Runtime Verification: From Propositional to First-Order Temporal Logic

Runtime Verification is a branch of formal methods concerned with analysis of execution traces for the purpose of determining the state or general quality of the executing system. The field covers numerous approaches, one of which is specification-based runtime verification, where execution traces are checked against formal specifications. The paper presents syntax, semantics, and monitoring algorithms for respectively propositional and first-order temporal logics. In propositional logics the observed events in the execution trace are represented using atomic propositions, while first-order logic allows universal and existential quantification over data occurring as arguments in events. Monitoring of the first-order case is drastically more challenging than the propositional case, and we present a solution for this problem based on BDDs. We furthermore discuss monitorability of temporal properties by dividing them into different classes representing different degrees of monitorability.