TR01-01 (2001) – On Concurrency-Degrees for Petri Nets

Cristian Vidrascu, Toader Jucan

Petri nets are a mathematical model used for the specification and the analysis of parallel/distributed systems. It is very important to introduce a measure of concurrency for parallel/distributed systems, so that we can speak about what is the meaning of the fact that in the system S1 the concurrency is greater than in the system S2. The notion of concurrency-degrees for Petri nets has been formulated in [TJD93], and for jumping Petri nets in [JuV00]. But these definitions have a drawback: they take into consideration only distinct transitions which can fire simultaneously; thus, they ignore the auto-concurrency, i.e. the case of a transition fireable simultaneously with itself at a marking. In this paper we give a more general definition of concurrency-degree for Petri nets and for jumping Petri nets, which takes into consideration also the auto-concurrency, for replacing the old definitions which ignore the auto-concurrency. Moreover, we show how we can compute these more general concurrency-degrees.

Bibtex

@TechReport{cdpn,
  author = 	 {C. Vidrascu and T. Jucan},
  title = 	 {On Concurrency-Degrees for Petri Nets},
  institution =  {University ``A.I.Cuza'' of Iac{s}i, Faculty of
Computer Science},
  year = 	 {2001},
  number = 	 {TR 01-01},
  note = 	 {URL:http://www.infoiasi.ro/~tr/tr.pl.cgi}
}