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Coloured Petri Nets
Coloured Petri nets are a backward compatible extension of the mathematical concept of Petri nets. Coloured Petri nets preserve useful properties of Petri nets and at the same time extend the initial formalism to allow the distinction between tokens. Coloured Petri nets allow tokens to have a data value attached to them. This attached data value is called the token color. Although the color can be of arbitrarily complex type, places in coloured Petri nets usually contain tokens of one type. This type is called the color set of the place. Definition 1. A ''net'' is a tuple ''N'' = (''P'', ''T'', ''A'', Σ, ''C'', ''N'', ''E'', ''G'', ''I'' ) where: * ''P'' is a set of ''places''. * ''T'' is a set of ''transitions''. * ''A'' is a set of ''arcs'' In coloured Petri nets, sets of places, transitions and arcs are pairwise disjoint ''P'' ∩ ''T'' = ''P'' ∩ ''A'' = ''T'' ∩ ''A'' = ∅ * Σ is a set of color sets. This set contains all possible colors, operations and functions used ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Backward Compatibility
Backward compatibility (sometimes known as backwards compatibility) is a property of an operating system, product, or technology that allows for interoperability with an older legacy system, or with input designed for such a system, especially in telecommunications and computing. Modifying a system in a way that does not allow backward compatibility is sometimes called " breaking" backward compatibility. A complementary concept is forward compatibility. A design that is forward-compatible usually has a roadmap for compatibility with future standards and products. A related term from programming jargon is hysterical reasons or hysterical raisins (near-homophones for "historical reasons"), as the purpose of some software features may be solely to support older hardware or software versions. Usage In hardware A simple example of both backward and forward compatibility is the introduction of FM radio in stereo. FM radio was initially mono, with only one audio channel represented ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Petri Net
A Petri net, also known as a place/transition (PT) net, is one of several mathematical modeling languages for the description of distributed systems. It is a class of discrete event dynamic system. A Petri net is a directed bipartite graph that has two types of elements, places and transitions. Place elements are depicted as white circles and transition elements are depicted as rectangles. A place can contain any number of tokens, depicted as black circles. A transition is enabled if all places connected to it as inputs contain at least one token. Some sources state that Petri nets were invented in August 1939 by Carl Adam Petri—at the age of 13—for the purpose of describing chemical processes. Like industry standards such as UML activity diagrams, Business Process Model and Notation, and event-driven process chains, Petri nets offer a graphical notation for stepwise processes that include choice, iteration, and concurrent execution. Unlike these standards, Petri nets hav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CPN Tools
CPN Tools is a tool for editing, simulating, and analyzing high-level Petri nets. It supports basic Petri nets plus timed Petri nets and colored Petri nets. It has a simulator and a state space analysis tool is included. CPN Tools is originally developed by the CPN Group at Aarhus University from 2000 to 2010. The main architects behind the tool are Kurt Jensen, Søren Christensen, Lars M. Kristensen, and Michael Westergaard. From the autumn of 2010, CPN Tools is transferred to the AIS group, Eindhoven University of Technology, The Netherlands. CPN Tools comprises two main components, a graphical editor and a backend simulator component. The graphical editor is written in the academic language, BETA, and the simulator backend is written in the Standard ML variant SML/NJ Standard ML of New Jersey (SML/NJ; Standard Meta-Language of New Jersey) is a free and open-source compiler and programming environment for the Standard ML programming language. Aside from its runtime system, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
