Theory of Symmetry and Fault-Tolerance

Abstract

Abstract The goal of this work is investigation of system fault-tolerance, in particular, distributed and multiprocessor ones representable as planar or space graphs or figures. The research is based on the fundamental results of the theory of symmetry that can be precisely expressed in terms of the group invariance analysis. Fault- tolerance is shown to be closely related to the possibility of system representation as a graph or a spactial figure that possesses some mathematical symmetry. This approach allows one to obtain a complete fault-tolerance description arbitrary architecture system as well as to design FT minimal redundancy systems. The paper is focused on homogeneous systems since they lend themselves more naturally to fault-tolerant design. It is shown which heterogeneous structures can be made FT. New in the investigation, apart from the approach itself, are the enumeration of possible structures that can be made FT with minimum redundancy, and the proof of the fact that there are no other structures with the same properties.