ScanSTL: Parallel Robustness Evaluation for Signal Temporal Logic

2026-10-05

AI Summary

This study addresses the bottlenecks in Signal Temporal Logic (STL) robustness evaluation, where serial recursion limits parallelism and dense masking increases memory consumption. We propose ScanSTL, a method combining correlated temporal aggregation with parallel scan techniques to achieve exact computation with linear work and logarithmic parallel depth. ScanSTL innovatively employs range extrema for Eventually/Always operators and compact segment representations for Until operators, uniformly supporting bounded intervals and delayed witness guards. Our open-source JAX-based implementation enables automatic differentiation and compiler optimizations. Experiments demonstrate that CPU forward and gradient computations are accelerated by 243× and 104× over STLCG++, respectively, while GPU inference on one million samples achieves millisecond-level latency, significantly improving efficiency in robot plan repair and model predictive control.

Abstract

Repeated evaluation and differentiation of Signal Temporal Logic (STL) robustness can become a computational bottleneck in robot planning and control. Sequential temporal recurrences limit parallelism, while dense masking increases memory requirements. We propose ScanSTL, which combines associative temporal aggregation with parallel scans and ordered block reductions. Eventually and Always use range extrema, while inclusive strong Until composes compact segment representations. A common range engine handles bounded and shifted intervals, including the guards required before delayed Until witnesses. Each exact temporal operator computes complete robustness traces with linear work and storage and logarithmic parallel depth on uniformly sampled finite signals. An open source JAX implementation supports automatic differentiation, batching, and compilation. We compare ScanSTL with STLCG and STLCG++ using CPU and GPU operator benchmarks and nine composed specifications. Across these nine specifications at 512 samples, ScanSTL achieves geometric mean speedups of 243 times for forward evaluation and 104 times for gradient computation over STLCG++ in JAX on the CPU. On an RTX~5090 GPU, ScanSTL evaluates unbounded Until over more than two million samples with median times below 0.1 ms for forward evaluation and 0.25 ms for gradient computation. Simulated escort and patrol experiments with a robot dog further demonstrate faster repair of violating plans and greater solver capacity in model predictive control.

Problem

• Signal Temporal Logic
• Robustness Evaluation
• Parallel Computing
• Robot Planning and Control
• Computational Bottleneck

Innovation

• Signal Temporal Logic
• Parallel Scan
• Robustness Evaluation
• Automatic Differentiation
• JAX