982) Conservative logic. Int J Theor Phys 21:219–253
Ibrahim M, Chowdhury AR, Babu HMH (2008) Minimization of CTS of k-CNOT Circuits for SSF and MSF Model. In: Proceeidngs of IEEE International Symposium on Defect and Fault Tolerance of VLSI Systems, DFTVS’08, pp 290–298
Jha N, Gupta S (2003) Testing of digital systems. Cambridge University Press, Cambridge
Hayes JP, Polian I, Becker B (2004) Testing for Missing-Gate Faults in Reversible Circuits. In: Proceedings of 13th Asian Test Symposium. IEEE, pp 100–105
Landauer R (1961) Irreversibility and heat generation in the computing process. IBM J Res Dev 5(8):183–191
Loss D, DiVincenzo DP (1998) Quantum computation with quantum dots. Phys Rev A 57(1):120–126
Maslov D (2003) Reversible Logic Synthesis. Ph.D. diss. University of New Brunswick
Maslov D (2015) Reversible Logic Synthesis Benchmarks Page. Online: http://webhome.cs.uvic.ca/dmaslov/
Mei KCY (1974) Bridging and Stuck-At faults. IEEE Trans Comput 100(7):720–727
Nagamani AN, Abhishek B, Agrawal VK (2015) Deterministic approach for Bridging fault detection in Peres-Fredkin and Toffoli based Reversible circuits. In: Proceedings of International Conference on Computational Intelligence and Computing Research (ICCIC). IEEE, pp 1–6
Nagamani AN, Ashwin S, Abhishek B, Agrawal VK (2016) An Exact approach for Complete Test Set Generation of Toffoli-Fredkin-Peres based Reversible Circuits. J Electron Test 32(2):175–196
Nayeem NM, Rice JE (2011) A simple Approach for Designing Online Testable Reversible Circuits. In: Proceedings of IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PACRIM). IEEE, pp 85–90
Nielson MA, Chuang IL (2002) Quantum computation and quantum information. Am J Phys 70(5):558–559
Patel KN, Hayes JP, Markov IL (2004) Fault testing for reversible circuits. IEEE Trans Comput-Aided Des Integr Circ Syst 23(8):1220–1230
Peres A (1985) Reversible logic and quantum computers. Phys Rev 32(6):3266–3276
Polian I, Hayes JP, Fiehn T, Becker B (2005) A Family of Logical Fault Models for Reversible Circuits. In: Proceedings of 14th Asian Test Symposium. IEEE, pp 422–427
Rahaman H, Kole DK, Das DK, Bhattacharya BB (2007) Optimum Test Set for Bridging Fault Detection in Reversible Circuits. In Proceedings of 16th Asian Test Symposium (ATS 2007). IEEE, pp 125–128
Rahaman H, Kole DK, Das DK, Bhattacharya BB (2008) On the Detection of Missing-Gate Faults in Reversible Circuits by a Universal Test Set. In: Proceedings of 21st International Conference on VLSI design, VLSID. IEEE, pp 163– 168
Rice JE (2013) An overview of fault models and testing approaches for reversible logic. In: Proceeidngs of IEEE pacific rim conference on communications, computers and signal processing, PACRIM. IEEE, pp 125–130
Sarkar P, Chakrabarti S (2008) Universal Test Set for Bridging Fault Detection in Reversible circuit. In: Proceedings of 3rd International conference on Design and Test Workshop, IDT 2008. IEEE, pp 51–56
Sarkar P, Mondal B, Chakraborty S (2011) Optimal universal test set for bridging faults detection in reversible circuit using unitary matrix. In: Proceedings of 2nd IEEE International Workshop on Reliability Aware System Design and TEST (RASDAT), pp 37–42
Schaller RR (1997) MOORE’S LAW: past, present, and future. IEEE Spectr 34(6):52–59
Shende VV, Prasad AK, Markov IL, Hayes JP (2003) Synthesis of reversible logic circuits. IEEE Trans Comput-Aided Des Integr Circ Syst 22(6):710–722
Thapliyal H, Ranganathan N (2009) Design of efficient reversible binary subtractors based on a new reversible gate. In: Proceedings of IEEE computer society Annual symposium on VLSI, pp 229–234
Toffoli T (1980) Reversible Computing. In: Proceedings of the 7th Colloquium on Automata, Languages and Programming, pp 632–644
Wille R, Groe D, Teuber L, Dueck GW, Drechsler R (2008) Revlib: An Online Resource for Reversible Functions and Reversible Circuits. In: Proceedings of 38th International Symposium on Multiple Valued Logic (ISMVL 2008), pp 220–225
Zhong J, Muzio JC (2006) Analyzing fault models for reversible logic circuits. In: Proceedings of IEEE Congress on Evolutionary Computation (CEC 2006), pp 2422–2427
Author information
Authors and Affiliations
Corresponding author
Additional information
Responsible Editor: B. B. Bhattacharya
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Handique, M., Biswas, S. & Deka, J.K. Test Generation for Bridging Faults in Reversible Circuits Using Path-Level Expressions. J Electron Test 35, 441–457 (2019). https://doi.org/10.1007/s10836-019-05811-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10836-019-05811-1