Large Discrete Systems Research Articles

Accelerated Spectral Refinement with Applications to Integral Operators

Accelerated refinement procedures are developed for the resolution of nearly degenerate simple spectra associated with large discrete linear systems. Error expressions are obtained. The spectral analysis of integral operators is discussed and a numerical example of resolving an ill-conditioned spectrum is presented.

On a method of computing evolving discrete systems

The main concepts of a new method for modelling numerically the evolution of large discrete systems with interacting elements are analyzed. The typical properties of the corrected sets used in the method are considered. It is shown that the use of this method for computer-evaluating a specific class of processes (collision, coagulation or division processes etc.) leads to a reduction of computer time as compared with traditional methods. The reduction is proportional to the number of elements of the evolving system. Numerical experiments confirm the high efficiency of the method.

Tools For Verification Of A Large Discrete System

Tools for modeling and verification of discrete event systems are implemented in Mathematica. The tools are based on binary decision diagrams (BDD) for which a Mathematica interface is provided. For modeling a compiler is developed translating a restricted class of Pascal into boolean expressions represented by BDDs. The tools are used in an application of a landing gear system of a fighter aircraft. This system is controlled by a software consisting of 1200 lines of Pascal. This code represented as a BDD is then analyzed using temporal logics. This article demonstrates the principle of the Pascal compiler.