Deriving Real-Time Action Systems Controllers from Multiscale System Specifications

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

“…This paper adds to our series of papers on program derivation [16,17,19,20,24,25]. Of these, [16,24,25] consider concurrent program derivation and [17,19,20] consider real-time programs.…”

“…The derivation method builds on our method of enforced properties [15,16,17,19], which uses the verify-while-develop paradigm to incrementally obtain program code from the underlying specifications. Our framework incorporates a logic of time bands [9,10,49], which allows one to formalise properties at different time granularities and define relationships between these properties.…”

“…On the other hand, consideration of fine-grained interactions results in an increase in the complexity of the reasoning. In this paper, we use a high-level logic that allows one to describe the observable states that may occur when sampling variables at finer time-bands [10,19,21,30].…”

“…However, in the context of real-time reactive systems, this model turns out to be problematic because for example it is unable to properly address transient properties [19,20]. Such properties only hold for a brief amount of time, say an attosecond, and hence, a real-world implementation would never be able to reliably detect the property.…”

“…Instead, an implementation should be allowed to ignore transient properties because they cannot be reliably detected. In this paper, like [19,20], we modify the semantics so that an action system executes with its environment in a truly concurrent manner. This allows one to develop a theoretical model that properly addresses transient properties -an implementation is only required to handle non-transient properties.…”