This dissertation proposes a formalism for the specification and verification of timing properties of real-time systems. Reasoning about properties of a real-time system requires one to consider both relative and absolute timing of events. Relative timing concerns the order in which events occur, such as mutual exclusion and precedence constraint properties. Absolute timing concerns the stringent timing restrictions imposed on a system, such as a response time deadline or a minimum elapsed time between occurrences of two events. The approach is based on Real Time Logic (RTL), a logic invented primarily for the specification of both relative and absolute timing of events. The notion of an event occurrence is central to RTL; an event occurrence marks a point in time which is of significance to the behavior of a system. Hence, concurrency is modeled as a partial ordering of the event occurrences in the system. A system specification and a property to be verified can be expressed as arithmetical relations on algebraic expressions involving the event occurrences. To verify the property with respect to the system specification, we prove that the property is a theorem derivable from the specification. Relationship of RTL to Presburger Arithmetic is discussed and a verification technique based on inequality provers is explored. The dissertation also introduces a specification language, Modechart, for real-time systems. The semantics of Modechart is described in terms of RTL formulas. In Modechart, we make use of the concept of modes which can be thought of as partitioning the state space of a system. Intuitively, modes can be viewed as control information that impose structure on the operation of a system. Modes are arranged hierarchically. Furthermore, modes at the same level of hierarchy can be related in one of two ways: in series or in parallel. A transition can be specified between two modes in series, but no transition is allowed between modes in parallel. The language allows sporadic/periodic actions in modes as well as constructs for specifying timing constraints such as delays and deadlines on mode transitions. Verification procedures are introduced for showing a Modechart specification satisfies a property expressed as an RTL formula.Computer Science
