# Bounded and Approximate Strong Satisfiability in Workflows

## TL;DR

This paper introduces a new problem combining workflow satisfiability with costs and budgets, and provides a fixed-parameter tractable algorithm to determine if all workflow instances can meet the budget constraints.

## Contribution

It formulates a novel problem of bounded and approximate satisfiability in workflows and offers an efficient algorithm for its solution.

## Key findings

- The problem of bounded satisfiability is solvable with fixed-parameter tractability.
- The algorithm efficiently handles workflows with varying instances and soft constraints.
- Practical relevance for workflow management with cost and budget considerations.

## Abstract

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.