Abstract
KeYmaera is an interactive theorem prover and is used to verify safety properties of cyber-physical systems (CPSs). It implements a Dynamic Logic for Hybrid Programs (HPs), while a HP models a CPS very precisely. Verifying properties of a given system in KeYmaera can become a challenge for a user since the proof is authored in a classical sequent calculus framework and a successful proof requires from the user intimate knowledge of the available calculus rules. Another barrier for widespread application of KeYmaera is the purely textual representation of current proof goals, what requires from the user very good training, experience, and patience. In this paper, we present an alternative verification approach based on KeYmaera, which drastically improves usability and minimizes user interaction. The main idea is to let the user annotate invariants and contracts to states of the hybrid automaton. Thus, the user can employ the graphical representation of the modelled system and is not bound to the purely textual form of hybrid programs as in KeYmaera. Based on the user-provided contracts, one can generate proof obligations, which are much simpler than the original proof goal in KeYmaera. The article is published in the authors’ wording.
Highlights
We present an alternative verification approach based on KeYmaera, which drastically improves usability and minimizes user interaction
Verification of cyber-physical systems (CPSs) using KeYmaera In KeYmaera, a CPS is modelled in form of a Hybrid Program (HP), for which properties expressed in Dynamic Logic can be proven
We discussed one of the biggest barrier of verification tools such as KeYmaera to get widely acceptance in industry: They assume the user to be highly trained in mathematical logic and to know in detail the system’s proof rules
Summary
A cyber-physical system (CPS) is a system that tightly combines software with physical components. Logic-based analysis of a given hybrid automaton has been thoroughly investigated by Platzer in [12] and became practically feasible by the tool KeYmaera [14] This tool is an interactive theorem prover and allows the user to formally prove safety properties taken both discrete and continuous state variables into account. Floyd [7] for flowchart verification on the verification of a CPS: The user is allowed to annotate the control flow graph of hybrid program α with fine grained knowledge about intermediate states This additional knowledge can be given in form of invariants (similar to loop invariants) and contracts for long-running states. Based on the provided invariants and contracts, one can generate proof obligations, which are much simpler than the original proof goal in KeYmaera and can often be automatically discarded
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