Title: Static Analysis of Deterministic Negotiations,
Abstract: Negotiation diagrams are a model of concurrent computation akin to workflow
Petri nets. Deterministic negotiation diagrams, equivalent to the much studied
and used free-choice workflow Petri nets, are surprisingly amenable to
verification. Soundness (a property close to deadlock-freedom) can be decided
in PTIME. Further, other fundamental questions like computing summaries or the
expected cost, can also be solved in PTIME for sound deterministic negotiation
diagrams, while they are PSPACE-complete in the general case.
In this paper we generalize and explain these results. We extend the
classical "meet-over-all-paths" (MOP) formulation of static analysis problems
to our concurrent setting, and introduce Mazurkiewicz-invariant analysis
problems, which encompass the questions above and new ones. We show that any
Mazurkiewicz-invariant analysis problem can be solved in PTIME for sound
deterministic negotiations whenever it is in PTIME for sequential
flow-graphs---even though the flow-graph of a deterministic negotiation diagram
can be exponentially larger than the diagram itself. This gives a common
explanation to the low-complexity of all the analysis questions studied so far.
Finally, we show that classical gen/kill analyses are also an instance of our
framework, and obtain a PTIME algorithm for detecting anti-patterns in
free-choice workflow Petri nets.
Our result is based on a novel decomposition theorem, of independent
interest, showing that sound deterministic negotiation diagrams can be
hierarchically decomposed into (possibly overlapping) smaller sound diagrams.