Carl Adam Petri

Carl Adam Petri (b. July 12, 1926 in Leipzig) is a German mathematician and computer scientist. He is an Ehrenprofessor (Professor Emeritus) at the University of Hamburg. Petri invented the Petri net in 1962 as part of his dissertation titled: Kommunikation mit Automaten at University of Bonn. It significantly advanced the fields of parallel computing and distributed computing, helped define the modern studies of complex systems and workflow management. He officially retired in 1991. His contributions have been in the br

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An important part of the concept of place is the sociological implication. Place, for a person, may indicate not only location, but position in society, relative wealth, status, and so forth. Place may also refer to an individual's or family's relative status and relationship as compared to other individuals, groups, or families. Elements that turn space into a place are memories, feelings, social connections and the presenc ...

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There are many extensions to Petri nets. Some of them are completely backwards-compatible (e.g. colored Petri nets) with the original Petri net, some add properties that cannot be modelled in the original Petri net (e.g. timed Petri nets). If they can be modelled in the original Peti net, they are not real extensions, instead are convenient ways of showing the same thing, and can be transformed with mathematical formulas back to the original Petri net, without loosing any meaning. Extensions that cannot be transfomed are sometimes very powerful, but usually lack the amount of mathematical tools ...

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Petri net, Petri net - A Formal definition, Petri net - Basic Petri nets, Petri net - Basic mathematical properties, Petri net - Extensions, Petri net - Petri net theory, Petri net - Main Petri net types, Petri net - Subsequent models of concurrency, Petri net - Application areas, Petri net - Programming tools

Read more here: » Petri net: Encyclopedia II - Petri net - Extensions

A Petri net is a tuple (S,T,F,M0,W,K), where (see Desel and Juhás [1]) S is a set of places. T is a set of transitions. F is a set of arcs known as a flow relation. It is subject to the constraint that no ...

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Petri net, Petri net - A Formal definition, Petri net - Basic Petri nets, Petri net - Basic mathematical properties, Petri net - Extensions, Petri net - Petri net theory, Petri net - Main Petri net types, Petri net - Subsequent models of concurrency, Petri net - Application areas, Petri net - Programming tools

Read more here: » Petri net: Encyclopedia II - Petri net - A Formal definition

A Petri net consists of places, transitions and directed arcs. Arcs run between places and transitions - not between places and places or transitions and transitions. The input places of a transition are the places from which an arc runs to it; its output places are those to which an arc runs from it. Places may contain any number of tokens. A distribution of tokens over the places of a net is called a marking. Transitions can fire, that is, execute: when a transition fires, it consumes a token from each of ...

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Petri net, Petri net - A Formal definition, Petri net - Basic Petri nets, Petri net - Basic mathematical properties, Petri net - Extensions, Petri net - Petri net theory, Petri net - Main Petri net types, Petri net - Subsequent models of concurrency, Petri net - Application areas, Petri net - Programming tools

Read more here: » Petri net: Encyclopedia II - Petri net - Basic Petri nets

Subsequent to the invention of Petri nets other models of concurrency, which are based on message passing and feature compositionality (e.g. the Actor model and the various process calculi), have been introduced. Robin Milner and Carl Hewitt have argued that the lack of compositionality is a serious limitation of Petri nets because the deficiency limits modularity. In addition, Hewitt has argued that Petri nets lack locality because input tokens of a transition disappear simultaneously, which limits the realism of the model. He acknow ...

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Petri net, Petri net - A Formal definition, Petri net - Basic Petri nets, Petri net - Basic mathematical properties, Petri net - Extensions, Petri net - Petri net theory, Petri net - Main Petri net types, Petri net - Subsequent models of concurrency, Petri net - Application areas, Petri net - Programming tools

Read more here: » Petri net: Encyclopedia II - Petri net - Subsequent models of concurrency

The theoretical properties of Petri nets have been studied extensively. A marking of a Petri net is reachable if, starting in the initial marking, a sequence of transition firings exists that produces it. A Petri net is bounded if there is a maximum to the number of tokens in its reachable markings. Boundedness is decidable by looking at covering, by constructing the Karp-Miller Tree. Reachability is known to be decidable, however in at least exponential time. All known general algorithms so far, however, employ non-primitive r ...

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Petri net, Petri net - A Formal definition, Petri net - Basic Petri nets, Petri net - Basic mathematical properties, Petri net - Extensions, Petri net - Petri net theory, Petri net - Main Petri net types, Petri net - Subsequent models of concurrency, Petri net - Application areas, Petri net - Programming tools

Read more here: » Petri net: Encyclopedia II - Petri net - Petri net theory

The state of a Petri net is represented as an M vector, where the 1st value of the vector is the amount of tokens in the 1st place of the net, the 2nd is amount of tokens in the 2nd place, and so on. Such a representation fully describles the state of a Petri net. A state-transition list, , which can be shortened to simply is called a firing sequence if each and every transition satisfies the firing criteria (i.e. there are enough tokens in the input for every transition). In this case, the state-transition list of is called a trajectory, and is called reachable from ...

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Petri net, Petri net - A Formal definition, Petri net - Basic Petri nets, Petri net - Basic mathematical properties, Petri net - Extensions, Petri net - Petri net theory, Petri net - Main Petri net types, Petri net - Subsequent models of concurrency, Petri net - Application areas, Petri net - Programming tools

Read more here: » Petri net: Encyclopedia II - Petri net - Basic mathematical properties