Predictive Varanus: Combining CSP Conformance Monitoring with Predictive LTL Runtime Verification

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 \emph{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 \emph{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 \emph{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.

Swarms of LLM-assisted autonomous robots are increasingly proposed for cooperative intelligence, surveillance, and reconnaissance (ISR) in contested environments. A growing class of their assurance failures arises not within any single platform but across the swarm: individually-compliant actions compose into a mission-level violation: a prohibited objective split across platforms to evade per-platform lim- its, or a collective budget quietly exceeded. Per-platform guardrails miss these by construction, and contested communications let the violation hide behind lost or delayed evidence. We present a three-tier (platfor- m/squad/mission) compositional runtime-verification framework that de- composes a mission policy into per-agent and cross-agent aspects, aggre- gates per-platform verdicts over a verification-aware messaging fabric, and fuses them with an evidence-aware, two-axis (security x complete- ness) algebra whose provenance names the platforms that jointly trig- gered a violation. Because the fabric makes evidence loss and silence observable, unsupported negative verdicts are downgraded to an explicit unknown rather than reported as mission-wide all-clears. On a simulated ISR mission, an indirect prompt injection that causes real LLM planners to split a prohibited collection task across four platforms is invisible to every per-platform monitor yet detected compositionally with full prove- nance; under an injected fault campaign a best-effort central monitor emits silent false all-clears while the verification-aware fabric emits none

The integration of Formal Verification tools with Large Language Models (LLMs) offers a path to scale software verification beyond manual workflows. However, current methods remain unreliable: without a solid theoretical footing, the refinement process acts as a black box that may oscillate, loop, or diverge. This work bridges this critical gap by developing an LLM-Verifier Convergence Theorem, providing the first formal framework with provable guarantees for termination in multi-stage verification pipelines. We model the interaction not as a generic loop, but as a sequential absorbing Markov Chain comprising four essential engineering stages: \texttt{CodeGen}, \texttt{Compilation}, \texttt{InvariantSynth}, and \texttt{SMTSolving}. We prove that for any non-zero stage success probability ($δ> 0$), the system reaches the \texttt{Verified} state almost surely. Furthermore, because of the sequential nature of the pipeline, we derive a precise latency bound of $\mathbb{E}[n] \leq 4/δ$. We stress-tested this prediction in an extensive empirical campaign comprising over 90,000 trials. The results match the theory with striking consistency: every run reached verification, and the empirical convergence factor clustered tightly around $C_f\approx 1.0$, confirming that the $4/δ$ bound accurately mirrors system behavior rather than serving as a loose buffer. Based on this data, we identify three distinct operating zones -- marginal, practical, and high-performance -- and propose a dynamic calibration strategy to handle parameter drift in real-world environments. Together, these contributions replace heuristic guesswork with a rigorous architectural foundation, enabling predictable resource planning and performance budgeting for safety-critical software.