By Michel Herve
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Extra resources for Analytic and Plurisubharmonic Functions in Finite and Infinite Dimensional Spaces
Not every marking in an MA-PN equivalence class can execute all actions the corresponding rMA process can execute, thus this equivalence is no congruence. Processed markings are introduced as exit points of the equivalence classes: a processed marking can execute exactly the same actions as its original. rMA process term. 3 to processed markings. 1 Restoring rMA Process Terms We will use the respective trees to relate rMA process terms and MA-PN markings. With a fixed order on link names and buds we can establish a function rest(M) which produces an rMA proceaa term P out of an MA-PN marking M by dropping unnecessary information.
We have to check wether all transitions maintain the invariant. Of course we can restrict our search to those transitions which change ambient relations and assume that the invariant holds in the transition's pre-state. : . According to the invariant either a new parent for Bj should be installed or aj should be marked as free. ; and removing its complement token. nsition also goes from case 1 to case 1 now moving the token from aj -+ as to aj -+ ale. nsition requires case 1 on an ambient name a,; by the token on a.
P] if n ::F m 3. P Since we want to enlarge each quantifier's scope we apply the :first two rules in the opposite direction to the way they are written here. g. a From rMA to MA-PN 39 In every RNF process term the restrictions form one long chain above the actual tree with its behaviour. Each restricted name is unique in the tree jUBt like it is in an MA-PN marking. The net guarantees uniqueness by introducing so far unused names r E 1l. Afterwards it can drop the useless restrictions rather than moving them to the outside.
Analytic and Plurisubharmonic Functions in Finite and Infinite Dimensional Spaces by Michel Herve