Modelling and Verifying Dynamic Properties of Biological Neural Networks in Coq

Formal verification has become increasingly important because of the kinds of guarantees that it can provide for software systems. Verification of models of biological and medical systems is a promising application of formal verification. Human neural networks have recently been emulated and studied as a biological system. Some recent research has been done on modelling some crucial neuronal circuits and using model checking techniques to verify their temporal properties. In large case studies, model checkers often cannot prove the given property at the desired level of generality. In this paper, we provide a model using the Coq Proof Assistant and prove properties concerning the dynamic behavior of some basic neuronal structures. Understanding the behavior of these modules is crucial because they constitute the elementary building blocks of bigger neuronal circuits. By using a proof assistant, we guarantee that the properties are true for any input values, any length of input, and any amount of time. With such a model, there is the potential to detect inactive regions of the human brain and to treat mental disorders. Furthermore, our approach can be generalized to the verification of other kinds of networks, such as regulatory, metabolic, or environmental networks.