Abstract
We propose two unconventional arithmetic circuits: adder and subtracter defined on finite p-adic integers. These circuits are theoretically implemented on the plasmodium of Physarum polycephalum. Adder and subtracter are designed by means of spatial configurations of several attractants and repellents which are stimuli for the plasmodium behaviour. As a result, the plasmodium could form a network of protoplasmic veins connecting attractants and original points of the plasmodium. Occupying new attractants is considered in the way of adders and leaving some attractants because of repelling is considered in the way of subtracters. On the basis of p-adic adders and subtracters we can design complex p-adic valued arithmetic circuits within a p-adic valued logic proposed by us.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Adamatzky, A.: Physarum Machines: Computers from Slime Mould. World Scientific (2010)
Adamatzky, A., Erokhin, V., Grube, M., Schubert, T., Schumann, A.: Physarum chip project: growing computers from slime mould. Int. J. Unconventional Comput. 8(4), 319–323 (2012)
Agerwala, T., Flynn, M.: Comments on capabilities, limitations and ’correctness’ of Petri nets. In: Proceedings of the 1st Annual Symposium on Computer Architecture (ISCA’1973), pp. 81–86. Atlanta, USA (1973)
Baaz, M., Fermüller, C., Zach, R.: Systematic construction of natural deduction systems for many-valued logics. In: Proceedings of the 23rd International Symposium on Multiple Valued Logic, pp. 208–213. Sacramento, USA (1993)
Craig, I.: Object-Oriented Programming Languages: Interpretation. Springer, London (2007)
Henzinger, T.A., Manna, Z., Pnueli, A.: Timed transition systems. In: de Bakker, J., Huizing, C., de Roever, W., Rozenberg, G. (eds.) Real-Time: Theory in Practice. Lecture Notes in Computer Science, vol. 600, pp. 226–251. Springer, Berlin (1992)
Pancerz, K., Schumann, A.: Principles of an object-oriented programming language for Physarum polycephalum computing. In: Proceedings of the 10th International Conference on Digital Technologies (DT’2014), pp. 273–280. Zilina, Slovak Republic (2014)
Petri, C.A.: Kommunikation mit automaten. Schriften des IIM nr. 2, Institut für Instrumentelle Mathematik, Bonn (1962)
Schumann, A.: Non-archimedean fuzzy and probability logic. J. Appl. Non-Classical Logics 18(1), 29–48 (2008)
Schumann, A.: Non-archimedean valued extension of logic \(l\pi \) and p-adic valued extension of logic \(bl\). J. Uncertain Syst. 4(2), 99–115 (2010)
Schumann, A., Pancerz, K.: Towards an object-oriented programming language for Physarum polycephalum computing. In: Szczuka, M., Czaja, L., Kacprzak, M. (eds.) Proceedings of the Workshop on Concurrency, Specification and Programming (CS&P’2013), pp. 389–397. Warsaw, Poland (2013)
Schumann, A., Pancerz, K.: Timed transition system models for programming Physarum machines: extended abstract. In: Popova-Zeugmann, L. (ed.) Proceedings of the Workshop on Concurrency, Specification and Programming (CS&P’2014), pp. 180–183. Chemnitz, Germany (2014)
Schumann, A., Pancerz, K.: Towards an object-oriented programming language for Physarum polycephalum computing: a Petri net model approach. Fundamenta Informaticae 133(2–3), 271–285 (2014)
Schumann, A., Pancerz, K.: PhysarumSoft - a software tool for programming Physarum machines and simulating physarum games. In: Proceedings of the Federated Conference on Computer Science and Information Systems (FedCSIS’2015). Lodz, Poland (2015)
Verbeek, H., Wynn, M., van der Aalst, W., ter Hofstede, A.: Reduction rules for reset/inhibitor nets. J. Comput. Syst. Sci. 76(2), 125–143 (2010)
Acknowledgments
This research is being fulfilled by the support of FP7-ICT-2011-8.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Schumann, A., Pancerz, K. (2016). p-Adic Computation with Physarum. In: Adamatzky, A. (eds) Advances in Physarum Machines. Emergence, Complexity and Computation, vol 21. Springer, Cham. https://doi.org/10.1007/978-3-319-26662-6_29
Download citation
DOI: https://doi.org/10.1007/978-3-319-26662-6_29
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-26661-9
Online ISBN: 978-3-319-26662-6
eBook Packages: EngineeringEngineering (R0)