Sampling of Shape Expressions

TL;DR

This paper presents a systematic sampling method for shape expressions in cyber-physical systems, combining automata sampling and Monte Carlo techniques to explore complex temporal patterns and parameter spaces.

Contribution

It introduces a novel approach that integrates uniform automata sampling with hit-and-run Monte Carlo methods for shape expression analysis.

Findings

Effective exploration of temporal pattern automata

Enhanced sampling of multi-dimensional parameter spaces

Improved visualization and testing of CPS behaviors

Abstract

Cyber-physical systems (CPS) are increasingly becoming driven by data, using multiple types of sensors to capture huge amounts of data. Extraction and characterization of useful information from big streams of data is a challenging problem. Shape expressions facilitate formal specification of rich temporal patterns encountered in time series as well as in behaviors of CPS. In this paper, we introduce a method for systematically sampling shape expressions. The proposed approach combines methods for uniform sampling of automata (for exploring qualitative shapes) with hit-and-run Monte Carlo sampling procedures (for exploring multi-dimensional parameter spaces defined by sets of possibly non-linear constraints). We study and implement several possible solutions and evaluate them in the context of visualization and testing applications.