Decision Procedures for Several Properties of Reactive System Specifications

Reactive systems, such as operating systems or elevator control systems, are systems that ideally never terminate and are intended to maintain some interaction with their environment. Temporal logic is one of the methods for formal specification descriptions of reactive systems. By describing the formal specifications of reactive systems we can check the consistency of the specifications and whether they contain defects. By using a synthesis algorithm we also obtain reactive system programs from the formal specifications and prevent programming bugs. Therefore, it is important to describe reactive system formal specifications to secure reactive system programs. However, it is difficult to describe realizable reactive system specifications and it is important to revise unrealizable reactive system specifications into realizable reactive system specifications. In previous research, three properties have been introduced into unrealizable reactive system specifications. By using these properties, we can acquire more detailed information about the cause of the defects of unrealizable reactive system specifications in the specification description process. In this paper, we propose decision procedures that judge whether a reactive system specification has these properties. We also prove the soundness and completeness of these procedures.

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