# A Robust Genetic Algorithm for Learning Temporal Specifications from Data

arXiv: https://arxiv.org/abs/1711.06202 · HTML: https://mlsanity.com/paper/1711.06202/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Nov 2017.

## Built on by (most cited first, 11 of 11)

- [Learning Model Checking and the Kernel Trick for Signal Temporal Logic on Stochastic Processes](https://mlsanity.com/paper/2201.09928/) (2022)
- [Retrieval-Augmented Mining of Temporal Logic Specifications from Data](https://mlsanity.com/paper/2405.14355/) (2024)
- [Synthesizing Efficiently Monitorable Formulas in Metric Temporal Logic](https://mlsanity.com/paper/2310.17410/) (2023)
- [Learning Temporal Logic Predicates from Data with Statistical Guarantees](https://mlsanity.com/paper/2406.10449/) (2024)
- [Learning Probabilistic Temporal Logic Specifications for Stochastic Systems](https://mlsanity.com/paper/2505.12107/) (2025)
- [Joint Learning of Policy with Unknown Temporal Constraints for Safe Reinforcement Learning](https://mlsanity.com/paper/2305.00576/) (2023)
- [Concurrent Learning of Policy and Unknown Safety Constraints in Reinforcement Learning](https://mlsanity.com/paper/2402.15893/) (2024)
- [Bridging Logic and Learning: Decoding Temporal Logic Embeddings via Transformers](https://mlsanity.com/paper/2507.07808/) (2025)
- [Towards Interpretable Concept Learning over Time Series via Temporal Logic Semantics](https://mlsanity.com/paper/2508.03269/) (2025)
- [Automata Learning of Preferences over Temporal Logic Formulas from Pairwise Comparisons](https://mlsanity.com/paper/2505.18030/) (2025)
- [Guided by Stars: Interpretable Concept Learning Over Time Series via Temporal Logic Semantics](https://mlsanity.com/paper/2511.04244/) (2025)

## Abstract (arXiv)

We consider the problem of mining signal temporal logical requirements from a dataset of regular (good) and anomalous (bad) trajectories of a dynamical system. We assume the training set to be labeled by human experts and that we have access only to a limited amount of data, typically noisy. We provide a systematic approach to synthesize both the syntactical structure and the parameters of the temporal logic formula using a two-steps procedure: first, we leverage a novel evolutionary algorithm for learning the structure of the formula; second, we perform the parameter synthesis operating on the statistical emulation of the average robustness for a candidate formula w.r.t. its parameters. We compare our results with our previous work [{BufoBSBLB14] and with a recently proposed decision-tree [bombara_decision_2016] based method. We present experimental results on two case studies: an anomalous trajectory detection problem of a naval surveillance system and the characterization of an Ineffective Respiratory effort, showing the usefulness of our work.