Determinacy problem in relaxation method‐analysis of asynchronous parallel processing

Abstract

In image pattern understanding, global and unspecific processing are required. Thus it is important to develop an asynchronous processing algorithm with high efficiency and MIMD type. This paper formulates and analyzes the determinacy problem on the newly introduced transformation model, as a basic theory for the asynchronous parallel processing algorithm for the pattern information processing. The major results are as follows: (i) a transformation model is introduced which can describe and analyze the mathematically parallel processing algorithm, into the content of the processing; (ii) the determinacy problem is formulated, arriving at a convergence theorem representing a sufficient condition; (iii) a discussion is made from the viewpoint of the determinacy problem on the possibility of asynchronous parallel processing of the relaxation method, which is already applied to the image processing. It is concluded that the asynchronous parallel processing is possible in the discrete and fuzzy relaxations, but is impossible in the linear and nonlinear stochastic relaxations.

The performance of asynchronous algorithms on hypercubes

“…There are some alternate models, which we mention here. The first is the transition model [8], which is based on the idea of flow descriptions in software design [14]. This formalism has resulted in at least one convergence theorem.…”