A Logical Approach for the Schedulability Analysis of CCSL

The Clock Constraint Specification Language (CCSL) is a clock-based formalism for formal specification and analysis of real-time embedded systems. Previous approaches for the schedulability analysis of CCSL specifications are mainly based on model checking or SMT-checking. In this paper we propose a logical approach mainly based on theorem proving. We build a dynamic logic called 'clock-based dynamic logic' (cDL) to capture the CCSL specifications and build a proof calculus to analyze the schedule problem of the specifications. Comparing with previous approaches, our method benefits from the dynamic logic that provides a natural way of capturing the dynamic behaviour of CCSL and a divide-and-conquer way for 'decomposing' a complex formula into simple ones for an SMT-checking procedure. Based on cDL, we outline a method for the schedulability analysis of CCSL. We illustrate our theory through one example.