Response property is a kind of liveness property. Response property problem is defined as follows: Given two activities α and β, whenever α is executed, is β always executed after that? In this paper, we tackled the problem in terms of Workflow Petri nets (WF-nets for short). Our results are (i) the response property problem for acyclic WF-nets is decidable, (ii) the problem is intractable for acyclic asymmetric choice (AC) WF-nets, and (iii) the problem for acyclic bridge-less well-structured WF-nets is solvable in polynomial time. We illustrated the usefulness of the procedure with an application example.

The number of states is a very important matter for model checking approach in Petri net's analysis. We first gave a formal definition of state number calculation problem: For a Petri net with an initial state (marking), how many states does it have? Next we showed the problem cannot be solved in polynomial time for a popular subclass of Petri nets, known as free choice workflow nets, if P≠NP. Then we proposed a polynomial time algorithm to solve the problem by utilizing a representational bias called as process tree. We also showed effectiveness of the algorithm through an application example.

The purpose of this research is to analyze production rules with coupling modes in active databases and to exploit an assistant system for rule programming. Each production rule is a specification including an event, a condition, and an action. The action is automatically executed whenever the event occurs and the condition is satisfied. Coupling modes are useful to control execution order of transactions. For example, a transaction for consistency check should be executed after transactions for update. An active database, which is a database with production rules, can spontaneously update database states and check their consistency. Production rules provide a powerful mechanism for knowledge-bases. However it is very difficult in general to predict how a set of production rules will behave because of cascading rule triggers, concurrency, and so on. We are attempting to adopt a process algebra as a basic tool to analyze production rules. In order to describe and analyze concurrent and communicating systems, process algebras such as CCS, CSP, ACP, and π-calculus, are well known. However there are some difficulties to apply existing process algebras to analysis of production rules in growing process trees by process creation. In this paper we propose a process algebra named CCSPR (a Calculus of Communicating Systems with Production Rules), Which is an extension of CCS. An advantage of CCSPR is to syntactically describe growing process trees. Therefore, production rules can be appropriately analyzed in CCSPR. After giving definitions and properties of CCSPR, we show an example of analysis of production rules in CCSPR.