Subset languages of Petri nets part I: The relationship to string languages and normal forms

Petri Nets, Flat Languages and Linear Arithmetic

We present a method for characterizing the least xed-points of a certain class of Datalog programs in Presburger arithmetic. The method consists in applying some rules of decomposition that transform general sets of computation paths into \\at" ones. We apply the method for expressing the reachability relation of Petri nets as a linear arithmetic formula in order to prove (or disprove) their sa...

The Wadge Hierarchy of Petri Nets omega-Languages

SYNOPS - Generation of Partial Languages and Synthesis of Petri Nets

We present the command line tool SYNOPS. It allows the term-based construction of partial languages consisting of different kinds of causal structures representing runs of a concurrent system: labeled directed acyclic graphs (LDAGs), labeled partial orders (LPOs), labeled stratified directed acyclic graphs (LSDAGs) and labeled stratified order structures (LSOs). It implements region based algor...

The Wadge Hierarchy of Petri Nets ω-Languages

We describe the Wadge hierarchy of the ω-languages recognized by deterministic Petri nets. This is an extension of the celebrated Wagner hierarchy which turned out to be the Wadge hierarchy of the ω-regular languages. Petri nets are more powerful devices than finite automata. They may be defined as partially blind multi-counter automata. We show that the whole hierarchy has height ω 2 , and giv...

Interrelation of Languages of Colored Petri Nets and Some Traditional Languages

The article studies the interrelation of Languages of Colored Petri Nets and Traditional formal languages. The author constructed the graph of Colored Petri Net, which generates L Context-free language. This language may not be modeled using standard Petri Nets [1]. The Venn graph and diagram that the author modified [1], show the interrelation between languages of Colored Petri Nets and some T...