Abstract
Some of the fundamental problems concerning cellular automata (CA) are as follows: ― Are linear-time CA (lCA) more powerful than real-time CA (rCA)? ― Are nonlinear-time CA more powerful than linear-time CA? ― Does one-way communication reduce the power of a CA? These question have been open for a long time. In this paper, we address these questions with respect to tally languages in relativised worlds, interpreting timevarying CA (TVCA) as orale machines. We construct ― oracles with separate rCA from lCA and lCA from CA, ― oracle classes under which the CA classes coincide, and ― oracle which leave the CA classes unchanged. Further, with rCA and lCA at the base, we build a hierarchy of relativised CA complexity classes between rCA and CA, and study the dependencies between the classes in this hierarchy
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