Characterization of additive cellular automata (CA) on the basis of the invariant, minimal and characteristic polynomials is reported in this paper. It is shown how a topological parameter, namely depth of the state transition graph of a CA, can be correlated with its characteristic polynomial. The approach is illustrated with reference to the analysis for four example CAs. Combinatorial treatment is formulated for these CAs and expressions are derived for the depth in relation to the number of cells in these CAs.

We introduce a new tool for vector-space theoretic analysis of additive cellular automata (CA). Unlike the analysis based on polynomial algebra, the new tool is shown to be able to deal with hybrid CAs also. A matrix characterizing a CA is formulated, and it is emphasized how group and nongroup CAs are characterized by this matrix. The discussion of the CA properties connected with length reveals considerable universal behavior shown by the CAs.

Advances in microelectronics have made possible design of a wide variety of innovative structures with Very Large Scale Integrated (VLSI) circuits, However, design of complex VLSI circuits within reasonable cost demands two essential pre-requisites—'regularity' and 'simplicity'. These two qualities are inherent to the Cellular Automata (CA) structure. A large variety of physical systems have been simulated using this structure. A survey of all such major developments have been reported in the present paper. It highlights a wide variety of applications which can be tackled by the CA hardware built around VLSI technology. After surveying general CA structure, the paper concentrates on the theory and applications of additive cellular automata as a built-in-self-test structure within a VLSI chip.Indexing terms: Cellular automataVLSI circuits

In this paper we have outlined a comprehensive survey of the currently available Computer Aided Design (CAD) tools to incorporate Design For Testability (DFT) techniques in a VLSI circuit. We have also included a brief report of our expert CAD tool named as DFTEXPERT'. An integrated approach incorporating such a DFT tool with the overall design environment has been also proposed.