The complexity of propositional linear temporal logics
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We consider the problem of checking whether the operations of an organization conform to a body of regulation. The immediate motivation comes from the analysis of the U.S. Food and Drug Administration regulations that apply to bloodbanks - organizations that collect, process, store, and use donations of blood and blood components. Statements in such regulations convey constraints on operations or sequences of operations that are performed by an organization. It is natural to express these constraints in a temporal logic. There are two important features of regulatory texts that need to be accommodated by a representation in logic. First, the constraints conveyed by regulation can be obligatory (required) or permitted (optional). Second, statements in regulation refer to others for conditions or exceptions. An organization conforms to a body of regulation if and only if it satisfies all the obligations. However, permissions provide exceptions to obligations, indirectly affecting conformance. In this paper, we extend linear temporal logic to distinguish between obligations and permissions, and to allow statements to refer to others. While the resulting logic allows for a direct representation of regulation, evaluating references between statements has high complexity. We discuss an empirically motivated assumption that lets us replace references with tests of lower complexity, leading to efficient trace-checking algorithms in practice.