Triggering Graph Research Articles

Active rules termination analysis based on activation path and enhanced formula

While active rules have been applied in many areas including active databases, XML document and Semantic Web, current methods remain largely uncertain of how to detect the termination when analysing rules behaviours. Some methods are based on a logical formula for a rule set, but only those non-updatable or finitely updatable variables can be contained by a formula. Some other methods are based on triggering and activation graphs, but they do not consider whether all rules of a triggering cycle can be infinitely executed during a single cyclic execution. Most methods cannot conclude termination if a rule set contains only those cycles that can be executed for a finite number of times. This paper presents the concepts of activation path and the execution sequence of a triggering cycle as well as the method to construct a formula that is able to include updatable variables, and then many termination cases that cannot be determined by previous methods, can now be detected.

Design and development of algorithms for identifying termination of triggers in active databases

An active database system is a conventional database system extended with a facility for managing triggers (or active rules). Active database systems can react to the occurrence of some predefined events automatically. In many applications, active rules may interact in complex and sometimes unpredictable ways, thus possibly yielding infinite rule executions by triggering each other indefinitely causing non-termination. Almost all of the work to date on termination analysis for active databases relies on checking that a directed graph called the |triggering graph| for a set of rules is acyclic. This paper presents new algorithms for detecting termination/non-termination of rule execution using triggering graph. These algorithms detect termination/non-termination among the rules in a triggering graph without any limitation on the number of rules.

Analyzing Triggers in XML Data Integration Systems

Nowadays XML-based data integration systems are accepted as data service providers on the web. Currently the user is permitted to submit updates. Therefore it is necessary to establish the best possible data consistency in the whole data integration system. To that extend, we present an approach based on an XQuery trigger service. In the XQuery trigger service trigger termination should be ensured. The trigger analyzing problem is mainly discussed in this paper. We first define the three categories of trigger dependence including total independence, possible dependence and definite dependence. According to the three categories there are tolerant termination and absolute termination. Triggering graph is used to carry on the real analysis. DAG algorithm is used to find the cycle in the triggering graph. The implementation shows that the XQuery triggers are ensured to be terminated according to different levels.

Active Rule Termination Analysis: An Implementation and Evaluation of the Refined Triggering Graph Method

This paper describes the implementation of the Refined Triggering Graph (RTG) method for active rule termination analysis and provides an evaluation of the approach based on the application of the method to a sample active application. The RTG method has been defined in the context of an active-deductive, object-oriented database language known as CDOL (Comprehensive, Declarative, Object Language). The RTG method studies the contents of rule pairs and rule cycles in a triggering graph and tests for: (1) the successful unification of one rule‘s action with another rule‘s triggering event, and (2) the satisfiability of active rule conditions, asking whether it is possible for the condition of a triggered rule to evaluate to true in the context of the triggering rule‘s condition. If the analysis can provably demonstrate that one rule cannot trigger another rule, the directed vector connecting the two rules in a basic triggering graph can be removed, thus refining the triggering graph. An important aspect in the implementation of the method is the development of a satisfiability algorithm for CDOL conditions. This paper presents the tool that was developed based on the RTG method, describing how techniques from constraint logic programming are integrated with other techniques for testing the satisfiability of rule triggering conditions. The effectiveness of the approach within the context of a sample application is also addressed.