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The slime mould Physarum polycephalum has been used in developing unconventional computing devices for in which the slime mould played a role of a sensing, actuating, and computing device. These devices treated the slime mould rather as an active living substrate yet the slime mould is a self-consistent living creature which evolved for millions of years and occupied most part of the world, but in any case, that living entity did not own true cognition, just automated biochemical mechanisms. To "rehabilitate" the slime mould from the rank of a purely living electronics element to a "creature of thoughts" we are analyzing the cognitive potential of P. polycephalum. We base our theory of minimal cognition of the slime mould on a bottom-up approach, from the biological and biophysical nature of the slime mould and its regulatory systems using frameworks suh as Lyon's biogenic cognition, Muller, di Primio-Lengeler\'s modifiable pathways, Bateson's "patterns that connect" framework, Maturana's autopoetic network, or proto-consciousness and Morgan's Canon.

We discuss possible designs and prototypes of computing systems that could be based on morphological development of roots, interaction of roots, and analog electrical computation with plants, and plant-derived electronic components. In morphological plant processors data are represented by initial configuration of roots and configurations of sources of attractants and repellents; results of computation are represented by topology of the roots' network. Computation is implemented by the roots following gradients of attractants and repellents, as well as interacting with each other. Problems solvable by plant roots, in principle, include shortest-path, minimum spanning tree, Voronoi diagram, $\alpha$-shapes, convex subdivision of concave polygons. Electrical properties of plants can be modified by loading the plants with functional nanoparticles or coating parts of plants of conductive polymers. Thus, we are in position to make living variable resistors, capacitors, operational amplifiers, multipliers, potentiometers and fixed-function generators. The electrically modified plants can implement summation, integration with respect to time, inversion, multiplication, exponentiation, logarithm, division. Mathematical and engineering problems to be solved can be represented in plant root networks of resistive or reaction elements. Developments in plant-based computing architectures will trigger emergence of a unique community of biologists, electronic engineering and computer scientists working together to produce living electronic devices which future green computers will be made of., Comment: The chapter will be published in "Inspired by Nature. Computing inspired by physics, chemistry and biology. Essays presented to Julian Miller on the occasion of his 60th birthday", Editors: Susan Stepney and Andrew Adamatzky (Springer, 2017)

Theoretical constructs of logical gates implemented with plant roots are morphological computing asynchronous devices. Values of Boolean variables are represented by plant roots. A presence of a plant root at a given site symbolises the logical {\sc True}, an absence the logical {\sc False}. Logical functions are calculated via interaction between roots. Two types of two-inputs-two-outputs gates are proposed: a gate $\langle x, y \rangle \rightarrow \langle xy, x+y \rangle$ where root apexes are guided by gravity and a gate $\langle x, y \rangle \rightarrow \langle \overline{x}y, x \rangle$ where root apexes are guided by humidity. We propose a design of binary half-adder based on the gates.