Actor Network Procedures as Psi-calculi for Security Ceremonies

The actor network procedures of Pavlovic and Meadows are a recent graphical formalism developed for describing security ceremonies and for reasoning about their security properties. The present work studies the relations of the actor network procedures (ANP) to the recent psi-calculi framework. Psi-calculi is a parametric formalism where calculi like spi- or applied-pi are found as instances. Psi-calculi are operational and largely non-graphical, but have strong foundation based on the theory of nominal sets and process algebras. One purpose of the present work is to give a semantics to ANP through psi-calculi. Another aim was to give a graphical language for a psi-calculus instance for security ceremonies. At the same time, this work provides more insight into the details of the ANPs formalization and the graphical representation.Comment: In Proceedings GraMSec 2014, arXiv:1404.163

A coalgebraic semantics for causality in Petri nets

In this paper we revisit some pioneering efforts to equip Petri nets with compact operational models for expressing causality. The models we propose have a bisimilarity relation and a minimal representative for each equivalence class, and they can be fully explained as coalgebras on a presheaf category on an index category of partial orders. First, we provide a set-theoretic model in the form of a a causal case graph, that is a labeled transition system where states and transitions represent markings and firings of the net, respectively, and are equipped with causal information. Most importantly, each state has a poset representing causal dependencies among past events. Our first result shows the correspondence with behavior structure semantics as proposed by Trakhtenbrot and Rabinovich. Causal case graphs may be infinitely-branching and have infinitely many states, but we show how they can be refined to get an equivalent finitely-branching model. In it, states are equipped with symmetries, which are essential for the existence of a minimal, often finite-state, model. The next step is constructing a coalgebraic model. We exploit the fact that events can be represented as names, and event generation as name generation. Thus we can apply the Fiore-Turi framework: we model causal relations as a suitable category of posets with action labels, and generation of new events with causal dependencies as an endofunctor on this category. Then we define a well-behaved category of coalgebras. Our coalgebraic model is still infinite-state, but we exploit the equivalence between coalgebras over a class of presheaves and History Dependent automata to derive a compact representation, which is equivalent to our set-theoretical compact model. Remarkably, state reduction is automatically performed along the equivalence.Comment: Accepted by Journal of Logical and Algebraic Methods in Programmin

Declarative event based models of concurrency and refinement in psi-calculi

AbstractPsi-calculi constitute a parametric framework for nominal process calculi, where constraint based process calculi and process calculi for mobility can be defined as instances. We apply here the framework of psi-calculi to provide a foundation for the exploration of declarative event-based process calculi with support for run-time refinement. We first provide a representation of the model of finite prime event structures as an instance of psi-calculi and prove that the representation respects the semantics up to concurrency diamonds and action refinement. We then proceed to give a psi-calculi representation of Dynamic Condition Response Graphs, which conservatively extends prime event structures to allow finite representations of (omega) regular finite (and infinite) behaviours and have been shown to support run-time adaptation and refinement. We end by outlining the final aim of this research, which is to explore nominal calculi for declarative, run-time adaptable mobile processes with shared resources

Concurrency Models with Causality and Events as Psi-calculi

Psi-calculi are a parametric framework for nominal calculi, where standard calculi are found as instances, like the pi-calculus, or the cryptographic spi-calculus and applied-pi. Psi-calculi have an interleaving operational semantics, with a strong foundation on the theory of nominal sets and process algebras. Much of the expressive power of psi-calculi comes from their logical part, i.e., assertions, conditions, and entailment, which are left quite open thus accommodating a wide range of logics. We are interested in how this expressiveness can deal with event-based models of concurrency. We thus take the popular prime event structures model and give an encoding into an instance of psi-calculi. We also take the recent and expressive model of Dynamic Condition Response Graphs (in which event structures are strictly included) and give an encoding into another corresponding instance of psi-calculi. The encodings that we achieve look rather natural and intuitive. Additional results about these encodings give us more confidence in their correctness

An Operational Petri Net Semantics for the Join-Calculus

We present a concurrent operational Petri net semantics for the join-calculus, a process calculus for specifying concurrent and distributed systems. There often is a gap between system specifications and the actual implementations caused by synchrony assumptions on the specification side and asynchronously interacting components in implementations. The join-calculus is promising to reduce this gap by providing an abstract specification language which is asynchronously distributable. Classical process semantics establish an implicit order of actually independent actions, by means of an interleaving. So does the semantics of the join-calculus. To capture such independent actions, step-based semantics, e.g., as defined on Petri nets, are employed. Our Petri net semantics for the join-calculus induces step-behavior in a natural way. We prove our semantics behaviorally equivalent to the original join-calculus semantics by means of a bisimulation. We discuss how join specific assumptions influence an existing notion of distributability based on Petri nets.Comment: In Proceedings EXPRESS/SOS 2012, arXiv:1208.244