Abstract
This paper discusses the interplay between discrete time signal processing and symbolic computation under a general Turing Machine approach in the Cyber Physical systems framework. Discrete signals and symbols are analyzed for their Turing computing capabilities using either Kolmogorov axioms or quantum probability amplitudes. It analyzes the discrete time Trans Boolean gate √NOT and its impact on conventional computational theories used for embedded systems and Internet of Things.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Turing, A.M.: On computable numbers, with an application to the entscheidungsproblem. J. Math. 58(345–363), 5 (1936)
Herken, R.: The Universal Turing Machine: A Half-century Survey. Springer, Heidelberg (1988)
Wegner, P., Goldin, D.: Computation beyond turing machines. Commun. ACM 46(4), 100–102 (2003)
Cohen, D.I.A.: Introduction to Computer Theory, 2nd edn. Wiley, Hoboken (1996)
Yoeli, M., Rosenfeld, G.: Logical design of ternary switching circuits. IEEE Trans. Electron. Comput. 1(1), 19–29 (1965)
Van Orman Quine, W.: Quiddities: An Intermittently Philosophical Dictionary. Harvard University Press, Cambridge (1987)
Feynman, R.P.: Feynman Lectures on Computation. CRC Press, Boca Raton (2018)
Deutsch, D.E.: Quantum computational networks. Proc. R. Soc. London A Math. Phys. Sci. 425(1868), 73–90 (1989)
Velasques, F.J.F.: Aprimoramento de segurança a nível físico. Master’s thesis, NOVA School of Science and Technology (2022)
Landauer, R.: Dissipation and noise immunity in computation and communication. Nature 335, 779–784 (1988)
Lambson, B., Carlton, D., Bokor, J.: Exploring the thermodynamic limits of computation in integrated systems: Magnetic memory, nanomagnetic logic, and the landauer limit. Phys. Rev. Lett. 107(1), 010604 (2011)
Kennedy, R.A., Sadeghi, P.: Hilbert Space Methods in Signal Processing. Cambridge University Press, Cambridge (2013)
Celeghini, E., Gadella, M., Del Olmo, M.A.: Applications of rigged hilbert spaces in quantum mechanics and signal processing. J. Math. Phys. 57(7), 072105 (2016)
Puschel, M., Moura, J.M.F.: Algebraic signal processing theory: foundation and 1-D time. IEEE Trans. Signal Process. 56(8), 3572–3585 (2008)
Shi, J., Moura, J.M.F.: Graph signal processing: modulation, convolution, and sampling. arXiv preprint arXiv:1912.06762 (2019)
Marella, S.T., Parisa, H.S.K.: Introduction to quantum computing. In: Quantum Computing and Communications (2020)
Sigov, A., Ratkin, L., Ivanov, L.A.: Quantum information technology. J. Ind. Inf. Integr. 28, 100365 (2022)
Lesch, V., Züfle, M., Bauer, A., Iffländer, L., Krupitzer, C., Kounev, S.: A literature review of IoT and CPS—what they are, and what they are not. J. Syst. Softw. 200, 111631 (2023)
Aceto, G., Persico, V., Pescapé, A.: A survey on information and communication technologies for industry 4.0: state-of-the-art, taxonomies, perspectives, and challenges. IEEE Commun. Surv. Tutor. 21(4), 3467–3501 (2019)
Monostori, L.: Cyber-physical production systems: roots, expectations and R&D challenges. Procedia Cirp 17, 9–13 (2014)
Siegelmann, H.T.: Computation beyond the turing limit. Science 268(5210), 545–548 (1995)
Lee, E.A.: Constructive models of discrete and continuous physical phenomena. IEEE Access 2, 797–821 (2014)
Menin, B.: Construction of a model as an information channel between the physical phenomenon and observer. J. Am. Soc. Inf. Sci. 72(9), 1198–1210 (2021)
Rato, R.E.C.T.: Formalização da tolerância à ausência de dados no processamento de sinais discretos. Ph.D. thesis, Faculdade de Ciências e Tecnologia, October 2012
Ortigueira, M.: Processamento digital de sinais. Fundação Calouste Gulbenkian (2005)
Pattee, H.H.: Laws and constraints, symbols and languages. In: Biological Process in Living Systems, pp. 248–258. Routledge (2017)
Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27(3), 379–423 (1948)
Hamming, R.W.: Coding and Information Theory. Prentice-Hall Inc., Hoboken (1986)
Ortigueira, M.D., Valério, D.: Fractional Signals and Systems. De Gruyter, Berlin (2020)
Hippenstiel, R.D.: Detection Theory: Applications and Digital Signal Processing. CRC Press, Boca Raton (2017)
Barkat, M.: Signal Detection and Estimation, 2nd edn. Artech (2005)
Onik, M.M.H., Chul-Soo, K.I.M., Yang, J.: Personal Data Privacy Challenges of the Fourth Industrial Revolution, pp. 635–638 (2019). https://doi.org/10.23919/ICACT.2019.8701932
Rieffel, E., Polak, W.: Quantum Computing: A Gentle Introduction, 1st edn. The MIT Press, Cambridge (2011)
Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th Annual Symposium on Foundations of Computer Science, pp. 124–134 (1994). https://doi.org/10.1109/SFCS.1994.365700
Scarani, V., Kurtsiefer, C.: The black paper of quantum cryptography: real implementation problems. Theor. Comput. Sci. 560, 27–32 (2014). https://doi.org/10.1016/j.tcs.2014.09.015
Hirvensalo, M.: Quantum Computing, 2nd edn. Springer, Cham (2010)
Shende, V.V., Prasad, A.K., Markov, I.L., Hayes, J.P.: Reversible Logic Circuit Synthesis (2003)
Piguet, C.: Low-Power Electronics Design (2004)
Franks, L.E.: Signal Theory, revised edition. Dowden & Culver (1981)
Grochenig, K.: Foundations of Time–Frequency Analysis (2001). https://doi.org/10.1007/978-1-4612-0003-1
Stern, A.: Matrix Logic. Elsevier (1988)
Allouche, J., Shallit, J.: Automatic Sequences: Theory, Applications, Generalizations. Cambridge University Press, Cambridge (2003). https://doi.org/10.1017/CBO9780511546563
Imre, S., Balazs, F.: Quantum Computing and Communications: An Engineering Approach. Wiley, Hoboken (2005)
Yao, A.C.-C.: Quantum circuit complexity. In: Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science, pp. 352–361 (1993). https://doi.org/10.1109/SFCS.1993.366852
Moore, E.: Gedanken-experiments on sequential machines. In: Shannon, C., McCarthy, J. (ed.) Automata Studies. (AM-34), vol. 34, pp. 129–154. Princeton University Press, Princeton (2016). https://doi.org/10.1515/9781400882618-006
Fischer, P.: de Leeuw K., Moore E. F., Shannon C. E., and Shapiro N.. Computability by probabilistic machines. Automata studies, edited by Shannon C. E. and McCarthy J., Annals of Mathematics studies no. 34, lithoprinted, Princeton University Press, Princeton 1956, pp. 183–212. J. Symb. Logic 35. 481–482 (2014). https://doi.org/10.2307/2270759
Hayes, B.T.: The Square Root of NOT (2016)
Acknowledgments
The authors would like to thank professor Dr. Luís Camarinha-Matos for the useful instructions. This work was supported in part by the Portuguese FCT program UIDB/00066/2020.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Neves, F., Rato, R., Ortigueira, M. (2023). Trans-Boolean Cyber Physical Systems. In: Camarinha-Matos, L.M., Ferrada, F. (eds) Technological Innovation for Connected Cyber Physical Spaces. DoCEIS 2023. IFIP Advances in Information and Communication Technology, vol 678. Springer, Cham. https://doi.org/10.1007/978-3-031-36007-7_22
Download citation
DOI: https://doi.org/10.1007/978-3-031-36007-7_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-36006-0
Online ISBN: 978-3-031-36007-7
eBook Packages: Computer ScienceComputer Science (R0)