Networks of polarized evolutionary processors

•Definition of a new version of networks of evolutionary processors.•A uniform and linear time solution to the “3-colorability problem”.•A non-uniform, linear size and time solution to the “Common Algorithmic Problem” which can be easily extended to a uniform solution.

In this paper, we consider a new variant of networks of evolutionary processors which seems to be more suitable for a software and hardware implementation. Each processor as well as the data navigating throughout the network are now considered to be polarized. While the polarization of every processor is predefined, the data polarization is dynamically computed by means of a valuation mapping. Consequently, the protocol of communication is naturally defined by means of this polarization. This new variant is investigated here as a problem solver. We propose solutions based on networks of polarized evolutionary processors to two computationally hard problems, namely the “3-colorability problem”, and a more general one known as the “Common Algorithmic Problem”. Our solutions are uniform (they work for all instances of the same size) and time efficient (they work in linear time).