{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,26]],"date-time":"2025-04-26T08:40:08Z","timestamp":1745656808183,"version":"3.40.4"},"publisher-location":"Cham","reference-count":70,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031787560"},{"type":"electronic","value":"9783031787577"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"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":[],"published-print":{"date-parts":[[2025]]},"DOI":"10.1007\/978-3-031-78757-7_14","type":"book-chapter","created":{"date-parts":[[2025,4,26]],"date-time":"2025-04-26T07:59:44Z","timestamp":1745654384000},"page":"399-422","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Recent Insights into Number-Conserving Cellular Automata"],"prefix":"10.1007","author":[{"given":"Barbara","family":"Wolnik","sequence":"first","affiliation":[]},{"given":"Witold","family":"Bo\u0142t","sequence":"additional","affiliation":[]},{"given":"Bernard","family":"De Baets","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,4,27]]},"reference":[{"issue":"4","key":"14_CR1","first-page":"271","volume":"3","author":"L Baird","year":"2008","unstructured":"Baird, L., Fagin, B.: Conservation functions for 1-D automata: efficient algorithms, new results, and a partial taxonomy. J. Cell. Autom. 3(4), 271\u2013288 (2008)","journal-title":"J. Cell. Autom."},{"key":"14_CR2","doi-asserted-by":"publisher","first-page":"433","DOI":"10.1007\/s11047-018-9696-8","volume":"19","author":"K Bhattacharjee","year":"2020","unstructured":"Bhattacharjee, K., Naskar, N., Roy, S., Das, S.: A survey of cellular automata: types, dynamics, non-uniformity and applications. Nat. Comput. 19, 433\u2013461 (2020). https:\/\/doi.org\/10.1007\/s11047-018-9696-8","journal-title":"Nat. Comput."},{"issue":"28","key":"14_CR3","doi-asserted-by":"publisher","first-page":"6007","DOI":"10.1088\/0305-4470\/31\/28\/014","volume":"31","author":"N Boccara","year":"1998","unstructured":"Boccara, N., Fuk\u015b, H.: Cellular automaton rules conserving the number of active sites. J. Phys. A: Math. Gen. 31(28), 6007\u20136018 (1998). https:\/\/doi.org\/10.1088\/0305-4470\/31\/28\/014","journal-title":"J. Phys. A: Math. Gen."},{"issue":"1\u20133","key":"14_CR4","first-page":"1","volume":"52","author":"N Boccara","year":"2002","unstructured":"Boccara, N., Fuk\u015b, H.: Number-conserving cellular automaton rules. Fund. Inform. 52(1\u20133), 1\u201313 (2002)","journal-title":"Fund. Inform."},{"issue":"11","key":"14_CR5","doi-asserted-by":"publisher","first-page":"1605","DOI":"10.1142\/S0129183106010029","volume":"17","author":"N Boccara","year":"2006","unstructured":"Boccara, N., Fuk\u015b, H.: Motion representation of one-dimensional cellular automaton rules. Int. J. Mod. Phys. C 17(11), 1605\u20131611 (2006). https:\/\/doi.org\/10.1142\/S0129183106010029","journal-title":"Int. J. Mod. Phys. C"},{"doi-asserted-by":"publisher","unstructured":"Cattaneo, G., Dennunzio, A., Formenti, E., Provillard, J.: Non-uniform cellular automata. In: Proceedings of 3rd International Conference Language and Automata Theory and Applications, LATA, pp. 302\u2013313 (2009). https:\/\/doi.org\/10.1007\/978-3-642-00982-2_26","key":"14_CR6","DOI":"10.1007\/978-3-642-00982-2_26"},{"unstructured":"Chaudhuri, P.P., Chowdhury, D.R., Nandi, S., Chattopadhyay, S.: Additive cellular automata\u2014theory and applications, vol. 1. IEEE Computer Society Press, USA (1997)","key":"14_CR7"},{"issue":"3\/4","key":"14_CR8","first-page":"191","volume":"14","author":"M Dembowski","year":"2019","unstructured":"Dembowski, M., Wolnik, B., Bo\u0142t, W., Baetens, J.M., De Baets, B.: Two-dimensional affine continuous cellular automata solving the relaxed density classification problem. J. Cell. Autom. 14(3\/4), 191\u2013212 (2019)","journal-title":"J. Cell. Autom."},{"key":"14_CR9","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/j.ic.2012.02.008","volume":"215","author":"A Dennunzio","year":"2012","unstructured":"Dennunzio, A., Formenti, E., Provillard, J.: Non-uniform cellular automata: classes, dynamics, and decidability. Inf. Comput. 215, 32\u201346 (2012). https:\/\/doi.org\/10.1016\/j.ic.2012.02.008","journal-title":"Inf. Comput."},{"key":"14_CR10","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1016\/j.tcs.2012.05.013","volume":"504","author":"A Dennunzio","year":"2013","unstructured":"Dennunzio, A., Formenti, E., Provillard, J.: Local rule distributions, language complexity and non-uniform cellular automata. Theoret. Comput. Sci. 504, 38\u201351 (2013). https:\/\/doi.org\/10.1016\/j.tcs.2012.05.013","journal-title":"Theoret. Comput. Sci."},{"issue":"1","key":"14_CR11","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1016\/S0304-3975(02)00534-0","volume":"299","author":"B Durand","year":"2003","unstructured":"Durand, B., Formenti, E., R\u00f3ka, Z.: Number-conserving cellular automata I: decidability. Theoret. Comput. Sci. 299(1), 523\u2013535 (2003). https:\/\/doi.org\/10.1016\/S0304-3975(02)00534-0","journal-title":"Theoret. Comput. Sci."},{"doi-asserted-by":"publisher","unstructured":"Dzedzej, A., Dziemia\u0144czuk, M., Nenca, A., Wardyn, A., Wolnik, B.: The complete list of two-dimensional number-conserving ternary cellular automata [dataset] (2020). https:\/\/doi.org\/10.34808\/phjp-ah07","key":"14_CR12","DOI":"10.34808\/phjp-ah07"},{"issue":"7","key":"14_CR13","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/ab25df","volume":"2019","author":"A Dzedzej","year":"2019","unstructured":"Dzedzej, A., Wolnik, B., Dziemia\u0144czuk, M., Nenca, A., Baetens, J.M., De Baets, B.: A two-layer representation of four-state reversible number-conserving 2D cellular automata. J. Stat. Mech: Theory Exp. 2019(7), 073202 (2019). https:\/\/doi.org\/10.1088\/1742-5468\/ab25df","journal-title":"J. Stat. Mech: Theory Exp."},{"key":"14_CR14","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1016\/j.ic.2020.104534","volume":"274","author":"A Dzedzej","year":"2020","unstructured":"Dzedzej, A., Wolnik, B., Nenca, A., Baetens, J., De Baets, B.: Efficient enumeration of three-state two-dimensional number-conserving cellular automata. Inf. Comput. 274, 14 (2020). https:\/\/doi.org\/10.1016\/j.ic.2020.104534","journal-title":"Inf. Comput."},{"key":"14_CR15","doi-asserted-by":"publisher","first-page":"599","DOI":"10.1016\/j.ins.2021.06.041","volume":"577","author":"A Dzedzej","year":"2021","unstructured":"Dzedzej, A., Wolnik, B., Nenca, A., Baetens, J.M., De Baets, B.: Two-dimensional rotation-symmetric number-conserving cellular automata. Inf. Sci. 577, 599\u2013621 (2021). https:\/\/doi.org\/10.1016\/j.ins.2021.06.041","journal-title":"Inf. Sci."},{"doi-asserted-by":"publisher","unstructured":"Dziemia\u0144czuk, M., Wolnik, B., Dzedzej, A.: The complete lists of 1D reversible number-conserving cellular automata with radius one of up to 7 states [dataset] (2020). https:\/\/doi.org\/10.34808\/b8pn-1523","key":"14_CR16","DOI":"10.34808\/b8pn-1523"},{"key":"14_CR17","first-page":"195","volume":"6","author":"S El Yacoubi","year":"2011","unstructured":"El Yacoubi, S., Mingarelli, A.: An algebraic characterization of fuzzy cellular automata. J. Cell. Autom. 6, 195\u2013206 (2011)","journal-title":"J. Cell. Autom."},{"issue":"3","key":"14_CR18","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/BF01857727","volume":"21","author":"E Fredkin","year":"1982","unstructured":"Fredkin, E., Toffoli, T.: Conservative logic. Int. J. Theor. Phys. 21(3), 219\u2013253 (1982). https:\/\/doi.org\/10.1007\/BF01857727","journal-title":"Int. J. Theor. Phys."},{"key":"14_CR19","volume-title":"Hydrodynamic Limits and Related Topics","author":"H Fuk\u015b","year":"2000","unstructured":"Fuk\u015b, H.: A class of cellular automata equivalent to deterministic particle systems. In: Feng, A.T.L.S., Varadhan, R.S. (eds.) Hydrodynamic Limits and Related Topics. Fields Institute Communications Series. AMS, Providence, RI (2000)"},{"issue":"2","key":"14_CR20","first-page":"141","volume":"2","author":"H Fuk\u015b","year":"2007","unstructured":"Fuk\u015b, H., Sullivan, K.: Enumeration of number-conserving cellular automata rules with two inputs. J. Cell. Autom. 2(2), 141\u2013148 (2007)","journal-title":"J. Cell. Autom."},{"key":"14_CR21","doi-asserted-by":"publisher","first-page":"2081","DOI":"10.1103\/PhysRevE.55.R2081","volume":"55","author":"H Fuk\u015b","year":"1997","unstructured":"Fuk\u015b, H.: Solution of the density classification problem with two cellular automata rules. Phys. Rev. E 55, 2081\u20132084 (1997). https:\/\/doi.org\/10.1103\/PhysRevE.55.R2081","journal-title":"Phys. Rev. E"},{"doi-asserted-by":"publisher","unstructured":"Garc\u00eda-Ramos, F.: Product decomposition for surjective 2-block NCCA. Discret. Math. Theor. Comput. Sci. 147\u2013158 (2011). https:\/\/doi.org\/10.46298\/dmtcs.2971","key":"14_CR22","DOI":"10.46298\/dmtcs.2971"},{"unstructured":"Goles, E., Moreira, A.: Number-conserving cellular automata and communication complexity: a numerical exploration beyond elementary CAS. J. Cell. Autom. 7(3) (2012)","key":"14_CR23"},{"issue":"3","key":"14_CR24","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1016\/0167-2789(91)90150-8","volume":"49","author":"T Hattori","year":"1991","unstructured":"Hattori, T., Takesue, S.: Additive conserved quantities in discrete-time lattice dynamical systems. Phys. D 49(3), 295\u2013322 (1991). https:\/\/doi.org\/10.1016\/0167-2789(91)90150-8","journal-title":"Phys. D"},{"unstructured":"Hazari, R., Das, S.: On number conservation of non-uniform cellular automata (2016). arXiv:1604.06600","key":"14_CR25"},{"doi-asserted-by":"publisher","unstructured":"Hortensius, P.D., McLeod, R.D., Card, H.C.: Parallel random number generation for VLSI systems using cellular automata. IEEE Trans. Comput. C-38(10), 1466\u20131473 (1989). https:\/\/doi.org\/10.1109\/12.35843","key":"14_CR26","DOI":"10.1109\/12.35843"},{"doi-asserted-by":"publisher","unstructured":"Imai, K., Artiom, A.: On universality of radius 1\/2 number-conserving cellular automata. In: Calude, C., Hagiya, M., Morita, K., Rozenberg, G., Timmis, J. (eds.) Unconventional Computation. UC 2010, pp. 45\u201355. Springer, Berlin, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-13523-1_8","key":"14_CR27","DOI":"10.1007\/978-3-642-13523-1_8"},{"doi-asserted-by":"publisher","unstructured":"Imai, K., Ishizaka, H., Poupet, V.: 5-state rotation-symmetric number-conserving cellular automata are not strongly universal. In: Isokawa, T., Imai, K., Matsui, N., Peper, F., Umeo, H. (eds.) Cellular Automata and Discrete Complex Systems, AUTOMATA 2014, pp. 31\u201343. Springer International Publishing, Cham (2015). https:\/\/doi.org\/10.1007\/978-3-319-18812-6_3","key":"14_CR28","DOI":"10.1007\/978-3-319-18812-6_3"},{"doi-asserted-by":"publisher","unstructured":"Imai, K., Martin, B., Saito, R.: On radius 1 nontrivial reversible and number-conserving cellular automata. In: Reversibility and Universality, pp. 269\u2013277. Springer, Berlin (2018). https:\/\/doi.org\/10.1007\/978-3-319-73216-9_12","key":"14_CR29","DOI":"10.1007\/978-3-319-73216-9_12"},{"doi-asserted-by":"publisher","unstructured":"Ishizaka, H., Takemura, Y., Imai, K.: On enumeration of motion representable two-dimensional two-state number-conserving cellular automata. In: 2015 Third International Symposium on Computing and Networking (CANDAR), pp. 412\u2013417 (2015). https:\/\/doi.org\/10.1109\/CANDAR.2015.52","key":"14_CR30","DOI":"10.1109\/CANDAR.2015.52"},{"key":"14_CR31","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/j.tcs.2004.11.021","volume":"334","author":"J Kari","year":"2005","unstructured":"Kari, J.: Theory of cellular automata: a survey. Theoret. Comput. Sci. 334, 3\u201333 (2005). https:\/\/doi.org\/10.1016\/j.tcs.2004.11.021","journal-title":"Theoret. Comput. Sci."},{"unstructured":"Kari, J., Taati, S.: A particle displacement representation for conservation laws in two-dimensional cellular automata. In: Journ\u00e9es Automates Cellulaires, Proceedings, pp. 65\u201373 (2008)","key":"14_CR32"},{"issue":"1","key":"14_CR33","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1143\/PTP.81.47","volume":"81","author":"T Kohyama","year":"1989","unstructured":"Kohyama, T.: Cellular automata with particle conservation. Progress Theoret. Phys. 81(1), 47\u201359 (1989). https:\/\/doi.org\/10.1143\/PTP.81.47","journal-title":"Progress Theoret. Phys."},{"unstructured":"Kotze, L., Steeb, W.H.: Conservation laws in cellular automata. In: Finite Dimensional Integrable Nonlinear Dynamical Systems, pp. 333\u2013346. World Scientific (1988)","key":"14_CR34"},{"unstructured":"Miquey, \u00c9.: State-conserving cellular automata (2011). https:\/\/www.i2m.univ-amu.fr\/perso\/etienne.miquey\/stage\/utu.pdf","key":"14_CR35"},{"unstructured":"Moreira, A.: NCCA\u2014some of my work (2003). http:\/\/www.dim.uchile.cl\/~anmoreir\/ncca\/mywork.html. Accessed 31 Oct 2023","key":"14_CR36"},{"unstructured":"Moreira, A.: Two-dimensional number-conserving cellular automata (2003). http:\/\/www.dim.uchile.cl\/~anmoreir\/ncca\/res_2d.pdf. Unpublished report avaliable online","key":"14_CR37"},{"issue":"3","key":"14_CR38","doi-asserted-by":"publisher","first-page":"711","DOI":"10.1016\/S0304-3975(02)00065-8","volume":"292","author":"A Moreira","year":"2003","unstructured":"Moreira, A.: Universality and decidability of number-conserving cellular automata. Theoret. Comput. Sci. 292(3), 711\u2013721 (2003). https:\/\/doi.org\/10.1016\/S0304-3975(02)00065-8","journal-title":"Theoret. Comput. Sci."},{"issue":"2","key":"14_CR39","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1016\/j.tcs.2004.06.010","volume":"325","author":"A Moreira","year":"2004","unstructured":"Moreira, A., Boccara, N., Goles, E.: On conservative and monotone one-dimensional cellular automata and their particle representation. Theoret. Comput. Sci. 325(2), 285\u2013316 (2004). https:\/\/doi.org\/10.1016\/j.tcs.2004.06.010","journal-title":"Theoret. Comput. Sci."},{"issue":"12","key":"14_CR40","doi-asserted-by":"publisher","first-page":"2221","DOI":"10.1051\/jp1:1992277","volume":"2","author":"K Nagel","year":"1992","unstructured":"Nagel, K., Schreckenberg, M.: A cellular automaton model for freeway traffic. J. Phys. I 2(12), 2221\u20132229 (1992). https:\/\/doi.org\/10.1051\/jp1:1992277","journal-title":"J. Phys. I"},{"doi-asserted-by":"publisher","unstructured":"Nenca, A., Dzedzej, A., Wolnik, B.: The complete list of two-dimensional rotation-symmetric number-conserving septenary cellular automata [dataset] (2022). https:\/\/doi.org\/10.34808\/jr67-r637","key":"14_CR41","DOI":"10.34808\/jr67-r637"},{"issue":"05","key":"14_CR42","doi-asserted-by":"publisher","first-page":"2150072","DOI":"10.1142\/S0218127421500723","volume":"31","author":"S Pal","year":"2021","unstructured":"Pal, S., Sahoo, S., Nayak, B.K.: Construction of one-dimensional nonuniform number conserving elementary cellular automata rules. Int. J. Bifurc. Chaos 31(05), 2150072 (2021). https:\/\/doi.org\/10.1142\/S0218127421500723","journal-title":"Int. J. Bifurc. Chaos"},{"issue":"6","key":"14_CR43","doi-asserted-by":"publisher","first-page":"1781","DOI":"10.1088\/0951-7715\/15\/6\/305","volume":"15","author":"M Pivato","year":"2002","unstructured":"Pivato, M.: Conservation laws in cellular automata. Nonlinearity 15(6), 1781\u20131793 (2002). https:\/\/doi.org\/10.1088\/0951-7715\/15\/6\/305","journal-title":"Nonlinearity"},{"doi-asserted-by":"crossref","unstructured":"Pries, W., Thanailakis, A., Card, H.C.: Group properties of cellular automata and VLSI applications. IEEE Trans. Comput. C-35(12), 1013\u20131024 (1986)","key":"14_CR44","DOI":"10.1109\/TC.1986.1676709"},{"issue":"1","key":"14_CR45","doi-asserted-by":"publisher","first-page":"31","DOI":"10.3233\/FI-222129","volume":"187","author":"M Redeker","year":"2022","unstructured":"Redeker, M.: Number conservation via particle flow in one-dimensional cellular automata. Fund. Inform. 187(1), 31\u201359 (2022). https:\/\/doi.org\/10.3233\/FI-222129","journal-title":"Fund. Inform."},{"unstructured":"Ross, S.: A First Course in Probability. Pearson Education (2011)","key":"14_CR46"},{"key":"14_CR47","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/j.tcs.2014.07.031","volume":"559","author":"V Salo","year":"2014","unstructured":"Salo, V.: Realization problems for nonuniform cellular automata. Theoret. Comput. Sci. 559, 91\u2013107 (2014). https:\/\/doi.org\/10.1016\/j.tcs.2014.07.031","journal-title":"Theoret. Comput. Sci."},{"issue":"2","key":"14_CR48","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1142\/S012918319600017X","volume":"7","author":"M Sipper","year":"1996","unstructured":"Sipper, M., Tomassini, M.: Generating parallel random number generators by cellular programming. Int. J. Mod. Phys. C 7(2), 180\u2013190 (1996). https:\/\/doi.org\/10.1142\/S012918319600017X","journal-title":"Int. J. Mod. Phys. C"},{"doi-asserted-by":"publisher","unstructured":"Taati, S.: Conservation laws in cellular automata. In: Rozenberg, G., B\u00e4ck, T., Kok, J.N. (eds.) Handbook of Natural Computing, pp. 259\u2013286. Springer Berlin Heidelberg, Berlin, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-540-92910-9_8","key":"14_CR49","DOI":"10.1007\/978-3-540-92910-9_8"},{"issue":"2","key":"14_CR50","first-page":"149","volume":"9","author":"S Takesue","year":"1995","unstructured":"Takesue, S.: Staggered invariants in cellular automata. Complex Syst. 9(2), 149\u2013168 (1995)","journal-title":"Complex Syst."},{"key":"14_CR51","first-page":"39","volume":"4","author":"N Tanimoto","year":"2009","unstructured":"Tanimoto, N., Imai, K.: A characterization of von Neumann neighbor number-conserving cellular automata. J. Cell. Autom. 4, 39\u201354 (2009)","journal-title":"J. Cell. Autom."},{"doi-asserted-by":"crossref","unstructured":"Ulam, S.: On some mathematical problems connected with patterns of growth of figures. In: Proceedings of Symposia in Applied Mathematics, vol.\u00a014, pp. 215\u2013224 (1962)","key":"14_CR52","DOI":"10.1090\/psapm\/014\/9947"},{"key":"14_CR53","volume-title":"Theory of Self-Reproducing Automata","author":"J von Neumann","year":"1966","unstructured":"von Neumann, J.: Theory of Self-Reproducing Automata. University of Illinois Press, Champaign, IL, USA (1966)"},{"issue":"3","key":"14_CR54","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1103\/RevModPhys.55.601","volume":"55","author":"S Wolfram","year":"1983","unstructured":"Wolfram, S.: Statistical mechanics of cellular automata. Rev. Mod. Phys. 55(3), 601\u2013644 (1983). https:\/\/doi.org\/10.1103\/RevModPhys.55.601","journal-title":"Rev. Mod. Phys."},{"issue":"1\u20132","key":"14_CR55","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0167-2789(84)90245-8","volume":"10","author":"S Wolfram","year":"1984","unstructured":"Wolfram, S.: Universality and complexity in cellular automata. Phys. D 10(1\u20132), 1\u201335 (1984). https:\/\/doi.org\/10.1016\/0167-2789(84)90245-8","journal-title":"Phys. D"},{"unstructured":"Wolfram, S.: Theory and applications of cellular automata. World Scientific (1986)","key":"14_CR56"},{"unstructured":"Wolfram, S.: A New Kind of Science. Wolfram Media (2002)","key":"14_CR57"},{"key":"14_CR58","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.100.022126","volume":"100","author":"B Wolnik","year":"2019","unstructured":"Wolnik, B., De Baets, B.: All binary number-conserving cellular automata based on adjacent cells are intrinsically one-dimensional. Phys. Rev. E 100, 022126 (2019). https:\/\/doi.org\/10.1103\/PhysRevE.100.022126","journal-title":"Phys. Rev. E"},{"key":"14_CR59","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1016\/j.ins.2019.10.068","volume":"513","author":"B Wolnik","year":"2020","unstructured":"Wolnik, B., De Baets, B.: Ternary reversible number-conserving cellular automata are trivial. Inf. Sci. 513, 180\u2013189 (2020). https:\/\/doi.org\/10.1016\/j.ins.2019.10.068","journal-title":"Inf. Sci."},{"issue":"34","key":"14_CR60","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/aa7d86","volume":"50","author":"B Wolnik","year":"2017","unstructured":"Wolnik, B., Dembowski, M., Bo\u0142t, W., Baetens, J.M., De Baets, B.: Density-conserving affine continuous cellular automata solving the relaxed density classification problem. J. Phys. A: Math. Theor. 50(34), 345103 (2017). https:\/\/doi.org\/10.1088\/1751-8121\/aa7d86","journal-title":"J. Phys. A: Math. Theor."},{"issue":"43","key":"14_CR61","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/aa89cf","volume":"50","author":"B Wolnik","year":"2017","unstructured":"Wolnik, B., Dzedzej, A., Baetens, J.M., De Baets, B.: Number-conserving cellular automata with a von Neumann neighborhood of range one. J. Phys. A: Math. Theor. 50(43), 435101 (2017). https:\/\/doi.org\/10.1088\/1751-8121\/aa89cf","journal-title":"J. Phys. A: Math. Theor."},{"issue":"3","key":"14_CR62","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1007\/s11047-023-09949-y","volume":"22","author":"B Wolnik","year":"2023","unstructured":"Wolnik, B., Dzedzej, A., Dziemia\u0144czuk, M., Wardyn, A., De Baets, B.: An exploration of reversible septenary number-conserving cellular automata: a survey of known methods. Nat. Comput. 22(3), 463\u2013475 (2023). https:\/\/doi.org\/10.1007\/s11047-023-09949-y","journal-title":"Nat. Comput."},{"key":"14_CR63","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2021.133075","volume":"429","author":"B Wolnik","year":"2022","unstructured":"Wolnik, B., Dziemia\u0144czuk, M., Dzedzej, A., De Baets, B.: Reversibility of number-conserving 1d cellular automata: unlocking insights into the dynamics for larger state sets. Phys. D 429, 133075 (2022). https:\/\/doi.org\/10.1016\/j.physd.2021.133075","journal-title":"Phys. D"},{"key":"14_CR64","doi-asserted-by":"publisher","first-page":"851","DOI":"10.1016\/j.ins.2023.01.033","volume":"626","author":"B Wolnik","year":"2023","unstructured":"Wolnik, B., Dziemia\u0144czuk, M., De Baets, B.: Non-uniform number-conserving elementary cellular automata. Inf. Sci. 626, 851\u2013866 (2023). https:\/\/doi.org\/10.1016\/j.ins.2023.01.033","journal-title":"Inf. Sci."},{"key":"14_CR65","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2023.119680","volume":"649","author":"B Wolnik","year":"2023","unstructured":"Wolnik, B., Dziemia\u0144czuk, M., De Baets, B.: Non-uniform number-conserving elementary cellular automata on the infinite grid: a tale of the unexpected. Inf. Sci. 649, 119680 (2023). https:\/\/doi.org\/10.1016\/j.ins.2023.119680","journal-title":"Inf. Sci."},{"issue":"4","key":"14_CR66","first-page":"243","volume":"15","author":"B Wolnik","year":"2020","unstructured":"Wolnik, B., Mro\u017cek, N., Dzedzej, A., De Baets, B.: Three-dimensional rotation-symmetric number-conserving cellular automata. J. Cell. Autom. 15(4), 243\u2013259 (2020)","journal-title":"J. Cell. Autom."},{"key":"14_CR67","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2020.132645","volume":"413","author":"B Wolnik","year":"2020","unstructured":"Wolnik, B., Nenca, A., Baetens, J.M., De Baets, B.: A split-and-perturb decomposition of number-conserving cellular automata. Phys. D 413, 132645 (2020). https:\/\/doi.org\/10.1016\/j.physd.2020.132645","journal-title":"Phys. D"},{"key":"14_CR68","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2023.113795","volume":"953","author":"B Wolnik","year":"2023","unstructured":"Wolnik, B., Nenca, A., De Baets, B.: A decomposition theorem for number-conserving multi-state cellular automata on triangular grids. Theoret. Comput. Sci. 953, 113795 (2023). https:\/\/doi.org\/10.1016\/j.tcs.2023.113795","journal-title":"Theoret. Comput. Sci."},{"key":"14_CR69","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.107.024211","volume":"107","author":"B Wolnik","year":"2023","unstructured":"Wolnik, B., Nenca, A., Dzedzej, A., De Baets, B.: Seven-state rotation-symmetric number-conserving cellular automaton that is not isomorphic to any septenary one. Phys. Rev. E 107, 024211 (2023). https:\/\/doi.org\/10.1103\/PhysRevE.107.024211","journal-title":"Phys. Rev. E"},{"key":"14_CR70","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/j.tcs.2016.11.002","volume":"666","author":"DA Zaitsev","year":"2017","unstructured":"Zaitsev, D.A.: A generalized neighborhood for cellular automata. Theoret. Comput. Sci. 666, 21\u201335 (2017). https:\/\/doi.org\/10.1016\/j.tcs.2016.11.002","journal-title":"Theoret. Comput. Sci."}],"container-title":["Emergence, Complexity and Computation","Advances in Cellular Automata"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-78757-7_14","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,26]],"date-time":"2025-04-26T07:59:52Z","timestamp":1745654392000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-78757-7_14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783031787560","9783031787577"],"references-count":70,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-78757-7_14","relation":{},"ISSN":["2194-7287","2194-7295"],"issn-type":[{"type":"print","value":"2194-7287"},{"type":"electronic","value":"2194-7295"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"27 April 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}