A System, Signals and Identification Toolbox in Mathematica with Symbolic Capabilities

In this contribution we describe a signals, systems and identification toolbox for the symbolic computation system Mathematica. The toolbox provides functionality for computation of systems and signal theoretic ranging from frequency responses, zeros and poles to signal spectra and spectral factorizations. It also includes a wide range of identification algorithms ranging from spectral analysis to subspace and prediction error identification of models for non-linear systems. The symbolic capabilities of {\em Mathematica} are used to allow the user to construct very general model structures, and for pre-processing, such as gradient calculations, when optimizing the parameters in such structures

Formal Modeling of Connectionism using Concurrency Theory, an Approach Based on Automata and Model Checking

This paper illustrates a framework for applying formal methods techniques, which are symbolic in nature, to specifying and verifying neural networks, which are sub-symbolic in nature. The paper describes a communicating automata [Bowman & Gomez, 2006] model of neural networks. We also implement the model using timed automata [Alur & Dill, 1994] and then undertake a verification of these models using the model checker Uppaal [Pettersson, 2000] in order to evaluate the performance of learning algorithms. This paper also presents discussion of a number of broad issues concerning cognitive neuroscience and the debate as to whether symbolic processing or connectionism is a suitable representation of cognitive systems. Additionally, the issue of integrating symbolic techniques, such as formal methods, with complex neural networks is discussed. We then argue that symbolic verifications may give theoretically well-founded ways to evaluate and justify neural learning systems in the field of both theoretical research and real world applications