  We study the synthesis of inductive half spaces (IHS). These are linear
inequalities that form inductive invariants for Petri nets, capable of
disproving reachability or coverability. IHS generalize classic notions of
invariants like traps or siphons. Their synthesis is desirable for disproving
reachability or coverability where traditional invariants may fail.
  We formulate a CEGAR-loop for the synthesis of IHS. The first step is to
establish a structure theory of IHS. We analyze the space of IHS with methods
from discrete mathematics and derive a linear constraint system closely
over-approximating the space. To discard false positives, we provide an
algorithm that decides whether a given half space is indeed inductive, a
problem that we prove to be coNP-complete. We implemented the CEGAR-loop in the
tool INEQUALIZER and our experiments show that it is competitive against
state-of-the-art techniques.
