A Formal Methods Approach to Pattern Synthesis in Reaction Diffusion Systems

TL;DR

This paper introduces a formal methods framework using a novel spatial logic and model checking to detect and synthesize patterns in reaction-diffusion systems, enabling efficient pattern analysis and parameter optimization.

Contribution

It presents a new spatial superposition logic, an efficient learning and detection method, and a combined model checking and optimization framework for pattern synthesis.

Findings

Effective pattern detection on test data sets

Successful synthesis of parameters for desired patterns

Efficient learning of logic formulas from examples

Abstract

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.