Abstract
The topic of computational universality and efficiency of various types of abstract machines is still subject of intensive research. Besides many crucial open theoretical problems, there are also numerous potential applications, e.g., in construction of small physical computing machines (nano-automata), harnessing algorithmic processes in biology or biochemistry, efficient solving of computationally hard problems and many more. The study of computability and complexity of new abstract models can help to understand the borderline between non-universality and universality, or between tractable and intractable problems.
Here we study computational universality (in Turing sense) and computational complexity in the framework of morphogenetic (M) systems—computational models combining properties of membrane systems and algorithmic self-assembly of pre-defined atomic polytopes. Even very simple morphogenetic systems can exhibit complex self-organizing behaviour and phenomena such as controlled growth, self-reproduction, homeostasis and self-healing. We present two small universal M systems, one of which is additionally self-healing. Then we show how the borderline P versus NP can be characterized by some properties of morphogenetic systems.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Alhazov, A., Verlan, S.: Minimization strategies for maximally parallel multiset rewriting systems. Theor. Comput. Sci. 412(17), 1581–1591 (2011)
Altisen, K., Devismes, S., Dubois, S., Petit, F.: Introduction to distributed self-stabilizing algorithms. Synth. Lect. Distrib. Comput. Theory 8(1), 1–165 (2019)
Einstein, A.: Über die von der molekularkinetischen theorie der wärme geforderte bewegung von in ruhenden flüssigkeiten suspendierten teilchen. Ann. Phys. 322(8), 549–560 (1905)
Krasnogor, N., Gustafson, S., Pelta, D., Verdegay, J.: Systems Self-Assembly: Multidisciplinary Snapshots. Studies in Multidisciplinarity. Elsevier Science (2011)
Mange, D., Madon, D., Stauffer, A., Tempesti, G.: Von Neumann revisited: a Turing machine with self-repair and self-reproduction properties. Robot. Auton. Syst. 22(1), 35–58 (1997)
von Neumann, J.: Probabilistic logics and the synthesis of reliable organisms from unreliable components. Ann. Math. Stud. 34, 43–98 (1956)
Păun, A., Popa, B.: P systems with proteins on membranes. Fund. Inform. 72(4), 467–483 (2006)
Păun, A., Popa, B.: P systems with proteins on membranes and membrane division. In: Ibarra, O.H., Dang, Z. (eds.) DLT 2006. LNCS, vol. 4036, pp. 292–303. Springer, Heidelberg (2006). https://doi.org/10.1007/11779148_27
Păun, G., Rozenberg, G., Salomaa, A. (eds.): The Oxford Handbook of Membrane Computing. Oxford University Press, Oxford (2010)
Qang, H.: Proving theorems by pattern recognition - II. Bell Syst. Tech. J. 40(1), 1–41 (1961)
Rogozhin, Y.: Small universal Turing machines. Theor. Comput. Sci. 168(2), 215–240 (1996)
Smolka, V., Drastík, J., Bradík, J., Garzon, M., Sosík, P.: Morphogenetic systems: models and experiments. Biosystems 198, Article no. 104270 (2020). https://doi.org/10.1016/j.biosystems.2020.104270
Sosík, P.: Morphogenetic computing: computability and complexity results. Nat. Comput. (2022, submitted)
Sosík, P., Drastík, J., Smolka, V., Garzon, M.: From P systems to morphogenetic systems: an overview and open problems. J. Membrane Comput. 2(4), 380–391 (2020). https://doi.org/10.1007/s41965-020-00057-9
Sosík, P., Garzon, M., Drastík, J.: Turing-universal self-healing computations in morphogenetic systems. Nat. Comput. 20, 739–750 (2021)
Sosík, P., Garzon, M., Smolka, V., Drastík, J.: Morphogenetic systems for resource bounded computation and modeling. Inf. Sci. 547, 814–827 (2021)
Sosík, P., Smolka, V., Drastík, J., Bradík, J., Garzon, M.: On the robust power of morphogenetic systems for time bounded computation. In: Gheorghe, M., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) CMC 2017. LNCS, vol. 10725, pp. 270–292. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-73359-3_18
Sosík, P., Smolka, V., Drastík, J., Moore, T., Garzon, M.: Morphogenetic and homeostatic self-assembled systems. In: Patitz, M.J., Stannett, M. (eds.) UCNC 2017. LNCS, vol. 10240, pp. 144–159. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-58187-3_11
Turing, A.: The chemical basis of morphogenesis. Philos. Trans. R. Soc. Lond. B 237, 7–72 (1950)
van Emde Boas, P.: Machine models and simulations. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. A: Algorithms and Complexity, pp. 1–66. Elsevier, Amsterdam (1990)
Winfree, E.: Self-healing tile sets. In: Chen, J., Jonoska, N., Rozenberg, G. (eds.) Nanotechnology: Science and Computation. Natural Computing Series, pp. 55–66. Springer, Cham (2006). https://doi.org/10.1007/3-540-30296-4_4
Ziegler, G.: Lectures on Polytopes. Graduate Texts in Mathematics, Springer, New York (1995)
Acknowledgments
This work was supported by the Silesian University in Opava under the Student Funding Scheme, project SGS/8/2022.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Sosík, P., Drastík, J. (2022). Computational Universality and Efficiency in Morphogenetic Systems. In: Durand-Lose, J., Vaszil, G. (eds) Machines, Computations, and Universality. MCU 2022. Lecture Notes in Computer Science, vol 13419. Springer, Cham. https://doi.org/10.1007/978-3-031-13502-6_11
Download citation
DOI: https://doi.org/10.1007/978-3-031-13502-6_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-13501-9
Online ISBN: 978-3-031-13502-6
eBook Packages: Computer ScienceComputer Science (R0)