Applying regions

Adding A/Sync Places to the Synthesis Procedure for Whole-Place Operations Nets with Localities

“…Thanks to the clustering of the places, however, they still fit the ideas behind the definition of τ -nets and we can define a suitably extended net-type capturing the behaviour of sets of several places rather than the behaviour of single places. More precisely, for all k , k ≥ 0 with k + k ≥ 1, the k /k -wpoasl-net-type is a transition system τ k /k -generalising the net-type τ k wpo introduced and used in [24,23] -defined in the following way.…”

“…Conversely, one can transform any τ k /knet into an equivalent k /k -wpoasl-net, and trivially the wpoasl-net as in (4) is an n /(n − n )-wpoasl-net. All this implies that -just as in case of any synthesis problem that asks for a procedure to construct a τ -net with a given concurrent reachability graph, see, e.g., [24] -k /k -wpoasl-net synthesis involves the following two problems of τ k /k -net synthesis.…”

“…Together they provide a full characterisation of realisable transition systems, i.e., those that can be realised by a τ k /k -net executed under some cds lmax policy, as we later show in Theorem 1. T can be realised by a wpoasl-net if and only if Axioms 1 and 2 are satisfied (see, e.g., [24]). …”

“…Similarly as in [24,23], one can define a system of equations and inequalities encoding the conditions that must be satisfied by τ k /k -regions. Let Q = {q 0 , q 1 , .…”

“…The synthesis of wpoasl-nets from step transition system specifications will build on our previous work [24,23]. It will be based on a suitably adapted notion of region of a (step) transition system [17,4,3], as well as their locally maximal execution semantics, a special kind of step firing policy (see [25,14]).…”