Those LUT's have implied indexing internally, I suspect something akin to indexing is essential. Logic functions can be composed using any one of: NAND, NOR, X

Those LUT's have implied indexing internally, I suspect something akin to indexing is essential. Logic functions can be composed using any one of: NAND, NOR, XOR, IMPLY, or other units like full-adders etc. All memory depends on some form of persistance and/or refreshing. Sometimes this is a physical phenomenon like magnetism or electrical compatence or after-glow in a willian's tube. Short-lived effects need to be refreshed. Sometimes there is a feedback loop that continuously sustains latching, such as flip-flops. Magnetic core memory could be less transient than say, a mercury delay line, but needed to be rewriten after being read. But regarding your question, I think so. If it is possible to impliment one with the other (but memory usually has internal indexing).