We settle the complexity bounds of the model checking problem for the ambient calculus with public names against the ambient logic. We show that if either the calculus contains replication or the logic contains the guarantee operator, the problem is undecidable. In the case of the replication-free calculus and guarantee-free logic we prove that the problem is PSPACE-complete. For the complexity upper-bound, we devise a new representation of processes that remains of polynomial size during process execution; this allows us to keep the model checking procedure in polynomial space. Moreover, we prove PSPACE-hardness of the problem for several quite simple fragments of the calculus and the logic; this suggests that there are no interesting fragments with polynomial-time model checking algorithms.

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We investigate expressiveness of a fragment of the ambient calculus, a formalism for describing distributed and mobile computations. More precisely, we study expressiveness of the pure and public ambient calculus from which the has been removed, in terms of the reachability problem of the reduction relation. Surprisingly, we show that even for this very restricted fragment, the reachability problem is not decidable. At a second step, for a slightly weaker reduction relation, we prove that reachability can be decided by reducing this problem to markings reachability for Petri nets. Finally, we show that the name-convergence problem as well as the model-checking problem turn out to be undecidable for both the original and the weaker reduction relation. 1

First of all, I would like to thank my supervisor Dr. Iain C. C. Phillips, for his support and collaboration during this period of research. I thank Iain for having taught me to be more precise and sharp, and for long, detailed and inspiring discussions on the topic of this dissertation. Finally I thank him for his enormous patience towards my stubbornness. I would like to thank Dr. Nobuko Yoshida for many useful discussions and for being very supportive and positive about my work. To Sergio Maffeis go thanks for many discussions on various subjects of research and philosophy during the last two years at Imperial College. He suggested an improvement to the solution for the leader election problem for the Ambient Calculus. I would like to thank also Andrew Phillips, and the concurrency group at Imperial for the Monday lunch meetings. This has been a wonderful forum for discussing various aspects of my work. I like to thank Prof. Chris Hankin and Dr. Sophia Drossopoulou for helping me on various occasions with administrative problems and (especially Chris) for supporting most of my travelling. I do not know how I could have ever achieved this without my husband, Steffen van Bakel. He

1 Introduction Over the last 15 years, a lot of research has gone into calculi of mobile processes.Among these, the ss-calculus is the best known. A number of other calculi, how-ever, have been put forward to study aspects of mobility not directly covered