Petri net

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

There are various packages for creating flowcharts, according to different standards. The most common is UML, for which there are abundant packages for various platforms. See UML article for list. The creation of simple flowcharts on a computer is fairly easy with any vector-based drawing program, but Microsoft Word (versions 97 through 2003) and OpenOffice.org (Draw app) both have specialized tools for making consistent ch ...

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Flowchart, Flowchart - History of use, Flowchart - Creating flowcharts on a computer

Read more here: » Flowchart: Encyclopedia II - Flowchart - Creating flowcharts on a computer

There are two groups distinguished: Acceptors/Recognizers and Transducers. Finite state machine - Acceptors and recognizers. This kind of machine gives a binary output, saying either yes or no to answer whether the input is accepted by the machine or not. The machine can also be described as defining a language, in this case the language defined would contain every word accepted by the machine but none of the rejected ones. All states of the FSM are said to be either accepting or not acceptin ...

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Finite state machine, Finite state machine - Classification, Finite state machine - Acceptors and recognizers, Finite state machine - Transducers, Finite state machine - FSM logic, Finite state machine - Mathematical model, Finite state machine - Optimization, Finite state machine - Implementation, Finite state machine - Hardware applications, Finite state machine - Software applications, Finite state machine - Tools

Read more here: » Finite state machine: Encyclopedia II - Finite state machine - Classification

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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Depending on the type there are several definitions. An acceptor finite state machine is a quintuple <Σ, S, s0, δ, F>, where: Σ is the input alphabet (a finite non empty set of symbols). S is a finite non empty set of states. s0 is an initial state, an element of S. In a Nondeterministic finite state machine, s0 is a set of initial states. δ is the state transition function: δ: S x Σ → S. F is the ...

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Finite state machine, Finite state machine - Classification, Finite state machine - Acceptors and recognizers, Finite state machine - Transducers, Finite state machine - FSM logic, Finite state machine - Mathematical model, Finite state machine - Optimization, Finite state machine - Implementation, Finite state machine - Hardware applications, Finite state machine - Software applications, Finite state machine - Tools

Read more here: » Finite state machine: Encyclopedia II - Finite state machine - Mathematical model

Finite state machine - Hardware applications. In a digital circuit, a FSM may be built using a programmable logic device, a programmable logic controller, logic gates and flip flops or relays. More specifically, a hardware implementation requires a register to store state variables, a block of combinational logic which determines the state transition, and a second block of combinational logic that determines the output of a FSM. < ...

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Finite state machine, Finite state machine - Classification, Finite state machine - Acceptors and recognizers, Finite state machine - Transducers, Finite state machine - FSM logic, Finite state machine - Mathematical model, Finite state machine - Optimization, Finite state machine - Implementation, Finite state machine - Hardware applications, Finite state machine - Software applications, Finite state machine - Tools

Read more here: » Finite state machine: Encyclopedia II - Finite state machine - Implementation

In computer science, the Actor model, first published in 1973 (Hewitt et al. 1973), is a mathematical model of concurrent computation. The Actor model treats “Actors” as the universal primitives of concurrent digital computation: in response to a message that it receives, an Actor can make local decisions, create more Actors, send more messages, and determine how to respond to the next message received. The Actor model has been used both as a framework within which to develop a theor ...

Including:

• Actor model - History
• Actor model - Fundamental concepts
• Actor model - Formal systems
• Actor model - Applications
• Actor model - Models prior to the Actor model
• Actor model - Lambda calculus
• Actor model - Simula
• Actor model - Smalltalk
• Actor model - Petri nets
• Actor model - Message Passing Semantics
• Actor model - The unbounded nondeterminism controversy
• Actor model - Direct communication and asynchrony
• Actor model - Actor creation plus addresses in messages means variable topology
• Actor model - Inherently concurrent
• Actor model - No requirement on order of message arrival
• Actor model - Not sequentiality not buffering not synchrony and not fixed topology
• Actor model - Locality
• Actor model - Compositionality
• Actor model - Behaviors
• Actor model - Relationship to mathematical logic
• Actor model - Migration
• Actor model - Security
• Actor model - Synthesizing addresses of Actors
• Actor model - Why is the Actor model important now?
• Actor model - Actor researchers

Read more here: » Actor model: Encyclopedia - Actor model

To understand this concept, start with a fairly small everyday system. Visualize a set of three dominos lined up in a row with each domino less than a domino's length away from its neighbors, impervious to external environment influences. Once the first domino has toppled, the third domino will topple because the second will topple upon being contacted by the first domino. This could feasibly be shown by a scientist using a co ...

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Deterministic system philosophy, Deterministic system philosophy - An example system, Deterministic system philosophy - Some deterministic systems, Deterministic system philosophy - Some non-deterministic systems, Deterministic system philosophy - Systems with controversial classification, Deterministic system philosophy - The entire universe

Read more here: » Deterministic system philosophy: Encyclopedia II - Deterministic system philosophy - An example system

A classic form of a state diagram for a finite state machine is a directed graph where each edge is a transition between two states For a deterministic finite state machine (DFA), nondeterministic finite state machine (NFA), generalized nondeterministic finite state machine (GNFA), or Moore machine, input is signified on each edge For a Mealy machine, input and output are signified on each edge each vertex is a state For a Moore machine, output is signified on each state In practice, vertices are normally represented by circles and, if ne ...

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State diagram, State diagram - Directed graph, State diagram - Examples, State diagram - Harel statechart, State diagram - UML State diagram, State diagram - Other extensions

Read more here: » State diagram: Encyclopedia II - State diagram - Directed graph

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Diagram, Diagram - Basic diagram types, Diagram - Specific diagram types, Diagram - A, Diagram - B, Diagram - C, Diagram - D, Diagram - E, Diagram - F, Diagram - G, Diagram - H, Diagram - I, Diagram - J, Diagram - K, Diagram - L, Diagram - M, Diagram - N, Diagram - O, Diagram - P, Diagram - R, Diagram - S, Diagram - T, Diagram - U, Diagram - V, Diagram - Y

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The Actor model is about the semantics of message passing. Actor model - The unbounded nondeterminism controversy. Arguably, the first concurrent programs were interrupt handlers. During the course of its normal operation, a computer needed to be able to receive information from outside (characters from a keyboard, packets from a network, etc.). So when the information arrived execution of the computer was "interrupted" and special code called an interrupt handler was called to put the information in a b ...

See also:

Actor model, Actor model - History, Actor model - Fundamental concepts, Actor model - Formal systems, Actor model - Applications, Actor model - Models prior to the Actor model, Actor model - Lambda calculus, Actor model - Simula, Actor model - Smalltalk, Actor model - Petri nets, Actor model - Message Passing Semantics, Actor model - The unbounded nondeterminism controversy, Actor model - Direct communication and asynchrony, Actor model - Actor creation plus addresses in messages means variable topology, Actor model - Inherently concurrent, Actor model - No requirement on order of message arrival, Actor model - Not sequentiality not buffering not synchrony and not fixed topology, Actor model - Locality, Actor model - Compositionality, Actor model - Behaviors, Actor model - Relationship to mathematical logic, Actor model - Migration, Actor model - Security, Actor model - Synthesizing addresses of Actors, Actor model - Why is the Actor model important now?, Actor model - Actor researchers

Read more here: » Actor model: Encyclopedia II - Actor model - Message Passing Semantics

Harel statecharts (developed in 1987 by David Harel) are gaining some more widespread usage since a variant has become part of UML. The diagram type allows to model superstates, concurrent state diagrams and e.g. to model activities as part of a state. Classic state diagrams are so called "or" diagrams, because the machine can only be in one state or the other. With Harel statecharts it is possible to model "and" machines, where a machine is in two or more states at the same time. Thi ...

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State diagram, State diagram - Directed graph, State diagram - Examples, State diagram - Harel statechart, State diagram - UML State diagram, State diagram - Other extensions

Read more here: » State diagram: Encyclopedia II - State diagram - Harel statechart

The Actor model was first published in (Hewitt et al. 1973). The Actor model differs from previous models of computation in that the Actor model was inspired by the laws of physics (physical laws). It was also influenced by Lisp, Simula, capability-based systems, packet switching and early versions of Smalltalk. Development of the Actor model was "motivated by the prospect of highly parallel computing machines consisting of dozens, hundreds or even thousands of independent microproces ...

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Actor model, Actor model - History, Actor model - Fundamental concepts, Actor model - Formal systems, Actor model - Applications, Actor model - Models prior to the Actor model, Actor model - Lambda calculus, Actor model - Simula, Actor model - Smalltalk, Actor model - Petri nets, Actor model - Message Passing Semantics, Actor model - The unbounded nondeterminism controversy, Actor model - Direct communication and asynchrony, Actor model - Actor creation plus addresses in messages means variable topology, Actor model - Inherently concurrent, Actor model - No requirement on order of message arrival, Actor model - Not sequentiality not buffering not synchrony and not fixed topology, Actor model - Locality, Actor model - Compositionality, Actor model - Behaviors, Actor model - Relationship to mathematical logic, Actor model - Migration, Actor model - Security, Actor model - Synthesizing addresses of Actors, Actor model - Why is the Actor model important now?, Actor model - Actor researchers

Read more here: » Actor model: Encyclopedia II - Actor model - History

The Actor model built on previous models of computation. Actor model - Lambda calculus. The lambda calculus of Alonzo Church can be viewed as the earliest message passing programming language. For example the lambda expression below implements a tree data structure when supplied with parameters for a leftSubTree and rightSubTree. When such a tree is given a parameter message "getLeft", it returns leftSubTree and likewise when given th ...

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Actor model, Actor model - History, Actor model - Fundamental concepts, Actor model - Formal systems, Actor model - Applications, Actor model - Models prior to the Actor model, Actor model - Lambda calculus, Actor model - Simula, Actor model - Smalltalk, Actor model - Petri nets, Actor model - Message Passing Semantics, Actor model - The unbounded nondeterminism controversy, Actor model - Direct communication and asynchrony, Actor model - Actor creation plus addresses in messages means variable topology, Actor model - Inherently concurrent, Actor model - No requirement on order of message arrival, Actor model - Not sequentiality not buffering not synchrony and not fixed topology, Actor model - Locality, Actor model - Compositionality, Actor model - Behaviors, Actor model - Relationship to mathematical logic, Actor model - Migration, Actor model - Security, Actor model - Synthesizing addresses of Actors, Actor model - Why is the Actor model important now?, Actor model - Actor researchers

Read more here: » Actor model: Encyclopedia II - Actor model - Models prior to the Actor model

The Actor model adopts the philosophy that everything is an Actor. This is similar to the everything is an object philosophy used by some object-oriented programming languages, but differs in that object-oriented software is typically executed sequentially, while the Actor model is inherently concurrent. An Actor as a computational entity with a behavior such that in response to each message received can concurrently Send a finite number of messages to (other) Actors Create a finite number of new Actors Designate the beha ...

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Actor model, Actor model - History, Actor model - Fundamental concepts, Actor model - Formal systems, Actor model - Applications, Actor model - Models prior to the Actor model, Actor model - Lambda calculus, Actor model - Simula, Actor model - Smalltalk, Actor model - Petri nets, Actor model - Message Passing Semantics, Actor model - The unbounded nondeterminism controversy, Actor model - Direct communication and asynchrony, Actor model - Actor creation plus addresses in messages means variable topology, Actor model - Inherently concurrent, Actor model - No requirement on order of message arrival, Actor model - Not sequentiality not buffering not synchrony and not fixed topology, Actor model - Locality, Actor model - Compositionality, Actor model - Behaviors, Actor model - Relationship to mathematical logic, Actor model - Migration, Actor model - Security, Actor model - Synthesizing addresses of Actors, Actor model - Why is the Actor model important now?, Actor model - Actor researchers

Read more here: » Actor model: Encyclopedia II - Actor model - Fundamental concepts

Over the years, several different formal systems have been developed to permit reasoning about systems in the Actor model. These include: Operational semantics (Greif 1975), (Agha, Mason, Smith, and Talcott 1996) Laws for Actor systems(Baker and Hewitt 1977) Denotational semantics (Clinger 1981) Transition semantics See also:

Actor model, Actor model - History, Actor model - Fundamental concepts, Actor model - Formal systems, Actor model - Applications, Actor model - Models prior to the Actor model, Actor model - Lambda calculus, Actor model - Simula, Actor model - Smalltalk, Actor model - Petri nets, Actor model - Message Passing Semantics, Actor model - The unbounded nondeterminism controversy, Actor model - Direct communication and asynchrony, Actor model - Actor creation plus addresses in messages means variable topology, Actor model - Inherently concurrent, Actor model - No requirement on order of message arrival, Actor model - Not sequentiality not buffering not synchrony and not fixed topology, Actor model - Locality, Actor model - Compositionality, Actor model - Behaviors, Actor model - Relationship to mathematical logic, Actor model - Migration, Actor model - Security, Actor model - Synthesizing addresses of Actors, Actor model - Why is the Actor model important now?, Actor model - Actor researchers

Read more here: » Actor model: Encyclopedia II - Actor model - Formal systems

On the 40th anniversary of the publication of Moore's Law, hardware development is furthering both local and nonlocal massive concurrency. Local concurrency is being enabled by new hardware for 64-bit many-core (Platform 2015 Unveiled at IDF Spring 2005) microprocessors, multi-chip modules, and high performance interconnect. Nonlocal concurrency is being enabled by new hardware for wired and wireless broadband packet switched communications (see Wi-Fi and Ultra wideband). ...

See also:

Actor model, Actor model - History, Actor model - Fundamental concepts, Actor model - Formal systems, Actor model - Applications, Actor model - Models prior to the Actor model, Actor model - Lambda calculus, Actor model - Simula, Actor model - Smalltalk, Actor model - Petri nets, Actor model - Message Passing Semantics, Actor model - The unbounded nondeterminism controversy, Actor model - Direct communication and asynchrony, Actor model - Actor creation plus addresses in messages means variable topology, Actor model - Inherently concurrent, Actor model - No requirement on order of message arrival, Actor model - Not sequentiality not buffering not synchrony and not fixed topology, Actor model - Locality, Actor model - Compositionality, Actor model - Behaviors, Actor model - Relationship to mathematical logic, Actor model - Migration, Actor model - Security, Actor model - Synthesizing addresses of Actors, Actor model - Why is the Actor model important now?, Actor model - Actor researchers

Read more here: » Actor model: Encyclopedia II - Actor model - Why is the Actor model important now?

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 ...

See also:

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

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 ...

See also:

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

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