[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Log in

Morphogenetic computing: computability and complexity results

  • Published:
Natural Computing Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Alhazov A, Verlan S (2011) Minimization strategies for maximally parallel multiset rewriting systems. Theor Comput Sci 412(17):1581–1591

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Article  Google Scholar 

  • Păun A, Popa B (2006) P systems with proteins on membranes. Fundamenta Informaticae 72(4):467–483

    MathSciNet  MATH  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • Rogozhin Y (1996) Small universal turing machines. Theor Comput Sci 168(2):215–240

    Article  MathSciNet  MATH  Google Scholar 

  • Smith A (2020) Universality of wolfram’s 2,3 turing machine. Complex Syst 29(1):1–44

    Article  MATH  Google Scholar 

  • 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

    Article  MathSciNet  MATH  Google Scholar 

  • Sosík P, Garzon M, Drastík J (2021) Turing-universal self-healing computations in morphogenetic systems. Natural Comput 20:739–750

    Article  MathSciNet  Google Scholar 

  • Sosík P, Garzon M, Smolka V, Drastík J (2021) Morphogenetic systems for resource bounded computation and modeling. Inform Sci 547:814–827

    Article  MathSciNet  MATH  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • von Neumann J (1956) Probabilistic logics and the synthesis of reliable organisms from unreliable components. Ann Math Stud 34:43–98

    MathSciNet  Google Scholar 

  • 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

    Chapter  Google Scholar 

  • Ziegler G (1995) Lectures on polytopes. Graduate texts in mathematics. Springer, New York

    Book  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the Silesian University in Opava under the Student Funding Scheme, project SGS/8/2022.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Petr Sosík.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sosík, P. Morphogenetic computing: computability and complexity results. Nat Comput 22, 161–170 (2023). https://doi.org/10.1007/s11047-022-09899-x

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11047-022-09899-x

Keywords

Navigation