Nielsen M, Rozenberg G, Thiagarajan P S 1990 Behavioural notions for elementary net systems, Distr. Comput. 4,1:45-57.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....We will restrict our attention to 1 safe net systems, in which every reachable marking M puts at most one token on each place, and thus can be identified by the subset of places that contain a token, i.e. M P . In the last years, 1 safe net systems have become a significant model [CEP95] In [NRT90] it has been shown that an instance of 1 safe nets, called Elementary Net Systems, correspond to other models of concurrency, such as (Mazurkiewicz) traces and prime event structures. They can naturally be interpreted as a synchronised product of several finite automata, and thus are frequently ....

M. Nielsen, G. Rozenberg, and P.S. Thiagarajan, Behavioural notions for elementary net systems, Distributed Computing 4 (1990), no. 1, 45--57.

....We will restrict our attention to 1 safe net systems, in which every reachable marking M puts at most one token on each place, and thus can be identified by the subset of places that contain a token, i.e. M P . In the last years, 1 safe net systems have become a significant model [CEP95] In [NRT90] it has been shown that an instance of 1 safe nets, called Elementary Net Systems, correspond to other models of concurrency, such as (Mazurkiewicz) traces and prime event structures. They can naturally be interpreted as a synchronised product of several finite automata, and thus they are ....

M. Nielsen, G. Rozenberg, and P.S. Thiagarajan, Behavioural notions for elementary net systems, Distributed Computing 4 (1990), no. 1, 45--57.

....We will restrict our attention to 1 safe net systems, in which every reachable marking M puts at most one token on each place, and thus can be identified by the subset of places that contain a token, i.e. M P . In the last years, 1 safe net systems have become a significant model [CEP95] In [NRT90] it has been shown that an instance of 1 safe nets, called Elementary Net Systems, correspond to other models of concurrency, such as (Mazurkiewicz) traces and prime event structures. They can naturally be interpreted as a synchronised product of several finite automata, and thus are frequently ....

M. Nielsen, G. Rozenberg, and P.S. Thiagarajan, Behavioural notions for elementary net systems, Distributed Computing 4 (1990), no. 1, 45--57.

....the correspondence we establish is not functorial. Nevertheless, we think that this is an interesting result, since it provides a natural and unified account of the algebraic, the processoriented, and the denotational views of net semantics. We remark that a similar approach has been followed in [16] in the case of elementary net systems a particular class of safe nets without self looping transitions for unfoldings and non sequential processes. To conclude this discussion, we would like to mention that the correspondence of semantics presented here can be lifted smoothly to infinite ....

M. Nielsen, G. Rozenberg, and P.S. Thiagarajan. Behavioural Notions for Elementary Net Systems. Distributed Computing, n. 4, pp. 45--57, 1990.

....though both have similar representations; for instance, finite Place Transition nets can have iniinite state spaces, but finite 1 safe nets cannot. The advantages of 1 safe nets are numerous, and they have become a significant model. Several semantics can be smoothly defined for 1 safe nets [4][31], but are however di#cult to extend to Place Transition nets. Nielsen, Rozenberg and Thiagarajan [36] 31] have shown that a model of 1 safe nets, called Elementary Net Systems, has strong categorical connections with many other models of concurrency, such as event structures (another good ....

....state spaces, but finite 1 safe nets cannot. The advantages of 1 safe nets are numerous, and they have become a significant model. Several semantics can be smoothly defined for 1 safe nets [4] 31] but are however di#cult to extend to Place Transition nets. Nielsen, Rozenberg and Thiagarajan [36][31] have shown that a model of 1 safe nets, called Elementary Net Systems, has strong categorical connections with many other models of concurrency, such as event structures (another good reference is [39] Finally, 1 safe nets are closer to classical language theory, and can be interpreted as a ....

Mogens Nielsen, Grzegorz Rozenberg, and P.S. Thiagarajan. Behavioural notions for elementary net systems. Distributed Computing, 4(1):45-57, 1990.

....object c 2 C, DP [ maps the marked net (N;u N ) to (u N ; DP [N] PreOrd is the category of preorders, h # i is the comma category functor (c;C) 7 hc#Ci, and L F returns the finite configurations of prime event structures ordered by inclusion. We remark that an analogous result is proved in (Nielsen et al. 1990) in the case of elementary net systems a particular class of safe nets without self looping transitions. We think that this is an interesting result, since it provides a unified account of the algebraic, the process oriented, and the denotational views of net semantics. Moreover, it shows that ....

Nielsen, M., Rozenberg, G. and Thiagarajan, P.S. (1990) Behavioural Notions for Elementary Net Systems.

....net (N, uN ) to (uN , DP[N ] Cat is the category of the categories, # # # is the comma category functor (c, C) ## #c#C# (see Definition 3.15) and LF returns the finite configurations of prime event structures ordered by inclusion. We remark that a similar approach has been followed in [20] in the case of elementary net systems a particular class of safe nets without self looping transitions for unfoldings and non sequential processes. It should be stressed that our concern here is at the level of a single net, which means that the diagram above is defined only at the object ....

....N is a PT net and uN # S # N is the initial marking. The formalization of nets as graphs with additional algebraic structure on the set of nodes suggests considering graph morphisms which respect such a structure as morphisms of nets; alternative definitions have been investigated in, e.g. [20, 3, 4, 18]. Definition 1.3 (PT Nets Morphisms) A morphism of PT nets f from N 0 to N 1 consists of a pair of functions #f t , f p #, where f t : TN0 # TN1 and f p : S # N0 # S # N1 is a monoid homomorphism, such that #f t , f p # respects source and target, i.e. it makes the two diagrams ....

M. Nielsen, G. Rozenberg, and P.S. Thiagarajan. Behavioural Notions for Elementary Net Systems. Distributed Computing, n. 4, pp. 45--57, Springer-Verlag, New York, 1990.

....even though both have similar representations; for instance, finite Place Transition nets can have infinite state spaces, but finite 1 safe nets cannot. The advantages of 1 safe nets are numerous, and they have become a significant model. Several semantics can be smoothly defined for 1 safe nets [3, 28], but are however difficult to extend to Place Transition nets. Nielsen, Rozenberg and Thiagarajan [33, 28] have shown that a model of 1 safe nets, called Elementary Net Systems, has strong categorical connections with many other models of concurrency, such as event structures (another good ....

....state spaces, but finite 1 safe nets cannot. The advantages of 1 safe nets are numerous, and they have become a significant model. Several semantics can be smoothly defined for 1 safe nets [3, 28] but are however difficult to extend to Place Transition nets. Nielsen, Rozenberg and Thiagarajan [33, 28] have shown that a model of 1 safe nets, called Elementary Net Systems, has strong categorical connections with many other models of concurrency, such as event structures (another good reference is [35] Finally, 1 safe nets are closer to classical language theory, and can be interpreted as a ....

Mogens Nielsen, Grzegorz Rozenberg, and P.S. Thiagarajan. Behavioural notions for elementary net systems. Distributed Computing, 4(1):45--57, 1990.

....that we have dealt with in this paper are closely related to each other. We have described how labelled net systems and labelled event structures give rise to dts s in a natural way. A strong relationship also exists between elementary net systems and prime event structures ( Nielsen et al. 1980] [Nielsen et al. 1990]) The connection between csa s and event structures is described in [Lodaya et al. 1989b] By establishing formal connections between models in this manner, we can translate results obtained using one class of models to other classes. As for the logics that we have described here, the main results ....

Nielsen M, Rozenberg G, Thiagarajan P S 1990 Behavioural notions for elementary net systems, Distr. Comput. 4,1:45-57.

....(s; a; s 0 ) denoting that the system can perform the (single) action a at the state s and, as a result, enter the state s 0 . Thus it is the so called interleaved behaviours of distributed systems that are represented by such transition systems. It has been observed by various researchers [BC, DM, NRT] that concurrency can be more explicitly represented by enriching the transition relation, for instance by putting more information on the labels of transitions. One of the simplest ways of doing so is to consider transitions of the form (s; u; s 0 ) where u is a finite set of actions. The idea ....

.... Sigma and are all at most countable. We have chosen the strong definition of dts s after examining a number of partial order models of distributed systems. We will consider two such models: event structures and net systems. Our presentation will be brief and the interested reader is referred to [Win, Thi, NRT] for more background material. A prime event structure is a triple ES = E; #) where ffl E is a set of event occurrences ffl E Theta E is a partial ordering relation called the causality relation. ffl # E Theta E is an irreflexive and symmetric relation called the conflict relation. ffl ....

Nielsen, M., Rozenberg, G., and Thiagarajan, P.S. (1990), Behavioural notions for elementary net systems, Distr. Comput. 4, 45-57.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC