The expressive power of modal logic with inclusion atoms

Modal inclusion logic is the extension of basic modal logic with inclusion atoms, and its semantics is defined on Kripke models with teams. A team of a Kripke model is just a subset of its domain. In this paper we give a complete characterisation for the expressive power of modal inclusion logic: a class of Kripke models with teams is definable in modal inclusion logic if and only if it is closed under k-bisimulation for some integer k, it is closed under unions, and it has the empty team property. We also prove that the same expressive power can be obtained by adding a single unary nonemptiness operator to modal logic. Furthermore, we establish an exponential lower bound for the size of the translation from modal inclusion logic to modal logic with the nonemptiness operator.Comment: In Proceedings GandALF 2015, arXiv:1509.0685

An Analysis Tool for Models of Virtualized Systems

This paper gives an example-driven introduction to modelling and analyzing virtualized systems in, e.g., cloud computing, using virtually timed ambients, a process algebra developed to study timing aspects of resource management for (nested) virtual machines. The calculus supports nested virtualization and virtual machines compete with other processes for the resources of their host environment. Resource provisioning in virtually timed ambients extends the capabilities of mobile ambients to model the dynamic creation, migration, and destruction of virtual machines. Quality of service properties for virtually timed ambients can be formally expressed using modal contracts describing aspects of resource provisioning and verified using a model checker for virtually timed ambients, implemented in the rewriting system Maude

Virtually Timed Ambients: A Calculus for Resource Management in Cloud Computing

Cloud computing is a paradigm of distributed computing in which users share resources by storing data and executing processes in common data centers. A key factor for the success of this paradigm is virtualization technology, which represents the resources of an execution environment as a software layer, a so-called virtual machine. Virtualization allows to share existing hardware and software resources, improves security by providing isolation of different users, which share the same resource, and enables dynamic assignment of resources according to the demand of the user. The sharing of resources creates business drivers which make cloud computing an economically attractive model for deploying software. This thesis introduces the calculus of virtually timed ambients, a formal model of hierarchical locations for execution with explicit resource provisioning. This calculus is based on the well-known calculus of mobile ambients and motivated by the use of nested virtualization in cloud computing applications. The investigation of cloud computing from the point of view of process calculi provides a formal specification of the subject, which is necessary in order to develop executable models for analysis and optimization. The main contributions of this thesis are the definition of the calculus of virtually timed ambients, and the reasoning about its essential characteristics. In order to enable static analysis we enhance the calculus with a type system. Furthermore, we define a modal logic and a corresponding model checker, which we deploy in the definition of resource-awareness of virtually timed ambients, enabling dynamic self management of processes. Lastly, we present virtually timed ambients as a framework to analyse virtualization in cloud computing utilizing a prototype implementation. All concepts are illustrated by examples

A Calculus of Virtually Timed Ambients

Part 4: Regular PapersInternational audienceA virtual machine, which is a software layer representing an execution environment, can be placed inside another virtual machine. As virtual machines at every level in a location hierarchy compete with other processes for processing time, the computing power of a virtual machine depends on its position in this hierarchy and may change if the virtual machine moves. These effects of nested virtualization motivate the calculus of virtually timed ambients, a formal model of hierarchical locations for execution with explicit resource provisioning, introduced in this paper. Resource provisioning in this model is based on virtual time slices as a local resource. To reason about timed behavior in this setting, weak timed bisimulation for virtually timed ambients is defined as an extension of bisimulation for mobile ambients. We show that the equivalence of contextual bisimulation and reduction barbed congruence is preserved by weak timed bisimulation. The calculus of virtually timed ambients is illustrated by examples

Virtually timed ambients: A calculus of nested virtualization

Nested virtualization enables a virtual machine, which is a software layer representing an execution environment, to be placed inside another virtual machine. Nested virtual machines form a location hierarchy where virtual machines at every level in the hierarchy compete with other processes at that level for processing time. With nested virtualization, the computing power of a virtual machine depends on its position in this hierarchy and may change if the virtual machine moves. This paper introduces the calculus of virtually timed ambients, a formal model of hierarchical locations for execution with explicit resource provisioning, motivated by these effects of nested virtualization. Resource provisioning in this model is based on virtual time slices as a local resource. To reason about timed behavior in this setting, weak timed bisimulation for virtually timed ambients is defined as an extension of bisimulation for mobile ambients. We show that the equivalence of contextual bisimulation and reduction barbed congruence is preserved by weak timed bisimulation. Simulation with time relaxation is defined to express that a system is slower than another system up to a given time bound. The calculus of virtually timed ambients is illustrated by examples

An Analysis Tool for Models of Virtualized Systems

This paper gives an example-driven introduction to modelling and analyzing virtualized systems in, e.g., cloud computing, using virtually timed ambients, a process algebra developed to study timing aspects of resource management for (nested) virtual machines. The calculus supports nested virtualization and virtual machines compete with other processes for the resources of their host environment. Resource provisioning in virtually timed ambients extends the capabilities of mobile ambients to model the dynamic creation, migration, and destruction of virtual machines. Quality of service properties for virtually timed ambients can be formally expressed using modal contracts describing aspects of resource provisioning and verified using a model checker for virtually timed ambients, implemented in the rewriting system Maude