# Static Analysis of Deterministic Negotiations

## TL;DR

This paper demonstrates that static analysis problems for sound deterministic negotiation diagrams, akin to workflow Petri nets, can be efficiently solved in polynomial time by extending classical analysis techniques and introducing a novel decomposition theorem.

## Contribution

It generalizes static analysis results to a concurrent setting, introduces Mazurkiewicz-invariant analysis, and provides a hierarchical decomposition theorem for sound deterministic negotiations.

## Key findings

- Soundness and other analysis problems are PTIME for deterministic negotiations.
- Classical analyses like gen/kill are efficiently solvable within this framework.
- Hierarchical decomposition simplifies analysis of complex negotiation diagrams.

## 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.

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Source: https://tomesphere.com/paper/1704.04190