Deriving real-time action systems with multiple time bands using algebraic reasoning

The verify-while-develop paradigm allows one to incrementally develop programs from their specifications using a series of calculations against the remaining proof obligations. This paper presents a derivation method for real-time systems with realistic constraints on their behaviour. We develop a high-level interval-based logic that provides flexibility in an implementation, yet allows algebraic reasoning over multiple granularities and sampling multiple sensors with delay. The semantics of an action system is given in terms of interval predicates and algebraic operators to unify the logics for an action system and its properties, which in turn simplifies the calculations and derivations

Reasoning about real-time teleo-reactive programs

The teleo-reactive programming model is a high-level approach to implementing real-time control programs that react dynamically to changes in their environment. Teleo-reactive programs are particularly useful for implementing controllers in autonomous agents. In this paper we present formal techniques for reasoning about robust teleo-reactive programs.We develop a temporal logic over continuous intervals, which we use to formalise the semantics of teleo-reactive programs. To facilitate compositional reasoning about a program and its environment, we use rely/guarantee style specications. We also present several theorems for simplifying proofs of teleo-reactive programs that control goal-directed agents

Reasoning about teleo-reactive programs under parallel composition

The teleo-reactive programming model is a high-level approach to implementing real-time controllers that react dynamically to changes in their environment. Teleo-reactive actions can be hierarchically nested, which facilitates abstraction from lower-level details. Furthermore, teleo-reactive programs can be composed using renaming, hiding, and parallelism to form new programs. In this paper, we present a framework for reasoning about safety, progress, and real-time properties of teleo-reactive programs under program composition. We use a logic that extends the duration calculus to formalise the semantics of teleo-reactive programs and to reason about their properties. We present rely/guarantee style specifications to allow compositional proofs and we consider an application of our theory by verifying a real-time controller for an industrial press

Continuous action system refinement

Action systems are a framework for reasoning about discrete reactive systems. Back, Petre and Porres have extended these action systems to continuous action systems, which can be. used to model hybrid systems. In this paper we define a refinement relation, and develop practical data refinement rules for continuous action systems. The meaning of continuous action systems is expressed in terms of a mapping from continuous action systems to action systems. First, we present a new mapping from continuous act ion systems to action systems, such that Back's definition of trace refinement is correct with respect to it. Second, we present a stream semantics that is compatible with the trace semantics, but is preferable to it because it is more general. Although action system trace refinement rules are applicable to continuous action systems with a stream semantics, they are not complete. Finally, we introduce a new data refinement rule that is valid with respect to the stream semantics and can be used to prove refinements that are not possible in the trace semantics, and we analyse the completeness of our new rule in conjunction with the existing trace refinement rules