Jens Chr. Godskesen

A calculus for mobile ad hoc networks

We suggest a Calculus for Mobile Ad Hoc Networks, CMAN. A node in a network is a process equipped with a location, it may communicate with other nodes using synchronous spatially oriented broadcast where only the current neighbors receive the message. Nodes may autonomously change their neighbor relationship and thereby change the network topology. We define a natural reduction semantics and a reduction congruence as well as a labeled transition semantics and prove a weak contextual bisimulation to be a sound and complete co-inductive characterization of the reduction congruence. Finally, we apply CMAN on a small example of a cryptographic routing protocol.

Mobility Models and Behavioural Equivalence for Wireless Networks

In protocol development for wireless systems, the choice of appropriate mobility models describing the movement patterns of devices has long been recognised as a crucial factor for the successful evaluation of protocols. More recently, wireless protocols have also come into the focus of formal approaches to the modelling and verification of concurrent systems. While in these approaches mobility is also given a central role, the actual mobility modelling remains simplistic since arbitrary node movements are allowed. This leads to a huge behavioural overapproximation that might prevent a successful reasoning about protocol properties. In this paper we describe how to extend a process calculus by realistic mobility models in an orthogonal way. The semantics of our calculus incorporates a notion of global time passing that allows us to express a wide range of mobility models currently used in protocol development practice. Using the behavioural equivalence and pre-order of our calculus, we are furthermore able to compare the strength of these models in our approach.

Extending howe's method to early bisimulations for typed mobile embedded resources with local names

We extend Howes method to prove that input-early strong and -delay contextual bisimulations are congruences for the Higher-order mobile embedded resources (Homer) calculus, a typed higher order process calculus with active mobile processes, nested locations and local names which conservatively extends the syntax and semantics of higher-order calculi such as Plain CHOCS and HOpi. We prove that the input-early strong and -delay contextual bisimulation congruences are sound co-inductive characterisations of barbed bisimulation congruence and in fact complete in the strong case. The extension of Howes method provides considerably simpler congruence proofs than established previously for similar calculi for mobile processes in nested locations.

A CPS encoding of name-passing in higher-order mobile embedded resources

We present an encoding of the synchronous π-calculus in the calculus of Higher-order mobile embedded resources (Homer), a pure higher-order calculus with mobile processes in nested locations, defined as a simple, conservative extension of the core process-passing subset of Thomsens Plain CHOCS. We prove that our encoding is fully abstract with respect to barbed bisimulation and sound with respect to barbed congruence. Our encoding demonstrates that higher-order process-passing together with mobile resources in, possibly local, named locations are sufficient to express π-calculus name-passing. The encoding uses a novel continuation passing style to facilitate the encoding of synchronous communication.

Probabilistic Mobility Models for Mobile and Wireless Networks

In this paper we present a probabilistic broadcast calculus for mobile and wireless networks whose connections are unreliable. In our calculus, broadcasted messages can be lost with a certain probability, and due to mobility the connection probabilities may change. If a network broadcasts a message from a location, it will evolve to a network distribution depending on whether nodes at other locations receive the message or not. Mobility of nodes is not arbitrary but guarded by a probabilistic mobility function (PMF), and we also define the notion of a weak bisimulation given a PMF. It is possible to have weak bisimular networks which have different probabilistic connectivity information. We furthermore examine the relation between our weak bisimulation and a minor variant of PCTL* [1]. Finally, we apply our calculus on a small example called the Zeroconf protocol [2].

A Calculus for Mobile Ad-hoc Networks with Static Location Binding

We present a process calculus for mobile ad hoc networks which is a natural continuation of our earlier work on the process calculus CMAN [J.C. Godskesen. A calculus for mobile ad hoc networks. In Proceedings of the 9th International Conference, COORDINATION 2007, volume 4467 of LNCS, pages 132-150, Paphos, Cyprus, June 2007. Springer-Verlag]. Essential to the new calculus is the novel restricted treatment of node mobility imposed by hiding of location names using a static binding operator, and we introduce the more general notion of unidirectional links instead of bidirectional links. We define a natural weak reduction semantics and a reduction congruence and prove our weak contextual bisimulation equivalence to be a sound and complete co-inductive characterization of the reduction congruence. The two changes to the calculus in [J.C. Godskesen. A calculus for mobile ad hoc networks. In Proceedings of the 9th International Conference, COORDINATION 2007, volume 4467 of LNCS, pages 132-150, Paphos, Cyprus, June 2007. Springer-Verlag] yields a much simpler bisimulation semantics, and importantly and in contrast to [J.C. Godskesen. A calculus for mobile ad hoc networks. In Proceedings of the 9th International Conference, COORDINATION 2007, volume 4467 of LNCS, pages 132-150, Paphos, Cyprus, June 2007. Springer-Verlag] we manage to provide a non-contextual weak bisimulation congruence facilitating ease of proofs and being strictly contained in the contextual bisimulation.

Observables for mobile and wireless broadcasting systems

We discuss the presence of localities in observables for process calculi for mobile and wireless broadcasting systems in the context of weak barbed congruences and demonstrate that observability of the locality of a broadcasting node may be unsuitable when abstracting from node mobility, a natural abstraction current calculi agree upon. The discussion is carried out through a calculus bAπ, a conservative extension of the Applied π-calculus and a contribution of its own. Through examples we demonstrate the applicability of bAπ and its weak reduction congruence, where the locality of a broadcasting node is not observable, and we prove our bisimulation equivalence to be a sound and complete co-inductive characterization of the weak reduction congruence.

A Calculus of Mobile Resources

We introduce a calculus of Mobile Resources (MR) tailored for the design and analysis of systems containing mobile, possibly nested, computing devices that may have resource and access constraints,an d which are not copyable nor modifiable per se. We provide a reduction as well as a labelled transition semantics and prove a correspondence between barbed bisimulation congruence and a higher-order bisimulation. We provide examples of the expressiveness of the calculus, and apply the theory to prove one of its characteristic properties.

Bisimulations meet PCTL equivalences for probabilistic automata

Probabilistic automata (PA) [20] have been successfully applied in the formal verification of concurrent and stochastic systems. Efficient model checking algorithms have been studied, where the most often used logics for expressing properties are based on PCTL [11] and its extension PCTL* [4]. Various behavioral equivalences are proposed for PAs, as a powerful tool for abstraction and compositional minimization for PAs. Unfortunately, the behavioral equivalences are well-known to be strictly stronger than the logical equivalences induced by PCTL or PCTL*. This paper introduces novel notions of strong bisimulation relations, which characterizes PCTL and PCTL* exactly. We also extend weak bisimulations characterizing PCTL and PCTL* without next operator, respectively. Thus, our paper bridges the gap between logical and behavioral equivalences in this setting.

Broadcast abstraction in a stochastic calculus for mobile networks

We introduce a continuous time stochastic broadcast calculus for mobile and wireless networks. The mobility between nodes in a network is modeled by a stochastic mobility function which allows to change part of a network topology depending on an exponentially distributed delay and a network topology constraint. We allow continuous time stochastic behavior of processes running at network nodes, e.g. in order to be able to model randomized protocols. The introduction of group broadcast and an operator to help avoid flooding allows us to define a novel notion of broadcast abstraction. Finally, we define a weak bisimulation congruence and apply our theory on a leader election protocol.