Constraint Branching in Workflow Satisfiability Problem

Abstract

There has been a considerable interest in recent years in the problem of workflow satisfiability which seeks an allocation of authorised users to every step of the workflow, subject to workflow specification constraints. Unfortunately, the workflow satisfiability problem (WSP) where arbitrary constraints are allowed, is computationally intractable. Wang and Li (2010) were the first to study WSP in the framework of parameterized complexity (with the parameter being the number of steps). Wang and Li proved that the WSP for arbitrary constraints is intractable even in the framework of parameterized complexity, i.e., it is highly unlikely to be fixed-parameter tractable (FPT). Extending the work of Wang and Li (2013) and Crampton et al. (2013), Cohen et al. (2014) introduced the family of user-independent (UI) constraints, which are constraints whose satisfiability does not depend on the identities of the users. Cohen et al. proved that WSP with UI constraints is FPT. Karapetyan et al. (2019) employed these ideas in practically efficient solution methods for WSP with UI constraints, including methods based on SAT and CSP general purpose solvers. While the family of UI constraints includes the most common constraints used in practice, some real-world cases are outside of the family. In this paper, we generalise the concept of authorizations by making them context-dependent and show how to absorb some non-UI constraints into context-dependent authorizations. This allows us to extend algorithms and their implementations developed for WSP with UI constraints to arbitrary constraints. We carry out computational experiments with a general-purpose SAT solver, SAT4J, to test practicality of solving WSP with UI and non-UI constraints using our approach.