اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدAbstract Processes of Place/Transition Systems
113
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
A well-known problem in Petri net theory is to formalise an appropriate causality-based concept of process or run for place/transition systems. The so-called individual token interpretation, where tokens are distinguished according to their causal history, giving rise to the processes of Goltz and Reisig, is often considered too detailed. The problem of defining a fully satisfying more abstract concept of process for general place/transition systems has so-far not been solved. In this paper, we recall the proposal of defining an abstract notion of process, here called BD-process, in terms of equivalence classes of Goltz-Reisig processes, using an equivalence proposed by Best and Devillers. It yields a fully satisfying solution for at least all one-safe nets. However, for certain nets which intuitively have different conflicting behaviours, it yields only one maximal abstract process. Here we identify a class of place/transition systems, called structural conflict nets, where conflict and concurrency due to token multiplicity are clearly separated. We show that, in the case of structural conflict nets, the equivalence proposed by Best and Devillers yields a unique maximal abstract process only for conflict-free nets. Thereby BD-processes constitute a simple and fully satisfying solution in the class of structural conflict nets.
قيم البحث
اقرأ أيضاً
For one-safe Petri nets or condition/event-systems, a process as defined by Carl Adam Petri provides a notion of a run of a system where causal dependencies are reflected in terms of a partial order. Goltz and Reisig have generalised this concept for
nets where places carry multiple tokens, by distinguishing tokens according to their causal history. However, this so-called individual token interpretation is often considered too detailed. Here we identify a subclass of Petri nets, called structural conflict nets, where no interplay between conflict and concurrency due to token multiplicity occurs. For this subclass, we define abstract processes as equivalence classes of Goltz-Reisig processes. We justify this approach by showing that there is a largest abstract process if and only if the underlying net is conflict-free with respect to a canonical notion of conflict.
We introduce a notion of real-valued reward testing for probabilistic processes by extending the traditional nonnegative-reward testing with negative rewards. In this richer testing framework, the may and must preorders turn out to be inverses. We sh
ow that for convergent processes with finitely many states and transitions, but not in the presence of divergence, the real-reward must-testing preorder coincides with the nonnegative-reward must-testing preorder. To prove this coincidence we characterise the usual resolution-based testing in terms of the weak transitions of processes, without having to involve policies, adversaries, schedulers, resolutions, or similar structures that are external to the process under investigation. This requires establishing the continuity of our function for calculating testing outcomes.
We present Hypersequent Classical Processes (HCP), a revised interpretation of the Proofs as Processes correspondence between linear logic and the {pi}-calculus initially proposed by Abramsky [1994], and later developed by Bellin and Scott [1994], Ca
ires and Pfenning [2010], and Wadler [2014], among others. HCP mends the discrepancies between linear logic and the syntax and observable semantics of parallel composition in the {pi}-calculus, by conservatively extending linear logic to hyperenvironments (collections of environments, inspired by the hypersequents by Avron [1991]). Separation of environments in hyperenvironments is internalised by $otimes$ and corresponds to parallel process behaviour. Thanks to this property, for the first time we are able to extract a labelled transition system (lts) semantics from proof rewritings. Leveraging the information on parallelism at the level of types, we obtain a logical reconstruction of the delayed actions that Merro and Sangiorgi [2004] formulated to model non-blocking I/O in the {pi}-calculus. We define a denotational semantics for processes based on Brzozowski derivatives, and uncover that non-interference in HCP corresponds to Fubinis theorem of double antiderivation. Having an lts allows us to validate HCP using the standard toolbox of behavioural theory. We instantiate bisimilarity and barbed congruence for HCP, and obtain a full abstraction result: bisimilarity, denotational equivalence, and barbed congruence coincide.
This is an extended abstract presenting new results on the topological complexity of omega-powers (which are included in a paper Classical and effective descriptive complexities of omega-powers available from arXiv:0708.4176) and reflecting also some
open questions which were discussed during the Dagstuhl seminar on Topological and Game-Theoretic Aspects of Infinite Computations 29.06.08 - 04.07.08.
This paper revisits the Interaction Abstract Machine (IAM), a machine based on Girards Geometry of Interaction, introduced by Mackie and Danos & Regnier. It is an unusual machine, not relying on environments, presented on linear logic proof nets, and
whose soundness proof is convoluted and passes through various other formalisms. Here we provide a new direct proof of its correctness, based on a variant of Sandss improvements, a natural notion of bisimulation. Moreover, our proof is carried out on a new presentation of the IAM, defined as a machine acting directly on $lambda$-terms, rather than on linear logic proof nets.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
