First-Order Timed Runtime Verification Using BDDs

Runtime Verification (RV) expedites the analyses of execution traces for detecting system errors and for statistical and quality analysis. Having started modestly, with checking temporal properties that are based on propositional (yes/no) values, the current practice of RV often involves properties that are parameterized by the data observed in the input trace. The specifications are based on various formalisms, such as automata, temporal logics, rule systems and stream processing. Checking execution traces that are data intensive against a specification that requires strong dependencies between the data poses a nontrivial challenge; in particular if runtime verification has to be performed online, where many events that carry data appear within small time proximities. Towards achieving this goal, we recently suggested to represent relations over the observed data values as BDDs, where data elements are enumerated and then converted into bit vectors. We extend here the capabilities of BDD-based RV with the ability to express timing constraints, where the monitored events include clock values. We show how to efficiently operate on BDDs that represent both relations on (enumerations of) values and time dependencies. We demonstrate our algorithm with an efficient implementation and provide experimental results.