Results in Workflow Resiliency: Complexity, New Formulation, and ASP Encoding

TL;DR

This paper analyzes the complexity of various workflow resiliency notions, proves new complexity bounds, introduces a new resiliency concept, and demonstrates how to encode these problems in Answer Set Programming for efficient reasoning.

Contribution

It establishes the $ ext{Pi}_2^p$-completeness of static resiliency, introduces one-shot resiliency, and shows how to encode these notions in ASP to leverage modern constraint-solving techniques.

Findings

Static resiliency is $ ext{Pi}_2^p$-complete.

One-shot resiliency remains in the third level of the polynomial hierarchy.

ASP encoding enables practical reasoning for lower-level resiliency notions.

Abstract

First proposed by Wang and Li in 2007, workflow resiliency is a policy analysis for ensuring that, even when an adversarial environment removes a subset of workers from service, a workflow can still be instantiated to satisfy all the security constraints. Wang and Li proposed three notions of workflow resiliency: static, decremental, and dynamic resiliency. While decremental and dynamic resiliency are both PSPACE-complete, Wang and Li did not provide a matching lower and upper bound for the complexity of static resiliency. The present work begins with proving that static resiliency is $\Pi_2^p$-complete, thereby bridging a long-standing complexity gap in the literature. In addition, a fourth notion of workflow resiliency, one-shot resiliency, is proposed and shown to remain in the third level of the polynomial hierarchy. This shows that sophisticated notions of workflow resiliency need not be PSPACE-complete. Lastly, we demonstrate how to reduce static and one-shot resiliency to Answer Set Programming (ASP), a modern constraint-solving technology that can be used for solving reasoning tasks in the lower levels of the polynomial hierarchy. In summary, this work demonstrates the value of focusing on notions of workflow resiliency that reside in the lower levels of the polynomial hierarchy.