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In my previous understanding, if a RAM program requires $T$ read/write operations to memory during its execution, then the runtime of this RAM program is $T$. However, as I have read some literature, I have realized that my understanding may not be correct.

For instance, there is a paper mentioning a $T$-time RAM program that can be transformed into a circuit of size $O(T^3 \log T)$. This is a result from complexity theory. However, if $T$ only represents the number of memory read/write operations, then this result is evidently incorrect because the size of the circuit when not performing read/write operations may be very large.

Therefore, what exactly $T$ represents? Thank you, everyone.

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    $\begingroup$ This uses "T-time RAM program". By my reading of it and one of it's references, they both use "T-time" to mean time (a fixed) polynomial in T (for the side doing the bulk of the computation), not proportional to T. I don't make this an answer because the paper mentioned in the second paragraph remains unknown, and it may use different definitions. $\endgroup$
    – fgrieu
    Commented Nov 20, 2023 at 16:44

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