Pseudo-random Sequences Generated by Cellular Automata

AbstractGeneration of pseudo random sequences by cellular automata, as well as by hy-brid cellular automata is surveyed. An application to the fast evaluation and FPGAimplementation of some classes of boolean functions is sketched out. Introduction Cellular Automata (CA) is a popular model of finite state mach ine with some pretentionto generality and universality. Pseudo Random Sequences (PRS) on the other hand,have a long history of applications to computational (Monte Carlo sampling, numericalsimulation) and comunications problems (coding theory,streamciphers). In that contextthe popular model is the Linear Feedback Shift Register (LFSR), another model oflinear finite state machine.In the present work we survey the known attempts to generate PRS by CA. Wegive an account of the synthesis of LFSR by arrays of variable CA (known as hybridCA or HCA). We sketch an application to the evaluation of boolean functions in nvariables which are related to cyclic codes of length 2 n − 1. This is aimed at VLSIimplementation, especially by programmable arrays.The material is organized as follows. Section 1 collects defi nitions and basic no-tions on PRS, CA and HCA. Section 2 reviews the synthesis theory of LFSR by HCA.Section 3surveysthe generationofPRS by elementaryCA. Section4 surveysthe gener-ation of PRS by HCA. Section 5 contains the application of synthesis theory to booleanfunctions evaluation.

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