The Ambient Calculus is a process calculus where processes may reside within a hierarchy of locations and modify it. The purpose of the calculus is to study mobility, which is seen as the change of spatial configurations over time. In order to describe properties of mobile computations we devise a modal logic that can talk about space as well as time, and that has the Ambient Calculus as a model. 1

The events of a security protocol and their causal dependency can play an important role in the analysis of security properties. This insight underlies both strand spaces and the inductive method. But neither of these approaches builds up the events of a protocol in a compositional way, so that there is an informal spring from the protocol to its model. By broadening the models to certain kinds of Petri nets, a restricted form of contextual nets, a compositional eventbased semantics is given to an economical, but expressive, language for describing security protocols; so the events and dependency of a wide range of protocols are determined once and for all. The net semantics is formally related to a transition semantics, strand spaces and inductive rules, as well as trace languages and event structures, so unifying a range of approaches, as well as providing conditions under which particular, more limited, models are adequate for the analysis of protocols. The net semantics allows the derivation of general properties and proof principles which are demonstrated in establishing an authentication property, following a diagrammatic style of proof.

We discuss the computational aspects of wide area networks, and we describe various facets of a process calculus devised to embody mobility, security, and wide area network semantics. These lecture notes are an abridged version of [8, 11, 27, 12, 13].

Much work in automatic verification considers families of similar finite-state systems. But an often overlooked property is that sometimes a single finite-state system can be used to describe a parameterized, infinite family of systems. Thus verification of unbounded state spaces can take place by reduction to finite ones.

Linear logic, introduced by Girard in 1987, has been called a resource conscious logic. In order to express a dynamic change in process environment, it is useful to consider a concept of resource such as data consumption. The expressive power of linear logic is evidenced by some very natural encodings of computational models such as Petri nets, counter machines, Turing machines, and others. For example, in Petri nets, tokens are considered as resources that are consumed and transitions are considered as reusable resources. It is well known that the reachability problem for ordinary Petri nets is equivalent to the provability for the corresponding sequent of linear logic. Also, as a formal logical system, linear logic satisfies some basic theorems. In it the cut elimination theorem and the soundness and completeness theorems for phase semantics which is a standard semantics of linear logic hold true. In particular, the cut elimination theorem can be applied to logic programming, uniform proof and proof search, and so on. We think that linear logic has been given various applications in computer science through its resource consciousness and usefulness as a formal system. However, since linear logic does not include a concept of time directly, it is not enough to treat a dynamic change in environments with the passage of time such as execution time and waiting time. A typical example is the encoding of timed Petri nets. Although ordinary Petri nets can be encoded into linear logic naturally as stated above, the encoding of timed Petri nets into the corresponding sequent is too complex for linear logic since the reachability problem for timed Petri nets includes a time concept. Thus, it can be considered to extend linear logic with respect to the time concept. The aim of t...

. We present an extension of the ambient logic with fixed points operators in the style of the -calculus. We give a simple syntactic condition for the equivalence between minimal and maximal fixpoint formulas and show how to subsume spatial analogues of the usual box and diamond operators. 1

The main objective of this paper is to show how to extend the ECATNet model, which is a form of high-level algebraic nets, with new objects and morphisms in order to have a more expressive modelbased diagnosis of concurrent systems. Our formulation is accomplished by exploiting the similarity between the categorical models of linear logic and those of ECATNets which are also categories in the rewriting logic framework. The categorical interpretation of the extra structure is inspired from that of some linear logic connectors. In particular, the useful interpretation of the extra object...

We present an approach to linear logic planning where an explicit correspondence between partial order plans and multiplicative exponential linear logic proofs is established. This is performed by extracting partial order plans from sound and complete encodings of planning problems in multiplicative exponential linear logic in a way that exhibits a non-interleaving behavioral concurrency semantics. Relying on this fact, we argue that this work is a crucial step for establishing a common language for concurrency and planning that will allow to carry techniques and methods between these two fields.

The Myhill-Nerode Theorem (that for any regular language, there is a canonical recognizing device) is of paramount importance for the computational handling of many formalisms about finite words. For infinite

The Ambient Calculus is a process calculus where processes may reside within a hierarchy of locations and modify it. The purpose of the calculus is to study mobility, which is seen as the change of spatial configurations over time. In order to describe properties of mobile computations we devise a modal logic that can talk about space as well as time, and that has the Ambient Calculus as a model.