Compositional Action System Derivation Using Enforced Properties

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

“…We say a state predicate is transient in a stream if the predicate only holds for a brief (e.g., an attosecond) amount of time, whereby it is not possible to reliably detect that the predicate held [17,20].…”

“…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.…”

“…To model the behaviour of a program in an environment one may include actions corresponding to the program and its environment within a single action system [7,17] so that the actions corresponding to the controller and its environment are interleaved with each other. 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].…”

“…Of these, [16,24,25] consider concurrent program derivation and [17,19,20] consider real-time programs. Our papers [17,19,20] increasingly consider more realistic assumptions in concurrent real-time systems and the most advanced of these [19] allows one to consider sampling issues and components that operate over multiple time granularities. However, the framework itself has become increasingly complex and becomes a bottleneck to achieving scalable derivations because program properties are expressed in an interval-based LTL-style [40] logic, whereas the requirements are expressed using interval predicates.…”