{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,26]],"date-time":"2025-04-26T05:07:29Z","timestamp":1745644049866,"version":"3.40.3"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T00:00:00Z","timestamp":1742860800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T00:00:00Z","timestamp":1742860800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci. China Inf. Sci."],"published-print":{"date-parts":[[2025,9]]},"DOI":"10.1007\/s11432-024-4252-7","type":"journal-article","created":{"date-parts":[[2025,4,4]],"date-time":"2025-04-04T08:50:55Z","timestamp":1743756655000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On control networks over finite lattices"],"prefix":"10.1007","volume":"68","author":[{"given":"Zhengping","family":"Ji","sequence":"first","affiliation":[]},{"given":"Daizhan","family":"Cheng","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,25]]},"reference":[{"key":"4252_CR1","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1016\/0022-5193(69)90015-0","volume":"22","author":"S A Kauffman","year":"1969","unstructured":"Kauffman S A. Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol, 1969, 22: 437\u2013467","journal-title":"J Theor Biol"},{"key":"4252_CR2","volume-title":"The Mathematical Analysis of Logic","author":"G Boole","year":"1847","unstructured":"Boole G. The Mathematical Analysis of Logic. New York: Philosophical Library, 1847"},{"key":"4252_CR3","doi-asserted-by":"publisher","first-page":"163","DOI":"10.2307\/2370324","volume":"43","author":"E L Post","year":"1921","unstructured":"Post E L. Introduction to a general theory of elementary propositions. Am J Math, 1921, 43: 163\u2013185","journal-title":"Am J Math"},{"key":"4252_CR4","doi-asserted-by":"publisher","first-page":"167","DOI":"10.2307\/2371676","volume":"64","author":"P C Rosenbloom","year":"1942","unstructured":"Rosenbloom P C. Post algebras. I. postulates and general theory. Am J Math, 1942, 64: 167\u2013188","journal-title":"Am J Math"},{"key":"4252_CR5","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1090\/S0002-9947-1960-0112855-8","volume":"95","author":"G Epstein","year":"1960","unstructured":"Epstein G. The lattice theory of post algebras. Trans Amer Math Soc, 1960, 95: 300\u2013317","journal-title":"Trans Amer Math Soc"},{"key":"4252_CR6","volume-title":"Proceedings of the Computer Science and Multiple-Valued Logic Theory and Applications","author":"T Traczyk","year":"1977","unstructured":"Traczyk T. Post algebras through P0 and P1 lattices, In: Proceedings of the Computer Science and Multiple-Valued Logic Theory and Applications, 1977"},{"key":"4252_CR7","first-page":"113","volume-title":"Proceedings of the 7th International Workshop on Signal Design and its Applications in Communications (IWSDA), Bengaluru","author":"K W Shum","year":"2015","unstructured":"Shum K W, Sun Q T. Lattice network codes over optimal lattices in low dimensions, In: Proceedings of the 7th International Workshop on Signal Design and its Applications in Communications (IWSDA), Bengaluru, 2015. 113\u2013117"},{"key":"4252_CR8","doi-asserted-by":"publisher","first-page":"5306","DOI":"10.1109\/TIT.2015.2451623","volume":"61","author":"N E Tunali","year":"2015","unstructured":"Tunali N E, Huang Y C, Boutros J J, et al. Lattices over Eisenstein integers for compute-and-forward. IEEE Trans Inform Theor, 2015, 61: 5306\u20135321","journal-title":"IEEE Trans Inform Theor"},{"key":"4252_CR9","first-page":"321","volume-title":"Proceedings of the 10th European Conference on Artificial Life, Budapest","author":"C Bouyioukos","year":"2009","unstructured":"Bouyioukos C, Kim J T. Gene regulatory network properties linked to gene expression dynamics in spatially extended systems. In: Proceedings of the 10th European Conference on Artificial Life, Budapest, 2009. 321\u2013328"},{"key":"4252_CR10","doi-asserted-by":"publisher","first-page":"126","DOI":"10.3390\/quantum2010010","volume":"2","author":"A Y Bykovsky","year":"2020","unstructured":"Bykovsky A Y. Heterogeneous network architecture for integration of AI and quantum optics by means of multiple-valued logic. Quantum Rep, 2020, 2: 126\u2013165","journal-title":"Quantum Rep"},{"key":"4252_CR11","doi-asserted-by":"publisher","first-page":"1263","DOI":"10.3390\/app12031263","volume":"12","author":"A Y Bykovsky","year":"2022","unstructured":"Bykovsky A Y. Multiple-valued logic modelling for agents controlled via optical networks. Appl Sci, 2022, 12: 1263","journal-title":"Appl Sci"},{"key":"4252_CR12","doi-asserted-by":"publisher","first-page":"2450","DOI":"10.1109\/TFUZZ.2022.3227400","volume":"31","author":"S Qiao","year":"2023","unstructured":"Qiao S, Zhu P, Feng J. Fuzzy bisimulations for nondeterministic fuzzy transition systems. IEEE Trans Fuzzy Syst, 2023, 31: 2450\u20132463","journal-title":"IEEE Trans Fuzzy Syst"},{"key":"4252_CR13","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1016\/j.jfranklin.2023.11.027","volume":"361","author":"S Qiao","year":"2024","unstructured":"Qiao S, Feng J, Zhu P. Distribution-based limited fuzzy bisimulations for nondeterministic fuzzy transition systems. J Franklin Inst, 2024, 361: 135\u2013149","journal-title":"J Franklin Inst"},{"key":"4252_CR14","doi-asserted-by":"publisher","first-page":"2403","DOI":"10.1016\/j.dam.2007.04.019","volume":"155","author":"A Richard","year":"2007","unstructured":"Richard A, Comet J P. Necessary conditions for multistationarity in discrete dynamical systems. Discrete Appl Math, 2007, 155: 2403\u20132413","journal-title":"Discrete Appl Math"},{"key":"4252_CR15","doi-asserted-by":"publisher","first-page":"2713","DOI":"10.1109\/TCOMM.2013.050813.120759","volume":"61","author":"Q T Sun","year":"2013","unstructured":"Sun Q T, Yuan J H, Huang T, et al. Lattice network codes based on Eisenstein integers. IEEE Trans Commun, 2013, 61: 2713\u20132725","journal-title":"IEEE Trans Commun"},{"key":"4252_CR16","volume-title":"Artificial Intelligence: A Modern Approach","author":"S J Russell","year":"2010","unstructured":"Russell S J, Norvig P. Artificial Intelligence: A Modern Approach. 3rd ed. Upper Saddle River: Prentice Hall, 2010","edition":"3rd ed"},{"key":"4252_CR17","doi-asserted-by":"publisher","first-page":"917","DOI":"10.1016\/S0960-0779(03)00063-8","volume":"18","author":"A Adamatzky","year":"2003","unstructured":"Adamatzky A. On dynamically non-trivial three-valued logics: oscillatory and bifurcatory species. Chaos Solitons Fractals, 2003, 18: 917\u2013936","journal-title":"Chaos Solitons Fractals"},{"key":"4252_CR18","volume-title":"Function Algebras on Finite Sets: Basic Course on Many-valued Logic and Clone Theory","author":"D Lau","year":"2006","unstructured":"Lau D. Function Algebras on Finite Sets: Basic Course on Many-valued Logic and Clone Theory. Berlin: Springer, 2006"},{"key":"4252_CR19","volume-title":"Computer Science and Multiple-valued Logic: Theory and Applications","author":"D C Rine","year":"2014","unstructured":"Rine D C. Computer Science and Multiple-valued Logic: Theory and Applications. New York: North-Holland Publishing Company, 2014"},{"key":"4252_CR20","doi-asserted-by":"publisher","first-page":"819","DOI":"10.1007\/s11071-013-1007-4","volume":"74","author":"M Garc\u00eda-Mart\u00ednez","year":"2013","unstructured":"Garc\u00eda-Mart\u00ednez M, Campos-Cant\u00f3n I, Campos-Cant\u00f3n E, et al. Difference map and its electronic circuit realization. Nonlinear Dyn, 2013, 74: 819\u2013830","journal-title":"Nonlinear Dyn"},{"key":"4252_CR21","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1007\/BF02703801","volume":"31","author":"M Suneel","year":"2006","unstructured":"Suneel M. Electronic circuit realization of the logistic map. Sadhana, 2006, 31: 69\u201378","journal-title":"Sadhana"},{"key":"4252_CR22","doi-asserted-by":"publisher","first-page":"512","DOI":"10.1109\/TNN.2008.2011359","volume":"20","author":"D Z Cheng","year":"2009","unstructured":"Cheng D Z. Input-state approach to Boolean networks. IEEE Trans Neural Netw, 2009, 20: 512\u2013521","journal-title":"IEEE Trans Neural Netw"},{"key":"4252_CR23","doi-asserted-by":"publisher","first-page":"1659","DOI":"10.1016\/j.automatica.2009.03.006","volume":"45","author":"D Cheng","year":"2009","unstructured":"Cheng D, Qi H. Controllability and observability of Boolean control networks. Automatica, 2009, 45: 1659\u20131667","journal-title":"Automatica"},{"key":"4252_CR24","doi-asserted-by":"publisher","first-page":"1390","DOI":"10.1109\/TAC.2012.2231592","volume":"58","author":"E Fornasini","year":"2013","unstructured":"Fornasini E, Valcher M E. Observability, reconstructibility and state observers of Boolean control networks. IEEE Trans Automat Contr, 2013, 58: 1390\u20131401","journal-title":"IEEE Trans Automat Contr"},{"key":"4252_CR25","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1007\/s11768-022-00122-x","volume":"21","author":"K Zhang","year":"2023","unstructured":"Zhang K. A survey on observability of Boolean control networks. Control Theor Technol, 2023, 21: 115\u2013147","journal-title":"Control Theor Technol"},{"key":"4252_CR26","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1016\/j.automatica.2017.06.043","volume":"83","author":"H Li","year":"2017","unstructured":"Li H, Wang Y. Further results on feedback stabilization control design of Boolean control networks. Automatica, 2017, 83: 303\u2013308","journal-title":"Automatica"},{"key":"4252_CR27","doi-asserted-by":"publisher","first-page":"2730","DOI":"10.1109\/TAC.2019.2944903","volume":"65","author":"X Zhang","year":"2020","unstructured":"Zhang X, Wang Y, Cheng D. Output tracking of Boolean control networks. IEEE Trans Automat Contr, 2020, 65: 2730\u20132735","journal-title":"IEEE Trans Automat Contr"},{"key":"4252_CR28","doi-asserted-by":"publisher","first-page":"110097","DOI":"10.1016\/j.automatica.2021.110097","volume":"137","author":"Y Li","year":"2022","unstructured":"Li Y, Zhu J. Necessary and sufficient vertex partition conditions for input-output decoupling of Boolean control networks. Automatica, 2022, 137: 110097","journal-title":"Automatica"},{"key":"4252_CR29","doi-asserted-by":"publisher","first-page":"2040","DOI":"10.1049\/iet-cta.2016.1659","volume":"11","author":"J Lu","year":"2017","unstructured":"Lu J, Li H, Liu Y, et al. Survey on semi-tensor product method with its applications in logical networks and other finite-valued systems. IET Control Theor Appl, 2017, 11: 2040\u20132047","journal-title":"IET Control Theor Appl"},{"key":"4252_CR30","doi-asserted-by":"publisher","first-page":"7562","DOI":"10.1016\/j.jfranklin.2022.07.039","volume":"359","author":"D Cheng","year":"2022","unstructured":"Cheng D, Ji Z. On networks over finite rings. J Franklin Institute, 2022, 359: 7562\u20137599","journal-title":"J Franklin Institute"},{"key":"4252_CR31","first-page":"81","volume-title":"Proceedings of the 42nd Chinese Control Conference (CCC), Tianjin","author":"S Zou","year":"2023","unstructured":"Zou S, Zhu J. On sub-networks over proper ideals of dynamical networks over finite rings. In: Proceedings of the 42nd Chinese Control Conference (CCC), Tianjin, 2023. 81\u201386"},{"key":"4252_CR32","doi-asserted-by":"publisher","first-page":"1016","DOI":"10.1109\/TAC.2021.3081621","volume":"67","author":"L Lin","year":"2021","unstructured":"Lin L, Cao J, Zhu S, et al. Synchronization analysis for stochastic networks through finite fields. IEEE Trans Automat Contr, 2021, 67: 1016\u20131022","journal-title":"IEEE Trans Automat Contr"},{"key":"4252_CR33","doi-asserted-by":"publisher","first-page":"878","DOI":"10.1109\/TCNS.2023.3314583","volume":"11","author":"L Lin","year":"2024","unstructured":"Lin L, Jiang Z, Lin H, et al. On quotients of stochastic networks over finite fields. IEEE Trans Control Netw Syst, 2024, 11: 878\u2013889","journal-title":"IEEE Trans Control Netw Syst"},{"key":"4252_CR34","doi-asserted-by":"publisher","first-page":"108877","DOI":"10.1016\/j.automatica.2020.108877","volume":"115","author":"M Meng","year":"2020","unstructured":"Meng M, Li X, Xiao G. Synchronization of networks over finite fields. Automatica, 2020, 115: 108877","journal-title":"Automatica"},{"key":"4252_CR35","doi-asserted-by":"publisher","first-page":"111201","DOI":"10.1007\/s11432-022-3538-4","volume":"66","author":"Y Yan","year":"2023","unstructured":"Yan Y, Cheng D, Feng J E, et al. Survey on applications of algebraic state space theory of logical systems to finite state machines. Sci China Inf Sci, 2023, 66: 111201","journal-title":"Sci China Inf Sci"},{"key":"4252_CR36","unstructured":"Ji Z, Zhang X, Cheng D. Aggregated (Bi-)simulation of finite-valued networks. 2023. ArXiv:2303.14390"},{"key":"4252_CR37","doi-asserted-by":"publisher","first-page":"1550","DOI":"10.1109\/TAC.2021.3070307","volume":"67","author":"J Zhong","year":"2022","unstructured":"Zhong J, Liu Y, Lu J, et al. Pinning control for stabilization of Boolean networks under knock-out perturbation. IEEE Trans Automat Contr, 2022, 67: 1550\u20131557","journal-title":"IEEE Trans Automat Contr"},{"key":"4252_CR38","doi-asserted-by":"publisher","first-page":"1527","DOI":"10.1109\/TNNLS.2015.2442593","volume":"27","author":"Y Zhao","year":"2015","unstructured":"Zhao Y, Ghosh B K, Cheng D. Control of large-scale Boolean networks via network aggregation. IEEE Trans Neural Netw Learn Syst, 2015, 27: 1527\u20131536","journal-title":"IEEE Trans Neural Netw Learn Syst"},{"key":"4252_CR39","volume-title":"An Inroduction to Semi-tensor Product of Matrices and Its Applications","author":"D Cheng","year":"2012","unstructured":"Cheng D, Qi H, Zhao Y. An Inroduction to Semi-tensor Product of Matrices and Its Applications. Singapore: World Scientific, 2012"},{"key":"4252_CR40","volume-title":"Analysis and Control of Boolean Networks, A Semi-tensor Product Approach","author":"D Cheng","year":"2011","unstructured":"Cheng D, Qi H, Li Z. Analysis and Control of Boolean Networks, A Semi-tensor Product Approach. New York: Springer, 2011"},{"key":"4252_CR41","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-11478-1","volume-title":"An Invitation to General Algebra and Universal Constructions. 2nd ed","author":"G M Bergman","year":"2015","unstructured":"Bergman G M. An Invitation to General Algebra and Universal Constructions. 2nd ed. Berlin: Springer, 2015"},{"key":"4252_CR42","volume-title":"Enumerative Combinatorics","author":"R P Stanley","year":"2012","unstructured":"Stanley R P. Enumerative Combinatorics. 2nd ed. Cambridge: Cambridge University Press, 2012","edition":"2nd ed"},{"key":"4252_CR43","doi-asserted-by":"publisher","first-page":"767","DOI":"10.1016\/j.sysconle.2010.09.002","volume":"59","author":"Y Zhao","year":"2010","unstructured":"Zhao Y, Qi H, Cheng D. Input-state incidence matrix of Boolean control networks and its applications. Syst Control Lett, 2010, 59: 767\u2013774","journal-title":"Syst Control Lett"},{"key":"4252_CR44","doi-asserted-by":"publisher","first-page":"111190","DOI":"10.1016\/j.automatica.2023.111190","volume":"156","author":"Y Guo","year":"2023","unstructured":"Guo Y, Gong P, Wu Y, et al. Stabilization of discrete-time switched systems with constraints by dynamic logic-based switching feedback. Automatica, 2023, 156: 111190","journal-title":"Automatica"},{"key":"4252_CR45","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1016\/j.arcontrol.2019.03.010","volume":"47","author":"G Pola","year":"2019","unstructured":"Pola G, Di Benedetto M D. Control of cyber-physical-systems with logic specifications: a formal methods approach. Annu Rev Control, 2019, 47: 178\u2013192","journal-title":"Annu Rev Control"},{"key":"4252_CR46","volume-title":"The Two-valued Iterative Systems of Mathematical Logic","author":"E L Post","year":"1941","unstructured":"Post E L. The Two-valued Iterative Systems of Mathematical Logic. Princeton: Princeton University Press, 1941"},{"key":"4252_CR47","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719796","volume-title":"Graph Classes: A Survey","author":"A Brandst\u00e4dt","year":"1999","unstructured":"Brandst\u00e4dt A, Le V B, Spinrad J P. Graph Classes: A Survey. Philadelphia: Society for Industrial and Applied Mathematics, 1999"},{"key":"4252_CR48","first-page":"19","volume-title":"Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans","author":"R M McConnell","year":"1999","unstructured":"McConnell R M, Spinrad J P. Linear-time transitive orientation. In: Proceedings of the 8th Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, 1999. 19\u201325"},{"key":"4252_CR49","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1016\/S0012-365X(98)00319-7","volume":"201","author":"R M McConnell","year":"1999","unstructured":"McConnell R M, Spinrad J P. Modular decomposition and transitive orientation. Discrete Math, 1999, 201: 189\u2013241","journal-title":"Discrete Math"},{"key":"4252_CR50","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1016\/j.sysconle.2018.03.004","volume":"115","author":"D Cheng","year":"2018","unstructured":"Cheng D, Li C, He F. Observability of Boolean networks via set controllability approach. Syst Control Lett, 2018, 115: 22\u201325","journal-title":"Syst Control Lett"}],"container-title":["Science China Information Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11432-024-4252-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11432-024-4252-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11432-024-4252-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,5]],"date-time":"2025-04-05T01:37:35Z","timestamp":1743817055000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11432-024-4252-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,25]]},"references-count":50,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["4252"],"URL":"https:\/\/doi.org\/10.1007\/s11432-024-4252-7","relation":{},"ISSN":["1674-733X","1869-1919"],"issn-type":[{"value":"1674-733X","type":"print"},{"value":"1869-1919","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,25]]},"assertion":[{"value":"4 August 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 October 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 December 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 March 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"192201"}}