A formal methods approach to pattern synthesis in reaction diffusion systems

Aydın Göl, Ebru
Belta, Calin
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.


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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 ...
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Citation Formats
E. Aydın Göl and C. Belta, “A formal methods approach to pattern synthesis in reaction diffusion systems,” 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/33259.