Transducer-based Algorithmic Verification of Retransmission Protocols over Noisy Channels

Abstract

Unreliable communication channels are a practical reality. They add to the complexity of protocol design and verification. In this work, we consider noisy channels which can corrupt messages. We present an approach to model and verify protocols which combine error detection and error control to provide reliable communication over noisy channels. We call these protocols retransmission protocols as they achieve reliable communication through repeated retransmissions of messages. These protocols typically use cyclic redundancy checks and sliding window protocols for error detection and control respectively. We propose models of these protocols as regular transducers operating on bit strings. Deterministic streaming string transducers provide a natural way of modeling these protocols and formalizing correctness requirements. The verification problem is posed as functional equivalence between the protocol transducer and the specification transducer. Functional equivalence checking is decidable for this class of transducers and this makes the transducer models amenable to algorithmic verification. In our transducer models, message lengths and retransmission rounds are unbounded. We present case studies based on TinyOS serial communication and the HDLC retransmission protocol.

We further extend our protocol models to capture the effects of a noisy channel with non-determinism. We present two non-deterministic yet decidable extensions of transducer models of retransmission protocols. For one of our models, we achieve decidable verification by bounding the retransmission rounds, whereas for the other, even retransmission rounds are unbounded.