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Summary: On Bisimilarities Induced by Relations on Actions
S. Arun-Kumar
Department of Computer Science and Engineering
Indian Institute of Technology, Delhi
Hauz Khas, New Delhi 110 016,India
sak@cse.iitd.ernet.in
Abstract
In this paper, we give a straightforward generalization
of bisimulations to "bisimulations induced by a pair of rela-
tions" on the underlying action set. We establish that many
of the nice properties of bisimulations and bisimilarities
may be thought of as actually being inherited from prop-
erties of the underlying relations on actions. We show that
many bisimulation-based orderings (including strong and
weak bisimilarity) defined in the literature are instances of
this generalization. We also show by an example that there
are instances where the equivalence of two systems (which
intuitively have the same functionality), cannot be estab-
lished directly by observational equivalence, but requires a
more general notion. We finally give an adaptation of the
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