Algebraic nets with flexible arcs

Abstract Algebraic Petri nets as defined by Reisig (Theoret. Comput. Sci. 80 (1991) 1–34.) lack a feature for modelling distributed network algorithms, viz. flexible arcs . In this paper, we equip algebraic Petri nets with flexible arcs and 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 insufficiency: There may be place invariants of the unfolded algebraic Petri net that cannot be expressed as a place invariant of the algebraic Petri net itself. By introducing algebraic system nets along with a more general concept of place invariants we eliminate this insufficiency too. 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 verified in the same style as classical place invariants of algebraic Petri nets.

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