An encoded problem specifies its instances, size parameter $n$, input array, admissibility promise and correct outputs. It is solvable with exponent $a$ if one finite word-RAM program solves every admissible instance within $C(n+2)^a$ instructions, for a constant $C>0$.

The word length is $b(1+\lfloor\log_2(n+2)\rfloor)$ for one fixed positive integer $b$. Thus words have $\Theta(\log(n+2))$ bits and the program is uniform in $n$. Both $b$ and the program are chosen before the input. Every encoded input entry and the full input length must fit in a word. These fitting conditions are requirements on the algorithm, so a choice of small words cannot discard difficult inputs.

The size parameter counts vertices for APSP and integers for 3-SUM. There is no arbitrary polynomial factor in these time bounds. The additive two makes the same constant bound meaningful at small sizes.