Equational Characterization of Covariant-Contravariant Simulation and Conformance Simulation Semantics

Covariant-contravariant simulation and conformance simulation generalize plain simulation and try to capture the fact that it is not always the case that "the larger the number of behaviors, the better". We have previously studied their logical characterizations and in this paper we present the axiomatizations of the preorders defined by the new simulation relations and their induced equivalences. The interest of our results lies in the fact that the axiomatizations help us to know the new simulations better, understanding in particular the role of the contravariant characteristics and their interplay with the covariant ones; moreover, the axiomatizations provide us with a powerful tool to (algebraically) prove results of the corresponding semantics. But we also consider our results interesting from a metatheoretical point of view: the fact that the covariant-contravariant simulation equivalence is indeed ground axiomatizable when there is no action that exhibits both a covariant and a contravariant behaviour, but becomes non-axiomatizable whenever we have together actions of that kind and either covariant or contravariant actions, offers us a new subtle example of the narrow border separating axiomatizable and non-axiomatizable semantics. We expect that by studying these examples we will be able to develop a general theory separating axiomatizable and non-axiomatizable semantics.Comment: In Proceedings SOS 2010, arXiv:1008.190

Model Checking Spatial Logics for Closure Spaces

Spatial aspects of computation are becoming increasingly relevant in Computer Science, especially in the field of collective adaptive systems and when dealing with systems distributed in physical space. Traditional formal verification techniques are well suited to analyse the temporal evolution of programs; however, properties of space are typically not taken into account explicitly. We present a topology-based approach to formal verification of spatial properties depending upon physical space. We define an appropriate logic, stemming from the tradition of topological interpretations of modal logics, dating back to earlier logicians such as Tarski, where modalities describe neighbourhood. We lift the topological definitions to the more general setting of closure spaces, also encompassing discrete, graph-based structures. We extend the framework with a spatial surrounded operator, a propagation operator and with some collective operators. The latter are interpreted over arbitrary sets of points instead of individual points in space. We define efficient model checking procedures, both for the individual and the collective spatial fragments of the logic and provide a proof-of-concept tool