Araki Keijiro

On All Sets of Optimal Controls for a Control System with State Feedback

We claim the sets of controls for control systems modeled with a multiple and simultaneous control (MSC) approach using controlled Dan/Petri nets, and the net structure Sigmac(q) is the optimal set compared with controlled Petri nets, however there are other control sets which are still optimal. In this paper we present an algorithm to find all sets of controls which are optimal, posses the MSC-logic and are modeled with a new net structure called Sigmaxf(q), explain the conditions when they are not optimal and a partial order for such sets.

Validation of stepwise refinement with test cases generated from formal specification

In software development, there is a problem that development cost increases by back track when bugs which are included in the phase of requirement definition are found in the after phases. As an effective method to solve the problem, we have a method with a formal specification language for requirement. A formal specification language can describe the functional requirement exactly with mathematical in and verifies the specification with tools. In formal method, we change the specification in a formal specification to executable program with stepwise refinement. At stepwise refinement step, we find bugs by proof of the specification. Herewith, we can get the program of the high level reliability. But, it is expensive to develop with proof. There is a method to verify specification with test cases generated by manpower. But, there are possibilities of including bugs in specification because of generating by manpower. We propose the method to validate stepwise refinement with lightweight method. We generate test cases from formal specification in VDM-SL before refinement, and test the specification after refinement. With this validation method, it is possible to validate of refinement focused state transition model. We implemented test case generator tool whose test case is executed with VDMUnit and VDMTools. We can confirm the availability of the validation of refinement with test case generator tool we implemented.