N-:)POV: Petri nets
Intro
Petri nets seem to become a hype. Not the worst one, I find. For a long, “Fachgruppe 0.0.1 – Petrinetze und verwandte Systemmodelle” (*) exists. Back in 1990 I tried to visualize a complex IT-system using graphs. Did not work.Therfore, Topic maps and Conceptual graphs are not sufficient. Using quivers, it worked. The more is possible with marked quivers. So a multidigraph is only the visualization of a set endowed with multiple poset-structures. An overview of the current state of usage is (1) in a page of the inventor of coloured Petri nets.
From the beginning of my contact with PNs, I did not primarily focus on concurrency, but on choice. Not only processes, but arbitrary structures can be represented. Almost exclusively therein a PN is similar to an RDF-structure. Lateral to their graphical modeling, as well as calculation (**), competence is a prominent restriction. The original Petri net, a P/T net, is not even equivalent to a Turing machine. By certain extensions, inhibitor arcs as the first applied, PNs are. The essential attribute of being capable to build hierarchies is inherent even to P/T nets.
Although I do not (***) agree with the article in Wikipedia it may serve as a start for an engagement in PNs. Besides cooking and serving Gazpacho, there are
Major n reasons why Petri nets are not located somewhere over the rainbow
- Top-down and bottom-up design is possible.
- UML is (?) the de facto standard for modelling various aspects of software systems in both industry and academia, despite the inconvenience that its current specification is complex and its syntax imprecise.
IICCC, n=many (n > 2)
Footnotes:
- * a kind of SIG
- ** e.g. computing invariants
- *** e.g. a P/T net is not synonymous with a Petri net, as a protozoon is not synonymous with a human (****)
- **** nor are trees and graphs
Tools
Meanwhile there are many (2). Formerly they used mostly a functional programming language, a specific hardware. Nowadays they are mostly using Java, only rarely as a plugin for Eclipse.
The following list of free tools for drawing PNs is not intended to be complete. First has to be mentioned, no doubt, the famous and elaborated cpntools. In alphabetical order, other general purpose PN-drawing-tools include, but are not limited to:
Some are heading in a specific direction (e.g., Snoopy -> biology, chemistry). For sure, most of them will offer the option to export to PNML, in the near future. Maybe, there will be a PNML2, as soon as the issues (already addressed, even identified) with Relax are sorted out. A good basis for compiler-compiler construction which is necessary, as most expect only EBNF (*) as input. With a tool above, I tried to fake the necessary extensions, but i not succee. If time permits, I shll implement it myself.
Footnotes:
Discourse analysis
Regarding terms, discontinuous when you mean at a different place. Nobody being more or less familiar with Mathematics would ever use it this way, as it is widely used there in a totally different sense. To call a certain process linearization establishes yet another provocation. Noticing the term category, I waited for it. Indeed, a bit later the term functor was dropped. So a local tree is merely of depth 1. How bizarre. After reading this, I had diner. Thus, my stomach must be excellent. After diner I continued and came to a discussion about the derivational theory of complexity. This did it.
There is a wealth of theories about grammar. A common notation would improve collaboration. For the grammar at hand, of course, a TAG is nearest. So, it is called YAESPTAG . I “rely on the intelligence of the understanding reader” to analyse a given language according to his own (*). In other words: Once someone dreamt of the figure 7. The next day he/she went to the turf and bet all his/her money for the seventh horse in the seventh race to win. Right, it finished being seventh. or And Noah said to the animals: “Go forth and multiply!” But the adders came to Noah and said: “But we cannot multiply, we are adders.” or “Forget it, adaptively!” (**)
For an ESP, a generative grammar seems appropriate. No phonetic definition, as this is already covered by the Alphabet-song (***). Lexicon and grammatical rules should be independent. An entry in the lexicon can be seen as a labeled tree. Regarding style, a metric can be defined on lexicon and grammar alone or in combination with the occurrence in a corpus, and so on. Whereas the lexicon (****) is given, grammar is sketched as a not so SKOS.
Footnotes:
- * it would, hopefully, not be based on hypergraphs
- ** Of course, these words are used in other places. As context and meaning are different there, a citation would be misleading. BTW, contrary to usual practices, I omit to list references for the articles “a” and “the” and for the equal sign. Even worse: Currently there is no DOI for this blog. Pointed out in the front page, the process at hand is not completed. Let us have a look, no particular direction, then we shall see. (me, according to Beckenbauer et alii)
- *** e.g. in this version
- **** Each entry has assignments of class and articulation. Depending, e.g. verbs a value for valency. Links/Tools/Top
External links
- Usage
- Tools
- How to work. In the end: Nobody expects emd-user documentation.
Proofs are availabe.
