Symbolic substitution, a parallel processing technique, has been proposed in computing literature to perform fast, carry-free addition of numbers. Several algorithms and corresponding symbolic substitution tables have been developed for addition of two numbers represented in binary, modified signed digit (MSD), and canonical modified signed digit (CMSD) number systems. In this paper, however, w...

We propose a parallel implementation method for optical symbolic substitution logic. The method uses shadow-casting principles for the efficient implementation of fundamental operations required in symbolic substitution logic; namely, image replication, spatial shifting, and combination. The use of light polarization allows for the implementation in parallel of several substitution rules withou...

We generalize the study of symbolic dynamical systems of nite type and ZZ 2 action, and the associated use of symbolic substitution dynamical systems, to dynamical systems with IR 2 action. The new systems are associated with tilings of the plane. We generalize the classical technique of the matrix of a substitution to include the geometrical information needed to study tilings, and we utilize ...

In this chapter, a general nonlinear symbolic LFT modelling framework and its support LFT tools are presented. The modelling approach developed combines the natural modularity and clarity of presentation from LFT modelling with the ease of manipulation from symbolic algebra. It results in an exact nonlinear symbolic LFT that represents an ideal starting point to apply subsequent assumptions and...