SpaTeL

Abstract

Networked dynamical systems are increasingly used as models for a variety of processes ranging from robotic teams to collections of genetically engineered living cells. As the complexity of these systems increases, so does the range of emergent properties that they exhibit. In this work, we define a new logic called Spatial-Temporal Logic (SpaTeL) that is a unification of signal temporal logic (STL) and tree spatial superposition logic (TSSL). SpaTeL is capable of describing high-level spatial patterns that change over time, e.g., "Power consumption in the northwest quadrant of the city drops below 100 megawatts if the power consumption in the southwest quadrant remains above 200 megawatts for two hours." We present a statistical model checking procedure that evaluates the probability with which a networked system satisfies a SpaTeL formula. We also develop a synthesis procedure that determines system parameters maximizing the average degree of satisfaction, a continuous measure that quantifies how strongly a system execution satisfies a given formula. We demonstrate our algorithms on two systems: a biochemical reaction-diffusion system and a demand-side management system for a smart neighborhood.