RT Book, Section T1 Constrained simulations, nested simulation semantics and counting bisimulations A1 Frutos Escrig, David De A1 Gregorio Rodríguez, Carlos AB Nested simulations define an interesting hierarchy of semantic preorders and equivalences in which every semantics refines the previous one and it is refined by the following. This nested nature provides a fruitful framework for the study of the formal meaning and the properties of concurrent processes. In this paper we present the notion of constrained simulation that, although rather simple, allows us to find general results for a wide family of semantics. In particular, we provide an axiomatization for both the preorder and the equivalence induced by any constrained simulation. Nested simulations are constrained simulations and therefore our results can be instantiated directly to them. Besides, constrained simulations suggest the definition of a new family of semantics, generalised nested simulation semantics, constructed over the base of any order relation, instead of plain simulation. Finally, we conclude the study of the (generalised) nested semantics defining a generalisation of bisimulation relations, counting bisimulation, that allows us to define a characterisation of nested semantics in terms of a bisimulation-like game. PB Elsevier Science SN 1571-0661 YR 2008 FD 2008 LK https://hdl.handle.net/20.500.14352/53216 UL https://hdl.handle.net/20.500.14352/53216 LA eng NO Proceedings of the Seventh Spanish Conference on Programming and Computer Languages (PROLE 2007, Zaragoza, Spain, 12–14 September 2007 NO Madrid Ciencia y Tecnología DS Docta Complutense RD 17 abr 2025