A Formal Methods Approach to Pattern Recognition and Synthesis in Reaction Diffusion Networks

Bartocci E., AYDIN GÖL E., Haghighi I., Belta C.

IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS, vol.5, no.1, pp.308-320, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 5 Issue: 1
  • Publication Date: 2018
  • Doi Number: 10.1109/tcns.2016.2609138
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.308-320
  • Keywords: Formal verification and synthesis, pattern recognition and formation, reaction diffusion networks
  • Middle East Technical University Affiliated: Yes


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.