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E. Bartocci, E. Aydin Gol, I. Haghighi, C. Belta:
"A Formal Methods Approach to Pattern Recognition and Synthesis in Reaction Diffusion Networks";
IEEE Transactions on Control of Network Systems, 5 (2018), 1; 308 - 320.

We introduce a formal framework for specifying, detecting, and generating spatial patterns in reaction diffusion networks. Our approach is based on a novel spatial superposition logic, whose semantics is defined over the quad-tree representation of a partitioned image. We demonstrate how to use rule-based classifiers to efficiently learn spatial superposition logic formulas for several types of patterns from positive and negative examples. We implement pattern detection as a model-checking algorithm and we show that it achieves very good results on test data sets which are different from the training sets. We provide a quantitative semantics for our logic and we develop computational framework where our quantitative model-checking algorithm works in synergy with a particle swarm optimization technique to synthesize the parameters leading to the formation of desired patterns in reaction diffusion networks.

http://dx.doi.org/10.1109/TCNS.2016.2609138

http://publik.tuwien.ac.at/files/publik_253798.pdf