Effect Of Noise On Long Term Memory In Cellular Automata With Asynchronous Delays Between The Processors

Cellular automata are simple computational models which are capable of exhibiting a wide range of complex dynamical behavior, see [4]. The computation is considered as proceeding synchronously via identical processors at each site on a regular lattice, usually ZP, and the computational rule is assumed to be spatially homogeneous. The interest in studying such automata comes from several points of view. For example,, there is a belief that the complex dynamical behavior exhibited by these automata is a good model for the natural statistical behavior of physical systems such as gases, consisting of large numbers of interacting elements. Another powerful source of reawakened interest in cellular automata has been the development of parallel computational systems employing different types of regular architectures, e.g. [l]. A remarkable property of certain cellular automaton updating rule is that they can admit more than one invariant configuration, representing the ability to maintain long term memory. Further, it is known that there are automata whose long term memory persists under noise. This ability is particularly important from the point of view of the automaton as a computational device, where the initial configuration is the input on which the processors perform their calculations. For the operation to be reliable in a noisy or unreliable environment, we would require the system to remember enough relevant information about its initial configuration over arbitrarily long periods of time, [2]. In this paper we deal with a class of cellular automata called monotonic binary tessellations (MBT’s). Let V er { ( s , t ) E ZP+l: t 2 -tw}, where t w > 0. Given v E V , let V(v) = {v + (ul,tl), . . . ,v + (u,.,t,.)), where U; E ZP and ti < 0, 1 5 i 5 r. An MBT evolves according to the rule