This special issue of Mathematical Structures in Computer Science contains a selection of papers presented at three satellite events of CONCUR'09, which was held between 31 August and 5 September 2009 in Bologna (Italy). Specifically, it contains three papers from the 16th International Workshop on Expressiveness in Concurrency (EXPRESS'09), one paper from the 2nd Interaction and Concurrency Experience (ICE'09) and two papers from the 6th Workshop on Structural Operational Semantics (SOS'09).

The concurrency theory literature offers a wealth of examples of characteristic-formula constructions for various behavioural relations over finite labelled transition systems and Kripke structures that are defined in terms of fixed points of suitable functions. Such constructions and their proofs of correctness have been developed independently, but have a common underlying structure. This paper provides a general view of characteristic formulae that are expressed in terms of logics that have a facility for the recursive definition of formulae. We show how several examples of characteristic-formula constructions in the literature can be recovered as instances of the proposed general framework, and how the framework can be used to yield novel constructions. The paper also offers general results pertaining to the definition of co-characteristic formulae and of characteristic formulae expressed in terms of infinitary modal logics.

We prove a compactness theorem in the context of Hennessy–Milner logic and use it to derive a sufficient condition on modal characterisations for the approximation induction principle to be sound modulo the corresponding process equivalence. We show that this condition is necessary when the equivalence in question is compositional with respect to the projection operators. Furthermore, we derive different upper bounds for the constructive version of the approximation induction principle with respect to simulation and decorated trace semantics.

We introduce a new fragment of linear temporal logic (LTL) called LIO and a new class of Büchi automata (BA) called almost linear Büchi automata (ALBA). We provide effective translations between LIO and ALBA showing that the two formalisms are expressively equivalent. As we expect there to be applications of our results in model checking, we use two standard sources of specification formulae, namely Spec Patterns and BEEM, to study the practical relevance of the LIO fragment, and to compare our translation of LIO to ALBA with two standard translations of LTL to BA using alternating automata. Finally, we demonstrate that the LIO to ALBA translation can be much faster than the standard translation, and the resulting automata can be substantially smaller.

We define session types as projections of the behaviour of processes with respect to the operations processes perform on channels. This calls for a parallel composition operator over session types denoting the simultaneous access to a channel by two or more processes. The proposed approach allows us to define a semantically grounded theory of session types that does not require the linear usage of channels. However, type preservation and progress can only be guaranteed for processes that never receive channels they already own. A number of examples show that the resulting framework validates existing session-type theories and unifies them to some extent.

This paper presents a bisimulation-based method for establishing the soundness of equations between terms constructed using operations whose semantics are specified by rules in the GSOS format of Bloom, Istrail and Meyer. The method is inspired by de Simone's FH-bisimilarity and uses transition rules as schematic transitions in a bisimulation-like relation between open terms. The soundness of the method is proved and examples showing its applicability are provided. The proposed bisimulation-based proof method is incomplete, but we do offer some completeness results for restricted classes of GSOS specifications. An extension of the proof method to the setting of GSOS languages with predicates is also offered.

Van Glabbeek and Goltz (and later Fecher) have investigated the relationships between various equivalences on stable configuration structures, including interleaving bisimulation (IB), step bisimulation (SB), pomset bisimulation and hereditary history-preserving (H-H) bisimulation. Since H-H bisimulation may be characterised by the use of reverse as well as forward transitions, it is of interest to investigate these and other forms of bisimulations where both forward and reverse transitions are allowed. Bednarczyk asked whether SB with reverse steps is as strong as H-H bisimulation. We answer this question negatively. We give various characterisations of SB with reverse steps, showing that forward steps do not add power. We strengthen Bednarczyk's result that, in the absence of auto-concurrency, reverse IB is as strong as H-H bisimulation, by showing that we need only exclude auto-concurrent events at the same depth in the configuration.

We consider several other forms of observations of reversible behaviour and define a wide range of bisimulations by mixing the forward and reverse observations. We investigate the power of these bisimulations and represent the relationships between them as a hierarchy with IB at the bottom and H-H at the top.