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Runtime Verification deals with the question of whether a run of a systemadheres to its specification.  This paper studies runtime verification in the presence of partial knowledgeabout the observed run, particularly where input values may not be precise ormay not be observed at all.  We also allow declaring assumptions on the execution which permits to obtainmore precise verdicts also under imprecise inputs.  To this end, we show how to understand a given correctness property as asymbolic formula and explain that monitoring boils down to solving this formulaiteratively, whenever more and more observations of the run are given.  We base our framework on stream runtime verification, which allows to expresstemporal correctness properties not only in the Boolean but also in richerlogical theories.  While in general our approach requires to consider larger and larger sets offormulas, we identify domains (including Booleans and Linear Algebra) for whichpruning strategies exist, which allows to monitor with constant memory (i.e.independent of the length of the observation) while preserving the sameinference power as the monitor that remembers all observations.  We empirically exhibit the power of our technique using a prototypeimplementation under two important cases studies: software for testing caremissions and heart-rate monitoring.

Symbolic Runtime Verification for Monitoring under Uncertainties and Assumptions