p-adic valued logical calculi in simulations of the slime mould behaviour

摘要

In this paper we consider possibilities for applying p-adic valued logic BL to the task of designing an unconventional computer based on the medium of slime mould (order Physarales, class Myxomecetes, subclass Myxogastromycetidae), the giant amoebozoa that looks for attractants and reaches them by means of propagating complex networks. If it is assumed that at any time step t of propagation the slime mould can discover and reach not more than p - 1 attractants, then this behaviour can be coded in terms of p-adic numbers. As a result, this behaviour implements some p-adic valued arithmetic circuits and can verify p-adic valued logical propositions.