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First-Order 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 parametrized 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 imposes strong dependencies between the data, poses a nontrivial challenges; in particular if runtime verification has to be performed online, while many events that carry data appear within small time proximities. Towards achieving this goal, it was recently suggested to represent relations over the observed data values, based on BDDs, where data elements are enumerated and then converted into bit vectors. This representation provided a very simple and natural extension of an RV algorithm from propositional to first-order LTL, but more importantly, was shown to contribute to the memory compactness and to the speed, as was demonstrated using a corresponding implementation. We extend here the capabilities of BDD-based RV with the ability to express timing constraints, where the monitored events include (integer) clock values. We show how to efficiently operate on BDDs that represent both relations on (enumerations of) values and time dependencies, as required by the addition of the time constraints. We demonstrate our algorithm with an efficient implementation and provide experimental results.
BDDs for Representing Data in Runtime Verification
A BDD (Boolean Decision Diagram) is a data structure for the compact representation of a Boolean function. It is equipped with efficient algorithms for minimization and for applying Boolean operators. The use of BDDs for representing Boolean functions, combined with symbolic algorithms, facilitated a leap in the capability of model checking for the verification of systems with a huge number of states. Recently BDDs were considered as an efficient representation of data for Runtime Verification (RV). We review here the basic theory of BDDs and summarize their use in model checking and specifically in runtime verification.