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There has been a considerable amount of interest in recent years in the problem of workflow satisfiability, which asks whether the existence of constraints in a workflow specification makes it impossible to allocate authorized users to each step in the workflow. Recent developments have seen the workflow satisfiability problem (WSP) studied in the context of workflow specifications in which the set of steps may vary from one instance of the workflow to another. This, in turn, means that some constraints may only apply to certain workflow instances. Inevitably, WSP becomes more complex for such workflow specifications. Other approaches have considered the possibility of associating costs with the violation of "soft'' constraints and authorizations. Workflow satisfiability in this context becomes a question of minimizing the cost of allocating users to steps in the workflow. In this paper, we introduce new problems, which we believe to be of practical relevance, that combine these approaches. In particular, we consider the question of whether, given a workflow specification with costs and a "budget'', all possible workflow instances have an allocation of users to steps that does not exceed the budget. We design a fixed-parameter tractable algorithm to solve this problem parameterized by the total number of steps, release points and xor branchings.

Bounded and Approximate Strong Satisfiability in Workflows