Structural Analysis of Precomplete Classes and Closure Diagrams in Multi-Valued Logic

[1] I. Aizenberg, R. Belardi, M. Bindi, F. Grasso, S. Manetti, A. Luchetta, M. C. Piccirilli, A neural network classifier
with multi-valued neurons for analog circuit fault diagnosis, Electronics, 10(3) (2021), 349. https://doi.org/10.
3390/electronics10030349

[2] G. Alwhishi, J. Bentahar, A. Elwhishi, W. Pedrycz, N. Drawel, Multi-valued model checking IoT and intelligent
systems with commitment protocols in multi-source data environments, Information Fusion, 102 (2024), 102048.
https://doi.org/10.1016/j.inffus.2023.102048

[3] A. A. Arratia-Quesada, S. R. Chauhan, I. A. Stewart, Hierarchies in classes of program schemes, Journal of Logic
and Computation, 9(6) (1999), 915-957. https://doi.org/10.1093/logcom/9.6.915

[4] H. M. H. Babu, Multiple-valued computing in quantum molecular biology: Sequential circuits, memory devices,
programmable logic devices, and nanoprocessors, CRC Press, 2023. https://doi.org/10.1201/9781003381921

[5] G. Bocewicz, J. Pempera, V. Toporkov, Performance evaluation models for distributed service networks, Springer
International Publishing, 2021. https://doi.org/10.1007/978-3-030-67063-4

[6] D. Cheng, J. E. Feng, J. Zhao, S. Fu, A minimum adequate set of multi-valued logic, Control Theory and Technology,
19 (2021), 425-429. https://doi.org/10.1007/s11768-021-00064-w

[7] A. A. Esin, Analysis and design principles of modern control systems based on multi-valued logic models, Upravlenie
Bol’shimi Sistemami, (88) (2020), 69-98. https://doi.org/10.25728/UBS.2020.88.4

[8] A. A. Esin, Characteristics of structurally finite classes of order-preserving three-valued logic maps, Logic Journal
of the IGPL, (2024), jzae128. https://doi.org/10.1093/jigpal/jzae128

[9] A. A. Esin, R. Yavorskiy, N. Zemtsov, Brief announcement monitoring of linear distributed computations, Springer
Berlin Heidelberg, (2006), 566-568. https://doi.org/10.1007/11864219_47

[10] F. A. Gadzhiev, The Kolmogorov-S lupecki theorem for a three-dimensional sphere, Russian Mathematical Surveys,
39(5) (1984). https://doi.org/10.1070/rm1984v039n05abeh004086

[11] E. Gradel, G. L. McColm, Hierarchies in transitive closure logic, stratified Datalog and infinitary logic, Proceedings.,
33rd Annual Symposium on Foundations of Computer Science, (1992), 167-176. https://doi.org/10.1109/SFCS.
1992.267775

[12] Y. Hassan, et al., Phase-engineered molybdenum telluride/black phosphorus van der waals heterojunctions for
tunable multivalued logic, ACS Applied Materials and Interfaces, 12(12) (2020), 14119-14124. https://doi.org/
10.1021/acsami.9b20041

[13] L. C. Holdon, A. Borumand Saeid, Regularity in residuated lattices, Iranian Journal of Fuzzy Systems, 16(6) (2019),
107-126. https://doi.org/10.22111/IJFS.2019.5023

[14] S. B. Jo, J. Kang, J. H. Cho, Recent advances on multivalued logic gates: A materials perspective, Advanced
Science, 8(8) (2021), 2004216. https://doi.org/10.1002/advs.202004216

[15] E. Y. Kalimulina, Analysis of unreliable open queueing network with dynamic routing, Springer International
Publishing, (2017), 355-367. https://doi.org/10.1007/978-3-319-66836-9_30

[16] E. Y. Kalimulina, On exponential convergence of dynamic queueing network and its applications, Springer International Publishing, (2020), 463-474. https://doi.org/10.1007/978-3-030-66471-8_35

[17] E. Y. Kalimulina, Lattice structure of some closed classes for three-valued logic and its applications, Mathematics,
10(1) (2022), 94. https://doi.org/10.3390/math10010094

[18] E. Y. Kalimulina, Finiteness of one-valued function classes in many-valued logic, Fractal and Fractional, 8(1)
(2024), 29. https://doi.org/10.3390/fractalfract8010029

[19] V. Levashenko, I. Lukyanchuk, E. Zaitseva, M. Kvassay, J. Rabcan, P. Rusnak, Development of programmable logic
array for multiple-valued logic functions, IEEE Transactions on Computer-Aided Design of Integrated Circuits and
Systems, 39(12) (2020), 4854-4866. https://doi.org/10.1109/TCAD.2020.2966676

[20] B. Li, X. B. Liang, S. M. Fei, Characterizing the superposition of arbitrary random quantum states and a known
quantum state, Results in Physics, 49 (2023), 106510. https://doi.org/10.1016/j.rinp.2023.106510

[21] D. U. Lim, S. B. Jo, B. Sae J. H. Cho, Monolithic tandem vertical electrochemical transistors for printed multi-valued
logic, Advanced Materials, 35(9) (2023), 2208757. https://doi.org/10.1002/adma.202208757

[22] X. Luo, J. Fang, Fuzzifying closure systems and closure operators, Iranian Journal of Fuzzy Systems, 8(1) (2011),
77-94. https://doi.org/10.22111/ijfs.2011.239

[23] S. S. Marchenkov, Existence of finite bases in closed classes of Boolean functions, Algebra and Logic, 23(1) (1984),
66-74. https://doi.org/10.1007/BF01979700

[24] M. A. Malkov, Algebra of finite-valued functions: Classification of functions and subalgebras, essential and fictitious
subalgebras, Pure and Applied Mathematics Journal, 8(2) (2019), 30-36. https://doi.org/10.11648/j.pamj.
20190802.11

[25] A. Mikhailovich, Some closed classes of three-valued logic generated by symmetric functions, arXiv, (2015). https:
//doi.org/10.48550/arXiv.1503.05998

[26] D. Panigrahi, R. Hayakawa, Y. Wakayama, High-performance multivalued logic circuits based on optically tunable
antiambipolar transistors, Journal of Materials Chemistry C, 10(14) (2022), 5559-5566. https://doi.org/10.1039/
D1TC05858D

[27] A. Platzer, Logical foundations of cyber-physical systems, Springer International Publishing, 2018. https://doi.
org/10.1007/978-3-319-63588-0

[28] D. K. Podol’ko, Classes of functions closed with respect to a special superposition operation, Moscow University
Mathematics Bulletin, 68 (2013), 303-306. https://doi.org/10.3103/s0027132213060090

[29] D. K. Podol’ko, A family of classes of functions closed with respect to a strengthened superposition operation,
Moscow University Mathematics Bulletin, 70(2) (2015), 79-83. https://doi.org/10.3103/S0027132215020059

[30] E. L. Post, The two-valued iterative systems of mathematical logic. (AM-5), Princeton University Press, 1941.

[31] E. Rogova, P. Chountas, Panagiotis, On imprecision intuitionistic fuzzy sets and OLAP – The case for KNOLAP,
Springer Berlin Heidelberg, (2007), 11-20. https://doi.org/10.1007/978-3-540-72434-6_2

[32] C. F. Silva, S. Ferlin, O. Alay, A. Brunstrom, B. Y. L. Kimura, IoT traffic offloading with multiPath TCP, IEEE
Communications Magazine, 59(4) (2021), 51-57. https://doi.org/10.1109/MCOM.001.2000915

[33] S. M. Srivastava, A course on mathematical logic, Universitext, 2013. https://doi.org/10.1007/
978-1-4614-5746-6

[34] M. V. Starostin, Implicitly maximal classes and implicit completeness criterion in the three-valued logic, Moscow
University Mathematics Bulletin, 73(2) (2018), 82-84. https://doi.org/10.3103/S0027132218020067

[35] I. E. Suleimenov, Y. S. Vitulyova, S. B. Kabdushev, A. S. Bakirov, Improving the efficiency of using multivalued
logic tools, Scientific Reports, 13(1) (2023). https://doi.org/10.1038/s41598-023-28272-1

[36] J. Vipra, Jai, S. M. West, Computational power and AI, AI Now Institute, 2023.

[37] Y. S. Vitulyova, D. Matrassulova, I. Suleimenov, A. Bakirov, Convolutional neural networks from the perspective
of the problems of multivalued logic, Research Square Platform LLC, (2023), 1-19. https://doi.org/10.21203/
rs.3.rs-3224688/v1

[38] S. Wang, H. Li, Graph-based function perturbation analysis for observability of multivalued logical networkss, IEEE
Transactions on Neural Networks and Learning Systems, 32(11) (2021), 4839-4848. https://doi.org/10.1109/
TNNLS.2020.3025912

[39] S. V. Yablonskii, Functional constructions in a k-valued logic, Trudy Matematicheskogo Instituta Imeni VA
Steklova, Russian Academy of Sciences, Steklov Mathematical Institute of Russian, 51 (1958), 5-142.

[40] Y. I. Yanov, A. A. Muchnik, The existence of a k-valued closed class that has no finite basis, Doklady Akad. Nauk
SSSR, 127(1) (1959), 44.