This paper gives some properties of companion matrix of polynomial over finite field with its application for evaluating period of linear shift register sequence and minimal length of cyclic code.

Then this thesis presents a new approach to solve top event occurrence rate and a new generation algorithm of minimal cut sequence of dynamic fault tree that deviate from Markov model completely.

The optimization of query sentences is to select operation sequence with minimal costs in terms of given query so as to make query a time-saving and space-saving process.