• Pi Calculus
• Lambda Calculus
• Cloud Computing
• Resource Usage Analsysis

Modern computing paradigms for distributed applications advocate a strong control on shared resources available on demand in order to guarantee their correct usages.
An illustrative example of such paradigms is Cloud Computing.
In this dissertation, we study formal models for distributed applications, paying particular attention to resource usage analysis. Formal methods for specifying and analysing different aspects of resource management could play an important role for the widespread usages of distributed resources. They provide not only the theoretical framework to understand the stages underlying the design and implementation issues,
but also the mathematically-based techniques for the specification and verifications of properties of such systems.
In this dissertation, we introduce two models, called lambda clouds and G-Local pi calculus, which are extensions of the lambda calculus and pi calculus respectively.

The lambda clouds is an extension of concurrent lambda calculus enriched with suitable mechanisms to express and enforce application-level security policies governing usages of resources available on demand in the clouds. We focus on the server side of cloud systems, by adopting a pro-active approach, where explicit security policies, which are expressed as a set of execution traces, regulate server's behaviour.
By providing an abstract cloud semantics, we ensure that enforcing security policies embedded in cloud applications is sound.

The G-Local pi calculus is built on top of the standard pi calculus by introducing new primitives to manage resources.
Unlike the previous model, where resources are highly abstract,
resources in this approach are modelled as stateful entities with local states and global policies. A high degree of loose coupling among applications and resources is achieved through the publish/subscribe model. Furthermore, we develop two static, language-based techniques, namely Control Flow Analysis (CFA) and Type and Effect Systems, to reason about resource usages and therefore able to predict \textit{bad} usages of resources.
The CFA mainly focuses on reachability properties related to resource usages. It computes an over-approximation of resource usages of applications. As a result, if the approximation does not contain bad usages, then it guarantees that applications correctly use resources. The type and effect system provides a closer view of resource behaviour. Resource behaviour is extracted in the form of side effect of the type system. We exploit side effect to verify regular linear time properties, expressed by Linear Time Logic formulas, of resource usages.