Flexibility in Algebraic Nets

Algebraic Petri nets as deened by Reisig 15] lack a feature for modelling distributed network algorithms, viz. exible arcs. In this paper we equip algebraic Petri nets with exible arcs and we call the resulting extension algebraic system nets. We demonstrate that algebraic system nets are better suited for modelling distributed algorithms. Besides this practical motivation for introducing algebraic system nets there is a theoretical one. The concept of place invariants introduced along with algebraic Petri nets has a slight insuuciency: There may be place invariants of an unfolded algebraic Petri net which cannot be expressed as a place invariant of the algebraic Petri net itself. By introducing algebraic system nets along with a slightly more general concept of place invariants we also eliminate this insuuciency. Moreover, we generalize the concept of place invariants which we call simulations. Many well-known concepts of Petri net theory such as siphons, traps, modulo-invariants, sur-invariants and sub-invariants are special cases of a simulation. Still, a simulation can be veriied in the same style as classical place invariants of algebraic Petri nets.