Through study of the termination of rule set corresponding to cyclic triggering graph and analysis of triggering graph and activation graph, we present the concept of united formula and thereby the algorithm to determine termination of rule set corresponding to cyclic triggering graph.

By a study of the basic triggering graph analysis method, depending on the behavior characteristic of active rule, a rule termination analysis method combining triggering graph with activation graph is concluded, and introduced to the active object oriented database system AO2DB for active rule termination analysis.

According to the transformation principle between triggers and the intuitive of Karnaugh map,a new method to achieve transformation between triggers by comparing the existing trigger\'s Karnaugh map with the target trigger\'s Karnaugh map is put forward,and it is used in the conversion from JK trigger to other triggers.

For the exist content-based Publish/Subscribe(P/S) systems,general peer-to-peer topology can not support subscription covering,on the base of absorbing their design ideas,with reverse path forwarding technique and dynamic receiver update and partition strategy,a new route algorithm for content-based P/S system which supports general cyclic topology and subscription covering is proposed.

In order to improve the efficiency of the algorithm for generating directed cutsets of directed cycling graph, directed cycling graph is converted to directed acyclic graph with contracted vertices by contracting edge of rings in directed cycling graph, and the algorithm for generating directed cutsets of directed acyclic graph is made to generate directed cutsets of directed cycling graph.