Progression- vs Automata-based Anticipatory Monitoring of LTL over Finite Traces (Extended Version)

Dynamic systems in AI are often complex and heterogeneous, so that an internal specification is not accessible and verification techniques such as model checking are not applicable. Monitoring is in such cases an attractive alternative, as it evaluates desirable properties along traces generated by an unknown dynamic system. In this work, we consider anticipatory monitoring of linear-time properties enriched with an arbitrary SMT theory over finite traces (LTLfMT). Anticipatory monitoring in this setting is highly challenging, as the monitoring state depends on both the trace prefix seen so far and all its possible finite continuations. Under reasonable assumptions on the background theory, we present and formally prove the correctness of a novel foundational framework for monitoring properties in an expressive fragment of LTLfMT. The framework combines automata-theoretic methods to handle the temporal aspects of the logic, with automated reasoning techniques to address the first-order dimension. Moreover, we identify for the first time decidable fragments of this monitoring problem that are practically relevant as they combine linear arithmetic with uninterpreted functions, which covers e.g. data-aware business processes and dynamic systems operating over a read-only database. Feasibility is witnessed by a prototype implementation and preliminary evaluation.

Runtime Verification is well suited to autonomous and robotic systems because it checks the behaviour that is actually observed during execution. Its main limitation, however, is that it is usually reactive: the monitor detects a violation only after the system has already performed a bad event. This can be too late in domains where failures are costly or unsafe. In this paper we present PREDICTIVE VARANUS, a two-stage verification pipeline that combines VARANUS, a runtime verifier that uses models written in the process algebra Communicating Sequential Processes (CSP), with predictive runtime verification for LTL. A CSP model is first used as a conformance gate over the observed event trace; the same model is then translated into a Buchi automaton that constrains the futures explored by a predictive LTL monitor. In this way, out-of-model behaviour is rejected immediately, while model-consistent prefixes can be classified as already guaranteeing satisfaction, already forcing violation, or still being inconclusive for the monitored temporal property. We formalise the combined monitor, explain its implementation, and illustrate the approach on a robotic rover for nuclear-store inspection. The case study shows how the combination of CSP validation and predictive LTL can provide earlier verdicts than standard runtime monitoring while reusing an existing design-time CSP model.

We study certified runtime monitoring of past-time signal temporal logic (ptSTL) from visual observations under partial observability. The monitor must infer safety-relevant quantities from images and provide finite-sample guarantees, while being reusable: once trained and calibrated, it should certify any formula in a target fragment without per-formula retraining. For fragments induced by a finite dictionary of temporal atoms, we prove that the semantic basis, the vector of atom robustness scores, is the minimum prediction target within the class of monotone, 1-Lipschitz reusable interfaces: any formula is evaluated by a deterministic decoder derived from the parse tree, and a single conformal calibration pass certifies the entire fragment with no union bound. We also introduce a rolling prediction monitor that predicts only current predicate values and reconstructs temporal history online; this is easier to learn but grows conservative at long horizons. On a pedestrian-crossroad benchmark, rolling achieves tighter certified bounds at short horizons while the semantic-basis monitor is up to 4-times tighter at long horizons. We validate the presented monitors on real-world Waymo driving data, where both monitors satisfy the conformal coverage guarantee empirically.