Continuation Semantics for Dynamic Hierarchical Systems

We present a denotational semantics designed with metric spaces and continuations for a simple concurrent language LMB embodying a representative set of features encountered in membrane computing. LMB is a multiset rewriting language. In LMB multisets of objects are encapsulated in hierarchical structures of compartments, or regions, delimited by membranes. The behaviour of each membrane is specified by means of multiset rewriting rules. The semantics of parallel composition in LMB is based on the concept of maximal parallelism. Computations proceed according to the multiset rewriting rules, nondeterministically choosing the rules and the objects. Membranes can be grouped into classes based on the rewriting rules that they encapsulate, LMB also provides a primitive for membrane creation, or instantiation. In this sense, LMB is similar to anobject oriented language. We use continuations and a powerdomain constructionto represent nondeterministic behavior. An element of a powerdomain is a collection of sequences of observables representing dynamic membrane structures. Our continuation semantics describes in a compositional manner the behavior of an LMB program as a dynamic hierarchical system. As far as we know, this is the firstpaper that presents a metric denotational semanticsfor the combination of features embodied in LMB.