Runtime verification of real-time event streams under non-synchronized arrival

We study the problem of online runtime verification of real-time event streams. Our monitors can observe concurrent systems with a shared clock, but where each component reports observations as signals that arrive to the monitor at different speeds and with different and varying latencies. We start from specifications in a fragment of the TeSSLa specification language, where streams (including inputs and final verdicts) are not restricted to be Booleans but can be data from richer domains, including integers and reals with arithmetic operations and aggregations. Specifications can be used both for checking logical properties and for computing statistics and general numeric temporal metrics (and properties on these richer metrics). We present an online evaluation algorithm for the specification language and a concurrent implementation of the evaluation algorithm. The algorithm can tolerate and exploit the asynchronous arrival of events without synchronizing the inputs. Then, we introduce a theory of asynchronous transducers and show a formal proof of the correctness such that every possible run of the monitor implements the semantics. Finally, we report an empirical evaluation of a highly concurrent Erlang implementation of the monitoring algorithm.