Logics for Contravariant Simulations
Ignacio Fábregas, David de Frutos-Escrig, Miguel Palomino
TL;DR
The paper studies covariant-contravariant and conformance simulations within a categorical framework and develops logical characterizations for them. Two modal languages are introduced to capture the respective liveness and safety properties, namely L_CC and L_CS. A core result shows that CC and CS orderings correspond to inclusion of the respective formula sets, i.e., $S_{CC}(p) ⊆ S_{CC}(q)$ or $S_{CS}(p) ⊆ S_{CS}(q)$, respectively. Through examples with input/output automata, the work clarifies when each semantics is appropriate and shows how the choice of semantics impacts specification procedures.
Abstract
Covariant-contravariant simulation and conformance simulation are two generalizations of the simple notion of simulation which aim at capturing the fact that it is not always the case that "the larger the number of behaviors, the better". Therefore, they can be considered to be more adequate to express the fact that a system is a correct implementation of some specification. We have previously shown that these two more elaborated notions fit well within the categorical framework developed to study the notion of simulation in a generic way. Now we show that their behaviors have also simple and natural logical characterizations, though more elaborated than those for the plain simulation semantics.