A faster P solution for the byzantine agreement problem

Abstract

We propose an improved generic version of P modules, an extensible framework for recursive composition of P systems. We further provide a revised P solution for the Byzantine agreement problem, based on Exponential Information Gathering (EIG) trees, for N processes connected in a complete graph. Each process is modelled by the combination of N∈+∈1 modules: one "main" module, plus one "firewall" communication module for each process (including one for itself). The EIG tree evaluation functionality is localized into a "main" single cell P module. The messaging functionality is localized into a three cells communication P module. This revised P solution improves overall running time from 9L∈+∈6 to 6L∈+∈1, where L is the number of messaging rounds. Most of the running time, 5L steps, is spent on the communication overhead. We briefly discuss if single cells can solve the Byzantine agreement without support and protection from additional communication cells; we conjecture that this is not possible, within the currently accepted definitions. © 2010 Springer-Verlag.