Some Remarks on Codes Defined by Petri Nets

Masami Ito (Department of Mathematics, Kyoto Sangyo University, Japan)

Jürgen Dassow (Otto-von-Guericke-Universität Magdeburg, Fakultät für Informatik, Germany)

Ralf Stiebe (Otto-von-Guericke-Universität Magdeburg, Fakultät für Informatik, Germany)

Abstract: With any Petri net we associated its CPN language which consists of all sequences of transitions which reach a marking with an empty place whereas all proper prefixes of the sequence lead to positive markings. We prove that any CPN language can be accepted by a partially blind multicounter machine, and that any partially blind multicounter language is the morphic image of some CPN language. As a corollary we obtain the decidability of membership, emptiness and finiteness problem for CPN languages. We characterize the very strictly bounded regular languages, which are CPN languages, and give a condition for a Petri net, which ensures that its generated language is regular. We give a dense CPN language and prove that no dense regular language is a CPN language.

Keywords: Petri nets, codes, formal languages

Categories: F.4.2, F.4.3