Formal Verification of the Implementability of Timing Requirements

Abstract

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.

Formal Verification of Real-Time Function Blocks Using PVS

“…Furthermore, we have expertise built from past experience in applying PVS to check requirements and designs in the nuclear domain [8] that gave us confidence in using the toolset. For modelling real-time behaviour, we reused parts of the PVS theories from [5,4] (see Sec. 2.3 to 2.5).…”

“…However, for the purpose of verification in PVS, we reformulate the non-deterministic behaviour of Fig. 7 in a recursive function 5 using the deterministic Held For I operator to impose the constraint that only a single value (i.e., k Sealindelay − delta L where both are declared constants) is chosen from the duration and is used consistently for detecting sustained events.…”