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.

A Novel Method to Verify Multilevel Computational Models of Biological Systems Using Multiscale Spatio-Temporal Meta Model Checking

“…A formal logic called Linear Spatial Superposition Logic (LSSL) and a corresponding model checking algorithm were introduced in order to encode specifications relative to spatial subdomains along a linear path through the quadtree. More recently both the formal logic and corresponding model checking algorithm were extended by Gol et al [ 87 ] to account for branching paths through quadtrees (Tree Spatial Superposition Logic), and by Haghighi et al [ 88 ] to account for the evolution of the quadtrees over time (SpaTel). Although efficient for pattern detection (and generation) these approaches could be potentially too restrictive for reasoning about general multiscale systems since only one spatial domain is considered and the relationship between consecutive levels/scales is fixed.…”

Monitoring mobile and spatially distributed cyber-physical systems

“…Monitoring spatial-temporal behaviors has started to receive more attention only recently with SpaTeL [13] and SSTL [18]. The Spatial-Temporal Logic (SpaTeL) [13] is the unification of Signal Temporal Logic [15] (STL) and Tree Spatial Superposition Logic (TSSL) introduced in [2, 3] to classify and detect spatial patterns. TSSL reasons over quad trees, spatial data structures that are constructed by recursively partitioning the space into uniform quadrants.…”

On Formal Methods for Collective Adaptive System Engineering. Scalable Approximated, Spatial Analysis Techniques. Extended Abstract.

“…We are not aware of other published work on spatial or spatio-temporal model-checking with the exception of [18,19,20,32].…”

“…However, this comes at the price of a complex formulation of spatial properties, which need to be learned from some template image. The combination of this spatial logic with linear time signal temporal logic, defined with respect to continuous-valued signals, has recently led to the spatio-temporal logic SpaTeL [20].…”