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theory additive cellular automata

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Fundamenta Informaticae XXI (2001) 1001–1021  1001  IOS Press Theory of Additive Cellular Automata Niloy Ganguly  Department of Computer Science and Engineering, Indian Instit ute of T echnology , Wara gpur , Ind ia Biplab K Sikdar  Department of Computer Science & Technology , Bengal Engineering College (DU), Botanic Garden,  Howrah,W est Bengal, India P Pal Chaudhuri Flat E4, Block H30, BP Township, Calcutta - 700 094. India. Abstract.  This paper reports the complete characterization of additive cellular automata ( ACA) that employ  xor  and  xnor logic as the next state function. Compared to linear cellul ar automata (LCA) [3], which employs only  xor  logic in its next state function, an  AC A display much wider varieties of state transition behavior and enhanced computing power. An analytical framework is developed to characterize the cyclic v ector subspaces generated by an ACA with refe rence to LC A. It identifies the conditions on which the state transition behavior of an  ACA differs from that of the corresponding LCA and also provides the theoretical analysis of the nature of difference. I. Intr oducti on This work develops the theory of additive cellular automata ( ACA). The theor etica l frame work pro-  posed, prov ides the complete characterization of the cyclic state space generated by an  AC A. An AC A is additive in the sense that it employs affine (also referred to as additive) transformation rather than a linear transformation implemented in a typical linear cellular automata ( LC A). The theory of  LC A  provide s the foundation of the proposed characterization of  AC A. ACA which employ xor and xnor logic to generate its next state function has been specially popular among researchers. Both AC A and its subset  LC A (which employ only xor  logic) have been used to develop a lot of applications in V LSI   and related fields. They have been used to develop pseudo-random Address for correspondence: Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur, India 721302

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