Finding Minimal Unsatisfiable Subsets in Linear Temporal Logic using BDDs

When writing specifications in linear temporal logic, it is common for human error to introduce unsatisfiability into the knowledge base, preventing any reasoning from being performed. Due to the complexity of this problem, such an error is difficult to diagnose by hand. This paper describes an algorithm which can be used to reduce an unsatisfiable PLTL specification into a minimal unsatisfiable subset of the input, thereby removing any formulae which do not directly contribute to the unsatisfiability. Reducing the input in this way allows the source of the error to be more easily diagnosed. The method presented uses binary decision diagrams (BDDs) as an efficient way to store satisfiability information about the input set, and requires only a single call to a BDD-based theorem prover to operate.