# A Formal Methods Approach to Pattern Synthesis in Reaction Diffusion Systems

arXiv: https://arxiv.org/abs/1409.5671 · HTML: https://mlsanity.com/paper/1409.5671/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2014.

## Built on by (most cited first, 3 of 3)

- [Formalizing and Evaluating Requirements of Perception Systems for Automated Vehicles using Spatio-Temporal Perception Logic](https://mlsanity.com/paper/2206.14372/) (2022)
- [Neural Network-based Control for Multi-Agent Systems from Spatio-Temporal Specifications](https://mlsanity.com/paper/2104.02737/) (2021)
- [Learning Spatio-Temporal Specifications for Dynamical Systems](https://mlsanity.com/paper/2112.10714/) (2021)

## Abstract (arXiv)

We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quad-tree of a partitioned image. We show that formulas in this logic can be efficiently learned from positive and negative examples of several types of patterns. We also demonstrate that pattern detection, which is implemented as a model checking algorithm, performs very well for test data sets different from the learning sets. We define a quantitative semantics for the logic and integrate the model checking algorithm with particle swarm optimization in a computational framework for synthesis of parameters leading to desired patterns in reaction-diffusion systems.