11 research outputs found
Metrics for Signal Temporal Logic Formulae
Signal Temporal Logic (STL) is a formal language for describing a broad range
of real-valued, temporal properties in cyber-physical systems. While there has
been extensive research on verification and control synthesis from STL
requirements, there is no formal framework for comparing two STL formulae. In
this paper, we show that under mild assumptions, STL formulae admit a metric
space. We propose two metrics over this space based on i) the Pompeiu-Hausdorff
distance and ii) the symmetric difference measure, and present algorithms to
compute them. Alongside illustrative examples, we present applications of these
metrics for two fundamental problems: a) design quality measures: to compare
all the temporal behaviors of a designed system, such as a synthetic genetic
circuit, with the "desired" specification, and b) loss functions: to quantify
errors in Temporal Logic Inference (TLI) as a first step to establish formal
performance guarantees of TLI algorithms.Comment: This paper has been accepted for presentation at, and publication in
the proceedings of, the 2018 IEEE Conference on Decision and Control (CDC),
to be held in Fontainebleau, Miami Beach, FL, USA on Dec. 17-19, 201
A Metric for Linear Temporal Logic
We propose a measure and a metric on the sets of infinite traces generated by
a set of atomic propositions. To compute these quantities, we first map
properties to subsets of the real numbers and then take the Lebesgue measure of
the resulting sets. We analyze how this measure is computed for Linear Temporal
Logic (LTL) formulas. An implementation for computing the measure of bounded
LTL properties is provided and explained. This implementation leverages SAT
model counting and effects independence checks on subexpressions to compute the
measure and metric compositionally
Formal Verification of Safety Critical Autonomous Systems via Bayesian Optimization
As control systems become increasingly more complex, there exists a pressing need to find systematic ways of verifying them. To address this concern, there has been significant work in developing test generation schemes for black-box control architectures. These schemes test a black-box control architecture's ability to satisfy its control objectives, when these objectives are expressed as operational specifications through temporal logic formulae. Our work extends these prior, model based results by lower bounding the probability by which the black-box system will satisfy its operational specification, when subject to a pre-specified set of environmental phenomena. We do so by systematically generating tests to minimize a Lipschitz continuous robustness measure for the operational specification. We demonstrate our method with experimental results, wherein we show that our framework can reasonably lower bound the probability of specification satisfaction
Learning Model Checking and the Kernel Trick for Signal Temporal Logic on Stochastic Processes
We introduce a similarity function on formulae of signal temporal logic (STL). It comes in the form of a kernel function, well known in machine learning as a conceptually and computationally efficient tool. The corresponding kernel trick allows us to circumvent the complicated process of feature extraction, i.e. the (typically manual) effort to identify the decisive properties of formulae so that learning can be applied. We demonstrate this consequence and its advantages on the task of predicting (quantitative) satisfaction of STL formulae on stochastic processes: Using our kernel and the kernel trick, we learn (i) computationally efficiently (ii) a practically precise predictor of satisfaction, (iii) avoiding the difficult task of finding a way to explicitly turn formulae into vectors of numbers in a sensible way. We back the high precision we have achieved in the experiments by a theoretically sound PAC guarantee, ensuring our procedure efficiently delivers a close-to-optimal predictor
Temporal Logic Specification-Conditioned Decision Transformer for Offline Safe Reinforcement Learning
Offline safe reinforcement learning (RL) aims to train a constraint
satisfaction policy from a fixed dataset. Current state-of-the-art approaches
are based on supervised learning with a conditioned policy. However, these
approaches fall short in real-world applications that involve complex tasks
with rich temporal and logical structures. In this paper, we propose temporal
logic Specification-conditioned Decision Transformer (SDT), a novel framework
that harnesses the expressive power of signal temporal logic (STL) to specify
complex temporal rules that an agent should follow and the sequential modeling
capability of Decision Transformer (DT). Empirical evaluations on the DSRL
benchmarks demonstrate the better capacity of SDT in learning safe and
high-reward policies compared with existing approaches. In addition, SDT shows
good alignment with respect to different desired degrees of satisfaction of the
STL specification that it is conditioned on
Tools and Algorithms for the Construction and Analysis of Systems
This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems