Anna Ingólfsdóttir

Graphical representation of covariant-contravariant modal formulae

Covariant-contravariant simulation is a combination of standard (covariant) simulation, its contravariant counterpart and bisimulation. We have previously studied its logical characterization by means of the covariant-contravariant modal logic. Moreover, we have investigated the relationships between this model and that of modal transition systems, where two kinds of transitions (the so-called may and must transitions) were combined in order to obtain a simple framework to express a notion of refinement over state-transition models. In a classic paper, Boudol and Larsen established a precise connection between the graphical approach, by means of modal transition systems, and the logical approach, based on Hennessy-Milner logic without negation, to system specification. They obtained a (graphical) representation theorem proving that a formula can be represented by a term if, and only if, it is consistent and prime. We show in this paper that the formulae from the covariant-contravariant modal logic that admit a graphical representation by means of processes, modulo the covariant-contravariant simulation preorder, are also the consistent and prime ones. In order to obtain the desired graphical representation result, we first restrict ourselves to the case of covariant-contravariant systems without bivariant actions. Bivariant actions can be incorporated later by means of an encoding that splits each bivariant action into its covariant and its contravariant parts.

Axiomatizing weak ready simulation semantics over BCCSP

Ready simulation has proven to be one of the most significant semantics in process theory. It is at the heart of a number of general results that pave the way to a comprehensive understanding of the spectrum of process semantics. Since its original definition by Bloom, Istrail and Meyer in 1995, several authors have proposed generalizations of ready simulation to deal with internal actions. However, a thorough study of the (non-)existence of finite (in)equational bases for weak ready simulation semantics is still missing in the literature. This paper presents a complete account of positive and negative results on the axiomatizability of weak ready simulation semantics over the language BCCSP. In addition, this study offers a thorough analysis of the axiomatizability properties of weak simulation semantics.