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We study the theory of safety and liveness in a reversible calculus wherereductions are totally ordered and rollbacks lead the systems to past states.Similar to previous work on communicating transactions, liveness and safetyrespectively correspond to the should-testing and inverse may-testingpreorders. We develop fully abstract models for these preorders in a reversiblecalculus, which are based only on forward transitions, thus providing a simpleproof technique for refinement of such systems. We show that with respect tosafety, total reversibility is a conservative extension to CCS. With respect toliveness, however, adding total reversibility to CCS distinguishes moresystems. To our knowledge, this work provides the first characterisations ofsafety and liveness, and the first testing theory for a reversible calculus.

A Safety and Liveness Theory for Total Reversibility (Extended Abstract)