Miguel Palomino Tarjuelo (Universidad Complutense de Madrid,
Spain)
Title: Non-Strongly Stable Orders and Simulation Relations
Abstract: We present a study of the notion of coalgebraic simulation
introduced by Hughes and Jacobs. Although in their original paper they
allow any functorial order in their definition of
coalgebraic simulation, for the simulation relations to have good
properties they focus their attention on functors with orders which
are strongly stable. This guarantees a so-called
composition-preserving property from which all the desired good
properties follow. We have noticed that the notion of strong stability
not only ensures such good properties but also distinguishes the
direction of the simulation. Our study was motivated by some
interesting classes of simulations that illustrate the application of
these results. Covariant-contravariant simulations handle two
alphabets of actions A and A', so that in (A, A')-simulations between
p and q we have to simulate the moves in A (resp. A') of p (resp. q)
by moves of q (resp. p). It is clear that they include as limit cases
the simulation, simulated by, and bisimulation relations. Another
interesting example is that of conformance simulations where the
classic notion of implementation relations in which deterministic
processes are implementations of (possibly) nondeterministic
specifications, and the classic simulation order, where p is simulated
by p + q, meet together in a nice way. Finally, we discuss how to to
obtain their modal characterizations in the coalgebraic framework.