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 paper sheds new light onto both approaches by testifying to their close relationship and brings the research into bisimulation–based faster– than preorders to a close. We introduce a general, very 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.