Petri, C. A., Fundamentals of a theory of asynchronous information flow., in: Proc. IFIP (1963), pp. 386--390.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and sub WRSs 37 C RPOs in edge nets 75 5.3 BRS functors and sub BRSs 39 C.1 Construction 75 5.4 BRSs for scoping and binding 41 C. 2 Validation 78 1 Introduction It is nearly forty years since Petri devised the first substantial model of concurrent computation, and it was a graphical model [26]. Since that time a great many models have been studied. They are not always graphical, but the spatial metaphor is never far away; we often use terms like linkage, location, mobility, and so on. As it was for Petri, it remains a challenge for us to deploy spatial intuition but to retain rigour. ....

Petri, C.A. (1962), Fundamentals of a theory of asynchronous information flow. Proc. IFIP Congress '62, North Holland, pp386--390.

....is about any co operative activity among independent agents even human organizations as well as distributed computing systems. One may even hope that a model of concurrency may attain a breadth of application comparable to physics; Petri expressed such hopes in his seminal work on concurrency [25], and was guided by this analogy. Because the field is indeed so large, we may doubt whether a single unified theory of concurrency is possible; or, even if possible, whether it is good research strategy to seek it so early. Another more modest strategy is to seize upon some single notion which ....

Petri, C.A., Fundamentals of a theory of asynchronous information flow, Proc. IFIP Congress '62, North Holland, pp386--390, 1962.

....logic (PTL) specifications of parameterized synchronous systems using a Vector Addition System With States (VASS) A VASS is a labeled graph in which the vertices represent states and the edges represent transitions between states. A VASS is similar to a Vector Addition System [20] or a Petri Net [21]. Each edge is labeled with a vector. In a VASS representing a parameterized system, the ith entry of a vector label has value a if a nodes are in state i. A model checking algorithm for PTL formulae on VASS models is developed and extended to include certain liveness properties. Both [18] and ....

C. Petri, "Fundamentals of a theory of asynchronous information flow," in Information Processing 62: Proceedings of the

....integers. However we discovered that most of these counts are actually zero in the explored states. To reduce space requirements, we use a sparse representation where we only maintain the non zero local state counts along with the corresponding local states. 5 Related Work Petri nets (PNs) Pet62] were introduced in 1962 by C. A. Petri in his doctoral dissertation. A few years later, Karp and Miller [KM69] independently proposed Vector Addition Systems (VASs) for analyzing the properties of parallel program schemata. Ultimately it was realised that they are mathematically equivalent. An ....

C. Petri. Fundamentals of a theory of asynchronous information flow. In Information Processing 62, Proceedings of the

....computation paradigm can be accounted for or suggest profoundly different perspectives. In this section, we give an overview of the most frequently cited calculi in the foundational study of mobile computation. 3. 1 Calculi for Concurrency Earlier formalisms of concurrency such as Petri Nets [24], CSP [25] and CCS [26] started by considering static connectivity. CCS and CSP provide an abstract model of computation where the basic resources are communication channels and the basic computation is carried out by input, output actions on these channels. Processes are constructed as ....

C. A. Petri. Fundamentals of theory of asynchronous information flow. In Proceedings of IFIP Congress '62, pages 386--390. North Holland, 1962.

....by Elsevier Science B. V. Pratt events while Scott domains with their information ordering consist of states. The duality that NPW found between them is a true categorical duality in the sense that it reverses the morphisms of the respective categories. The transitions and places of a Petri net [18] hint at this duality by being respectively universal and existential: a firing transition involves every incident edge whereas a token passing through a place involves just one path through that place. But it was only relatively recently observed [6,7] that this could be made a true duality in ....

C.A. Petri. Fundamentals of a theory of asynchronous information flow. In Proc. IFIP Congress 62, pages 386--390, Munich, 1962. North-Holland, Amsterdam. Pratt

....of models of concurrent processes have been discussed: branching time, true concurrency, action refinement, disjunctive enabling, conflict, interchangeable state and event based views, real time consistency etc. Various models, having many of these properties have been proposed: Petri nets [Pet62], synchronization trees [Mil80] Mazurkiewicz traces [Maz77] pomsets [Gra81, Pra82] event structures [NPW81, Win86] causal automata [Gun91, Gun92] etc. A careful examination of these models reveals that most of them exhibit concurrent behavior by explicitly inserting concurrency into a ....

C.A. Petri. Fundamentals of a theory of asynchronous information flow. In Proc. IFIP Congress 62, pages 386--390, Munich, 1962. North-Holland, Amsterdam.

....question what meaning might be attached to motion to the left, a feature of both Feynman diagrams and time machines. Conventional automata are asymmetric with respect to time and information: states are vertices (points, 0 cells) while events are edges (line segments, 1 cells) Petri nets [Pet62, Rei85] on the other hand are symmetric: both states and events are vertices of a bipartite graph. The states, called places, are on one side, the transitions are on the other. The edges of a Petri net denote neither states nor events but rather connections between places and transitions. Edges from ....

C.A. Petri. Fundamentals of a theory of asynchronous information flow. In Proc. IFIP Congress 62, pages 386--390, Munich, 1962. North-Holland, Amsterdam.

....tree. The passage from tree to language may be understood as the teasing apart of the paths of the tree, moving all branching points up to the root. 2. 2 True concurrency The second objection to the language interpretation of automata, raised sporadically by various people over a long period [Pet62, Gre75, Maz77, Gra81, NPW81, Pra82], was that the standard model assigned a well defined order to every pair of events (symbol occurrences) in the same string. Besides contradicting relativity, this assumption also contradicts practical engineering issues at all scales, from data skew on parallel signal lines within a single chip ....

C.A. Petri. Fundamentals of a theory of asynchronous information flow. In Proc. IFIP Congress 62, pages 386--390, Munich, 1962. North-Holland, Amsterdam.

....exclusion or mutex. Trace semantics in contrast obtains the meaning of akb by decomposing a and b into their atomic constituents and identifying akb with ab ba for atoms a and b. This distinction was understood as an issue earlier than branching time, the earliest proponents including Petri [Pet62], Greif [Gre75] Mazurkiewicz [Maz77] Grabowski [Gra81] Nielsen, Plotkin, and Winskel [NPW81] and the second author [Pra82] Yet the need for this distinction has proved even more controversial than the need for branching time. Here are our reasons for making this distinction. First, the ....

C.A. Petri. Fundamentals of a theory of asynchronous information flow. In Proc. IFIP Congress 62, pages 386--390, Munich, 1962. North-Holland, Amsterdam.

.... on interaction categories as exemplified by the category SProc [GN95] and of Milner on the calculus [MPW92] and more recently action calculi [Mil93] Moreover its conception of network is more the channel connected modules of Kahn [Kah74] than the alternating places and transitions of Petri [Pet62]. Petri nets express the duality of events and states in terms of a token game played on a bipartite graph. This bipartiteness is the distinguishing feature of Petri nets, resulting in finegrained or move based execution where tokens move alternately between events or transitions and states or ....

C.A. Petri. Fundamentals of a theory of asynchronous information flow. In Proc. IFIP Congress 62, pages 386--390, Munich, 1962. North-Holland, Amsterdam.

....to hand. Milner proposed a logic that took deferred branching into account by abandoning the equation a(b c) ab ac, along with a model, synchronization trees, to serve as counterexamples for this equation. The second objection, raised sporadically by various people over a long period [Pet62, Gre75, Maz77, Gra81, NPW81, Pra82], was that the standard model assigned a well defined order to every pair of events (symbol occurrences) in the same string. Besides contradicting relativity, this assumption also contradicts practical engineering issues at all scales, from data skew on parallel signal lines within a single chip ....

C.A. Petri. Fundamentals of a theory of asynchronous information flow. In Proc. IFIP Congress 62, pages 386--390, Munich, 1962. North-Holland, Amsterdam.

....applications of general morphisms are indicated. 1 Introduction For mathematically oriented people Petri nets are quite complex objects. The following observation should put the above statement into a proper perspective: it took a quarter of a century from the inception of Petri nets, cf. [12], to the definition of their morphisms, cf. 14, 15] Winskel s solution to the problem of defining a suitable notion of Petri net morphism was algebraic. He noticed that Petri nets can be viewed as certain 2 sorted algebras. Consequently, Petri net morphisms defined in [14] are homomorphisms of ....

C. A. Petri. Fundamentals of a theory of asynchronous information flow. In Proc. IFIP'62 . North Holland, 1962.

....Petri nets is discussed. Keywords: Petri nets, Reachability Problem, Equality Problem, Canonical Algebraic Simplification, Grobner Bases Algorithm. 1 Introduction Petri nets are named after A.C. Petri who introduced them in 1962 as formal models for representing and analysing parallel processes, [11, 12]. Since then, they gained increasing importance because their expressive power allows to model, graphically, complex systems with concurrency: parallel, distributed, synchronous 1 This work was done in the framework of the project Parallel Symbolic Computation, No S5302 PHY, supportedby: ....

C. A. Petri. Fundamentals of a theory of asynchronous information flow. In Proc. of IFIP Congress 62., pages 386--390, Amsterdam, 1963. North Holland Publ. Comp.

....for Scientific Research (KBN) grant 8 T11C 018 11 1 Introduction For mathematically oriented people Petri nets are quite complex objects. The following observation should put the above statement into a proper perspective: it took the quarter of a century from the inception of Petri nets, cf. [11] to the definition of their morphisms, cf. 13, 14] The dynamic behaviour of a (marked) Petri net N is always described by means of the case graph of N. The case graphs are nothing else than just transition systems. A (labelled) transition system S is a tuple S = #S, s 0 , A, ##, where S is ....

C. A. Petri. Fundamentals of a theory of asynchronous information flow. In Proc. IFIP'62. North Holland, 1962.

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Petri, C. A., Fundamentals of a theory of asynchronous information flow., in: Proc. IFIP (1963), pp. 386--390.

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C. A. Petri. Fundamentals of a theory of asynchronous information flow. In IFIP Congress, pages 386--390, 1962.

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C. A. Petri. Fundamentals of a theory of asynchronous information flow. In Proc. IFIP, pages 386--390, Amsterdam, 1963. North Holland Publ. Comp.

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C.A. Petri, \Fundamentals of a Theory of Asynchronous Information Flow," Proceedings of IFIP Congress 62, pp. 386-390.

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C.A. Petri, "Fundamentals of a Theory of Asynchronous Information Flow," Proceedings of IFIP Congress 62, pp. 386-390.

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C.A. Petri. Fundamentals of a theory of asynchronous information flow. In Proc. IFIP Congress '62, 1962.

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C.A. Petri. Fundamentals of a theory of asynchronous information flow. In Proc. IFIP Congress '62, 1962.

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C.A. Petri. Fundamentals of a theory of asynchronous information flow. In Proc. IFIP Congress '62, 1962.

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Carl Adam Petri. Fundamentals of a theory of asynchronous information flow. In Proc. of IFIP Congress 62, pages 386--390, Amsterdam, 1963. North Holland Publ. Comp.

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Petri, C.A., Fundamentals of a theory of asynchronous information flow, Proc. IFIP Congress '62, North Holland, pp386--390, 1962.

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