Abstract
A morphogenetic (M) system is an abstract computational model combining properties of membrane (P) systems, such as computing via abstract particles in separate compartments regulating their workflow, with algorithmic self-assembly generalizing original Wang tiles to arbitrary polytopes forming complex shapes in 2D/3D (or generally, dD) space. Even very simple morphogenetic systems can exhibit complex self-organizing behaviour and, at the abstract level, one can observe characteristic properties of morphogenetic phenomena such as controlled growth, self-reproduction, homeostasis and self-healing. Here we focus on computational aspects of the morphogenetic systems. After summarizing a series of results related to their computational universality (in the Turing sense) and computational complexity, we present two small universal M systems (one of them self-healing) and we also demonstrate how morphogenetic systems relate to the classes P and NP.
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Alhazov A, Verlan S (2011) Minimization strategies for maximally parallel multiset rewriting systems. Theor Comput Sci 412(17):1581–1591
Einstein A (1905) Über die von der molekularkinetischen theorie der wärme geforderte bewegung von in ruhenden flüssigkeiten suspendierten teilchen. Annalen der Physik 322(8):549–560
Freund R, Kari L, Oswald M, Sosík P (2005) Computationally universal P systems without priorities: two catalysts are sufficient. Theor Comput Sci 330:251–266
Krasnogor N, Gustafson S, Pelta D, Verdegay J (2011) Systems self-assembly: multidisciplinary snapshots. Studies in Multidisciplinarity, Elsevier Science
Mange D, Madon D, Stauffer A, Tempesti G (1997) Von Neumann revisited: A turing machine with self-repair and self-reproduction properties. Robot Autonomous Syst 22(1):35–58
Păun A, Popa B (2006) P systems with proteins on membranes. Fundamenta Informaticae 72(4):467–483
Păun A, Popa B (2006) P systems with proteins on membranes and membrane division. In: Ibarra O, Dang Z (eds) DLT 2006, vol 4036. Lecture notes in computer science. Springer, Berlin, pp 292–303
Păun G, Rozenberg G, Salomaa A (eds) (2010) The oxford handbook of membrane computing. Oxford University Press, Oxford
Qang H (1961) Proving theorems by pattern recognition-ii. Bell Syst Tech J 40(1):1–41
Rogozhin Y (1996) Small universal turing machines. Theor Comput Sci 168(2):215–240
Smith A (2020) Universality of wolfram’s 2,3 turing machine. Complex Syst 29(1):1–44
Smolka V, Drastík J, Bradík J, Garzon M, Sosík P (2020) Morphogenetic systems: Models and experiments. Biosystems 198, art. no. 104270
Sosík P, Drastík J, Smolka V, Garzon M (2020) From P systems to morphogenetic systems: an overview and open problems. J Membr Comput 2(4):380–391
Sosík P, Garzon M, Drastík J (2021) Turing-universal self-healing computations in morphogenetic systems. Natural Comput 20:739–750
Sosík P, Garzon M, Smolka V, Drastík J (2021) Morphogenetic systems for resource bounded computation and modeling. Inform Sci 547:814–827
Sosík P, Smolka V, Drastík J, Bradík J, Garzon M (2018) On the robust power of morphogenetic systems for time bounded computation. In: Gheorghe M (ed) Membrane Computing, 18th International Conference, CMC18, vol 10725. Lecture Notes in Computer Science. Springer, Berlin, pp 270–292
Sosík P, Smolka V, Drastík J, Moore T, Garzon M (2017) Morphogenetic and homeostatic self-assembled systems. In: Patitz, M.J., Stannett, M. (eds.) Unconventional Computation and Natural Computation: 16th International Conference, UCNC 2017. Lecture Notes in Computer Science, vol. 10240, pp. 144–159. Springer, Berlin
Turing A (1950) The chemical basis of morphogenesis. Philos Trans R Soc Lond B 237:7–72
van Emde Boas P (1990) Machine models and simulations. In: van Leeuwen J (ed) Handbook of theoretical computer science. Algorithms and complexity. Elsevier, AmsterdamAmsterdamAmsterdam, pp 1–66
von Neumann J (1956) Probabilistic logics and the synthesis of reliable organisms from unreliable components. Ann Math Stud 34:43–98
Winfree E (2006) Self-healing tile sets. In: Chen J, Jonoska N, Rozenberg G (eds) Nanotechnology: science and computation. Natural computing series. Springer, New York, pp 55–66
Ziegler G (1995) Lectures on polytopes. Graduate texts in mathematics. Springer, New York
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This work was supported by the Silesian University in Opava under the Student Funding Scheme, project SGS/8/2022.
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Sosík, P. Morphogenetic computing: computability and complexity results. Nat Comput 22, 161–170 (2023). https://doi.org/10.1007/s11047-022-09899-x
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DOI: https://doi.org/10.1007/s11047-022-09899-x