Matching trace patterns with regular policies

We consider policies that are described by regular expressions, finite automata, or formulae of linear temporal logic (LTL). Such policies are assumed to describe situations that are problematic, and thus should be avoided. Given a trace pattern u, i.e., a sequence of action symbols and variables, were the variables stand for unknown (i.e., not observed) sequences of actions, we ask whether u potentially violates a given policy L, i.e., whether the variables in u can be replaced by sequences of actions such that the resulting trace belongs to L. We also consider the dual case where the regular policy L is supposed to describe all the admissible situations. Here, we want to know whether u always adheres to the given policy L, i.e., whether all instances of u belong to L. We determine the complexity of the violation and the adherence problem, depending on whether trace patterns are linear or not, and on whether the policy is assumed to be fixed or not.