Bisimulation on speed: A unified approach

Two process-algebraic approaches have been developed for comparing two bisimulation-equivalent processes with respect to speed: the one of Moller/Tofts equips actions with lower time bounds, while the other by Lüttgen/Vogler considers upper time bounds instead.

This article sheds new light on both approaches by testifying to their close relationship. We introduce a general, intuitive concept of “faster-than”, which is formalised by a notion of amortised faster-than preorder. When closing this preorder under all contexts, exactly the two faster-than preorders investigated by Moller/Tofts and Lüttgen/Vogler arise. For processes incorporating both lower and upper time bounds we also show that the largest precongruence contained in the amortised faster-than preorder is not a proper preorder but a timed bisimulation. In the light of this result we systematically investigate under which circumstances the amortised faster-than preorder degrades to an equivalence.