M. Nielsen, G. Plotkin, and G. Winskel (1981), Petri Nets, Event Structures and Domains, Part 1. Theoretical Computer Science 13, 85--108, Elsevier.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....all the computations together in a single structure. An elegant way of achieving this is to use event structures. Event structures are behavioural models of distributed systems in which causality, concurrency and choice (con ict) are represented explicitly. Prime event structures, introduced in [Nielsen et al. 1980], are the simplest type of event structures. They have a rich theory and are closely related to both net systems and domains. Since we deal only with prime event structures in this paper, henceforth we shall simply call them event structures. De nition 3.1 An event structure is a triple ES = E; ....

....; e 8 g is not a con guration because it is not con ict free. We are particularly interested in a restricted subset of con gurations called local con gurations. The notion of a local con guration is based on a simple but crucial observation which lies at the heart of the theory of event structures [Nielsen et al. 1980]. Proposition 3.3 Let ES = E; #) be an event structure and e 2 E. Then #e is a con guration. We now de ne LCES = f#e j e 2 Eg to be the set of local con gurations of the event structure ES = E; #) We do so because a (general) con guration c E can be viewed as a global state of the ....

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Nielsen M, Plotkin G, Winskel G 1980 Petri nets, event structures and domains I, Theor. Comput. Sci. 13,1:86-108.

....event structure semantics, auto concurrency is filtered out from the behaviour of Petri nets. It turns out that this limited event structure semantics for Petri nets is nevertheless a non trivial and conservative extension of the (prime) event structure semantics of 1 safe Petri nets provided in [NPW]. We also show that the strong relationship between prime event structures and 1 safe Petri nets established in a categorical framework in [W3] can be extended to the present setting, provided we restrict our attention to the subclass of Petri nets whose behaviours do not exhibit any ....

....can be smoothly related to local event structures and that similarly prime event structures can be related to UL event structures. Introduction Prime event structures can be used to represent the behaviour of 1 safe Petri nets. This basic result was shown by Nielsen, Plotkin, and Winskel in [NPW]. The universality of their construction which associates a prime event structure with a 1 safe Petri net was later shown by Winskel [W3] in a categorical setting, and in the process provided strong evidence that the construction in [NPW] is not merely an ad hoc translation. An extended ....

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Nielsen, M., Plotkin, G., and Winskel, G., (1981), Petri nets, event structures and domains, Part I, Theoretical Computer Science 13, 85-108.

....representation of the semantics should therefore be of a #ne granularity, be #exible and adaptive in the waycontext a#ects interpretation, and be able to support concurrent activities in the memory storage, retrieval, and indexing process. Our observations suggest the use of process semantics #Nielsen et al. 1981# to characterize the deep semantics of causal narratives. Of special interest to us is the possibility of modeling such processes in structured connectionist models #Feldman 1989#. This work attempts to develop computational models based on a synthesis from process theory, insights from ....

....activation mechanism for inference#. The requirements outlined above suggest a net based model of process semantics. The requirements of learnability and connectionist implementation require us to de#ne special modi#cations to standard concurrency models #suchasPetri Nets and Event Logics #Nielsen et al. 1981##. Wehave done some preliminary investigation of sucha model by using variantofPetri Nets to model aspectual distinctions made by di#erent languages. # Mapping the abstract social domain structures into the relevant concrete spatial and experiential domain structures. This includes the ....

Nielsen, M., G. Plotkin,&G. Winskel. 1981. Petri nets, event structures, and domains, Part I. Theoretical Computer Science 13.

....well supported by the process based approach. Ideally, deter ministic) processes are computations carrying some explicit causal information between transition firings (called events) This originates in an abstract view of processes as posets whose elements are labelled by transitions of the net [27, 35, 36], i.e. as pomsets. Concretely, such computations are represented by suitable, structure preserving maps from a special class of nets into the net under inspection. The role of such maps is to disambiguate different firings of the same transition, and, at the same time, to give a precise account ....

M. Nielsen, G. Plotkin, and G. Winskel (1981), Petri Nets, Event Structures and Domains, Part 1. Theoretical Computer Science 13, 85--108, Elsevier.

....models based on (distributed transitions yielded by) prime event structures from the general class of models. As a result, the axiomatization in Section 2 is complete for the restricted class as well. 2 Using the well known relationships between elementary net systems and prime event structures [NPW] we then show that similar results can also be established for the subclass of models based on elementary net systems. Starting from Section 4 we begin to study subclasses of distributed transition systems and establish a sequence of (predominantly negative) results about subclasses of distributed ....

....in nondeterministic exponential time and the axiom system of Section 2 is sound and complete for this class. We can similarly characterize the state space of elementary net systems. The crucial step is again provided by establishing a step bisimulation. In this case, we can use the work of [NPW] and provide a bijection. Lemma 3.5 Let ES = E; #; OE) be a labelled event structure. Then there exists a labelled net system N = B; E; F; c in ; OE) and a bijection h : TSES TSN such that for every configuration x 2 CES , x u )ES x 0 iff h(x) u )N h(x 0 ) Proof: Set B = B id [ B ....

Nielsen, M., Plotkin, G., and Winskel, G. (1980), Petri nets, event structures and domains I, Theoret. Comput. Sci. 13, 86-108.

....it is well supported by the process based approach. Ideally, deterministic) processes are computations carrying some explicit causal information between transition firings (events) This originates in an abstract view of processes as posets whose elements are labelled by transitions of the net [14,20,21]. Concretely, such computations are represented by suitable, structure preserving maps from a special class of nets into the net under inspection. The role of such maps is to disambiguate different firings of the same transition, and, at the same time, to give a precise account of the causal and ....

M. Nielsen, G. Plotkin, and G. Winskel (1981), Petri Nets, Event Structures and Domains, Part 1. Theoretical Computer Science 13, 85--108, Elsevier.

....representation of the semantics should therefore be of a fine granularity, be flexible and adaptive in the way context affects interpretation, and be able to support concurrent activities in the memory storage, retrieval, and indexing process. Our observations suggest the use of process semantics (Nielsen et al. 1981) to characterize the deep semantics of causal narratives. Of special interest to us is the possibility of modeling such processes in structured connectionist models (Feldman 1989) This work attempts to develop computational models based on a synthesis from process theory, insights from structured ....

....activation mechanism for inference) The requirements outlined above suggest a net based model of process semantics. The requirements of learnability and connectionist implementation require us to define special modifications to standard concurrency models (such as Petri Nets and Event Logics (Nielsen et al. 1981)) We have done some preliminary investigation of such a model by using variant of Petri Nets to model aspectual distinctions made by different languages. ffl Mapping the abstract social domain structures into the relevant concrete spatial and experiential domain structures. This includes the ....

Nielsen, M., G. Plotkin, & G. Winskel. 1981. Petri nets, event structures, and domains, Part I. Theoretical Computer Science 13.

....we seek would be an adjoint functor assigning an abstract denotation to each PT net and preserving certain compositional properties in the assignment. This is exactly what Winskel has done for the subcategory of safe nets (Winskel 1986) In that work which builds on the previous important work (Nielsen et al. 1981) the denotation of a safe net is a Scott domain (Scott 1970) and Winskel shows that there exists a coreflection a particularly nice form of adjunction between the category Dom of (coherent) finitary prime algebraic domains and the category Safe of safe Petri nets. Winskel s coreflection ....

Nielsen, M., Plotkin, G. and Winskel, G. (1981) Petri Nets, Event Structures and Domains, Part 1. Theoretical Computer Science 13, 85--108.

....the space of computations of a net. Our interest, instead, resides on abstract models that capture the mathematical essence of such spaces, possibly axiomatically, roughly in the same way as a prime algebraic domain (or, equivalently, a prime event structure) models the computations of a safe net [9]. The research detailed in [6, 3, 4, 14, 7, 8, 16] identifies such structures as symmetric monoidal categories where objects are states, i.e. multisets of tokens, arrows are processes, and the tensor product and the arrow composition model, respectively, the operations of parallel and ....

....any discussion on related work in the literature. 1991 Mathematics Subject Classification. Primary 68Q55, 68Q10, 68Q05. Key words and phrases. Semantics of Concurrency, Noninterleaving, Processes, Petri Nets. 1. Petri Nets as Monoids The idea of looking at nets as algebraic structures, e.g. [13, 9, 18, 2], has been given an original interpretation in [6] where nets are viewed essentially as internal graphs in categories of sets with structure, and monoidal categories are first used as a suitable semantic framework for them. Concerning the algebraic representation of net computations, along the ....

M. NIELSEN, G. PLOTKIN, AND G. WINSKEL (1981), Petri Nets, Event Structures and Domains, Part 1, Theoretical Computer Science n. 13, 85--108.

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M. Nielsen, G. Plotkin, and G. Winskel (1981), Petri Nets, Event Structures and Domains, Part 1. Theoretical Computer Science 13, 85--108, Elsevier.

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M. Nielsen, G. Plotkin, and G. Winskel (1981), Petri Nets, Event Structures and Domains, Part 1. Theoretical Computer Science 13, 85--108, Elsevier.

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