Performance preorder and competitive equivalence

Towards parallelization of concurrent systems

“…(c\b) seems, intuitively, to be more parallel than P (confirmed also by the fact that Q E p P and Q Ç. /P where Q p and Ç j are the performance preorder and the location preorder studied, respectively, in [CGR95,CGR97] and [BCHK92]). Process P also shows that persistency does not hold because, after the exécution of action a, the resulting process is not factorized.…”

“…These are crucial criteria for assessing the merits of a notion of parallelization; hence, the problem we are facing sheds new light on the rôle of truly concurrent semantics, which should be used to check structural properties of Systems, rather than their functionality (already expressed by the interleaving semantics). Indeed, in [Mar96] our parallelization preorder is compared with the location preorder [BCHK92] and with the performance preorder [CGR95,CGR97]. These two preorders are, as ours, bisimulation-based and interleaving bisimulation équivalence preserving.…”

Bisimulation on Speed: A Unified Approach

“…Last, but not least, Corradini et al [5] introduced the ill-timed-but-wellcaused approach for relating processes with respect to speed [1,6]. This approach allows system components to attach local time stamps to actions.…”

“…However, as a byproduct of interleaving semantics, local time stamps may decrease within action sequences exhibited by concurrent processes. These "ill-timed" runs make it difficult to relate the faster-than preorder of [5] to ours.…”

On Bisimilarities Induced by Relations on Actions

“…It is also not clear at the moment, what the right generalization would be, to capture other cost-based preorders and equivalences such as those of [9,3,4,6]. In [7] there is yet another kind of bisimulation which does not fit into this framework, though one component of the pair of relations on actions was used there to define the bisimulation notion.…”