By Susanne Göbel
The grasp thesis of Susanne Göbel generates the deep figuring out of the cellular Ambient (MA) calculus that's essential to use it as a modeling language. rather than calculus phrases a way more handy illustration through MA bushes evidently maps to the applying region of networks the place methods go hierarchical security domain names like firewalls. The paintings analyses MA’s functionality rules and derives a translation into secure Petri nets. It extends to arbitrary MA methods yet finiteness of the web and consequently decidability of reachability is just assured for bounded procedures. the development is polynomial in method measurement and limits in order that reachability research is simply PSPACE-complete.
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Additional info for A Polynomial Translation of Mobile Ambients into Safe Petri Nets: Understanding a Calculus of Hierarchical Protection Domains
Again, already rest(Mt ) = rest(M2) holds, so that the equivalence between the markings is kept. 2 is enabled in the 8BBumed situation if some unused link name r is present (r ...... ). 26 to be sure that a name is markable as unused.
Table MA-PN marking. Al into an equivalent processed marking M'. Proof. We depict how to mark forgotten restricted link names as unused first. P. II The desired position in 'R. 2) to mark any forgotten restricted name as unused while maintaining the equivalence. The necessary steps for different names may not interfere since they are working on rustinct places (each place uses the link name r as reference). tenatioD of these steps will yield an equivalent marking in which each name is either in use or marked as unused.
Proof. It is obvious that the condition holds for the initial marking root[Tl ~I] itself. Now we will prove that any transition (sequence) from one stable macking 81 to the next one 8 2 maintains this invariant. We only care for transitions which influence the parent-child relations between ambients and twigs. One can easily verify that only one transition sequence with intermediate unstable markings can be executed at a time since each first step consumes the semaphore and each later step requires the one before.
A Polynomial Translation of Mobile Ambients into Safe Petri Nets: Understanding a Calculus of Hierarchical Protection Domains by Susanne Göbel