Abstract. Many safety-critical software applications are hard real-time systems. They have stringent timing requirements that have to be met. We present a description of timing behaviour that includes precise definitions as well as analysis of how functional timing requirements interact with performance timing requirements, and how these concepts can be used by software designers. The definitions and analysis presented explicitly deal with tolerances in all timing durations. Preliminary work indicates that some requirements may be met at significantly reduced CPU bandwidth through reduced variation in cycle time.

Abstract. While there has been a large amount of work on validation of timing requirements, there has been relatively little work on the implementability of timing requirements. We have previously provided definitions of fundamental timing operators that explicitly considered tolerances on property durations and intersample jitter [1]. In this work we refine the model and formalize the analysis of the Held for operator of [1] in the PVS theorem prover. We formalize different implementation environments incorporating nonuniform samples with bounded jitter and for one of the environments provide a full formal proof of necessary and sufficient conditions for when it is possible to implement a Held for requirement. We briefly describe how these results can then be used to formally verify a sample module implementing a requirement that utilizes the Held for operator and describe an example application.