Hardness Results for the Synthesis of b-bounded Petri Nets

摘要

Synthesis for a type r of Petri nets is the following search problem: For a transition system A, find a Petri net N of type T whose state graph is isomorphic to A, if there is one. To determine the computational complexity of synthesis for types of bounded Petri nets we investigate their corresponding decision version, called feasibility. We show that feasibility is NP-complete for (pure) b-bounded P/T-nets if b ∈ N~+. We extend (pure) b-bounded P/T-nets by the additive group Z_(b+1) of integers modulo (b+1) and show feasibility to be NP-complete for the resulting type. To decide if A has the event state separation property is shown to be NP-complete for (pure) b-bounded and group extended (pure) 6-bounded P/T-nets. Deciding if A has the state separation property is proven to be NP-complete for (pure) b-bounded P/T-nets.