A Pre-congruence Format for XY-simulation

XY -simulation is a generalization of bisimulation that is parameterized with two subsets of actions. XY -simulation is known in the literature under different names such as modal refinement, partial bisimulation, and alternating simulation. In this paper, we propose a precongruence rule format for XY -simulation. The format allows for checking compositionality of XY -simulation for an arbitrary language with structural operational semantics, by performing very simple checks on the syntactic shape of the rules. We apply our format to derive concrete compositionality results for different notions of behavioral pre-order with respect to different process calculi in the literature.