The B-book: assigning programs to meanings
The B-book: assigning programs to meanings
Compositional refinement of interactive systems
Journal of the ACM (JACM)
Guarded commands, nondeterminacy and formal derivation of programs
Communications of the ACM
Compositional Refinement of Interactive Systems Modelled by Relations
COMPOS'97 Revised Lectures from the International Symposium on Compositionality: The Significant Difference
An Extended Duration Calculus for Hybrid Real-Time Systems
Hybrid Systems
Towards Industrially Applicable Formal Methods: Three Small Steps, and One Giant Leap
ICFEM '98 Proceedings of the Second IEEE International Conference on Formal Engineering Methods
Three perspectives in formal engineering
ICFEM'06 Proceedings of the 8th international conference on Formal Methods and Software Engineering
Control law diagrams in circus
FM'05 Proceedings of the 2005 international conference on Formal Methods
Proving properties of stateflow models using ISO standard z and CADiZ
ZB'05 Proceedings of the 4th international conference on Formal Specification and Development in Z and B
| Hi-index | 0.00 |
Embedded continuous control systems can be thought of as implementing complex (piecewise and pipelined) differential functions. Each 'piece' of the function may be preconditioned with a 'domain of applicability', which prescribes the circumstances the piece was designed to handle. The preconditions often involve rate of change, i.e. differentials, as well as range constraints. In this paper we present an adaptation of the substitution calculus which can be used to reason about such systems. Our approach is based on generalising the traditional view that a component is a fragment of a sequential programme. We consider a component to be an autonomous transformation which is 'clocked' to perform its computation at regular intervals, over and over again. In the case of such a component we can generalise the notion of weakest precondition to traces (sequences of values) of inputs and outputs. In our approach we characterise such traces by 'step' predicates over adjacent elements in the trace. We also generalise our calculus to cover nth order differentials. Since analysis can be performed at a comparable complexity to regular wp, our techniques are a powerful tool in the validation of continuous control systems.