Theory and Applications of Nonlinear Cellular Automata In VLSI Design A report in partial fulfillment for the Degree of Doctor of Philosophy in Computer Science and Technology

In recent years, Cellular Automata (CA) have been found as an attractive modeling tool for various applications, such as, pattern recognition, image processing, data compression, encryption and specially V LSI design & test. However, for all such applications, a special class of CA, called as linear/additive CA, has been utilized. Since linear CA limit the search space, we may not reach to the best result while searching for the solution to a problem. Nonlinear CA can be an alternative to linear/additive CA for achieving desired solutions in different applications. However, the nonlinear CA are yet to be characterized to fit the design for modeling an application. This thesis targets characterization of the nonlinear CA and utilizes the huge search space of nonlinear CA in developing applications in V LSI design. The interconnection among the CA cells (CA rules) are completely classified for efficient synthesis of reversible cellular automata. An analytical framework is developed to explore the properties of CA rules for 3-neighborhood 1-dimensional CA. It is found that in two-state 3-neighborhood CA, the CA rules fall into 6 groups depending on their potential to form reversible CA. The proposed classification of CA rules enables synthesis of reversible CA in linear time. An efficient design of Pseudo-Random Pattern Generators (PRPGs), based on the nonlinear reversible CA, has also been reported. The performance of the PRPG is evaluated with the battery of diehard tests. It is found that the proposed PRPG is the best among state-of-the-art designs in terms of its randomness quality. The structure of the proposed nonlinear CA based PRPG is utilized to design a cost optimal Test Pattern Generator (TPG) for a CUT (Circuit Under Test). The TPG can avoid patterns prohibited to the CUT and can ensure better fault efficiency compared to existing designs. Further, we exploit the scalable structure of the nonlinear CA in designing TPGs for multiple cores without investing the disparate hardware for the different TPGs. The thesis reports a new BIST (Built-In Self-Test) structure, referred to as the UBIST (Universal BIST ). UBIST can generate any one of the four kinds of test patterns – (i) pseudo-random, (ii) pseudo-exhaustive, (iii) pseudo-random without PPS (Prohibited Pattern Set), and (iv) deterministic. Finally, the nonlinear CA theory is employed to address the issue of data services in cellular mobile network. CA act as an efficient query processor, resulting a hardwired solution to data service. The CA based query processor is found to be twice faster than the state-of-the-art designs with soft computation.