Verifying an Arbiter Circuit

This paper presents the verification of an asynchronous arbiter modeled at the circuit level with non-linear ordinary differential equations. We use Brockett\´s annulus to represent the allowed families of continuous waveforms for input and output signals and show that the metastability filter of the arbiter can be understood as a "Brockett annulus transformer." Improvements to the Coho verification tool are described that reduce the over approximation errors when working with non- convex reachable regions. The verification shows that the arbiter observes a four-phase handshake protocol with its clients and maintains mutual exclusion. We also show several liveness properties including bounded time response to uncontested requests and that grants are issued fairly.