Lutz (1987) introduced resource-bounded category and showed the circuit size class SIZE($\frac{2^n}{n}$) is meager within ESPACE. Li (2024) established that the symmetric alternation class $S^E_2$ contains problems requiring circuits of size $\frac{2^n}{n}$. In this note, we extend resource-bounded category to $S^E_2$ by defining meagerness relative to single-valued $FS^P_2$ strategies in the Banach-Mazur game. We show that Li's $FS^P_2$ algorithm for the Range Avoidance problem yields a winning strategy, proving that SIZE($\frac{2^n}{n}$) is meager in $S^E_2$. Consequently, languages requiring exponential-size circuits are comeager in $S^E_2$: they are typical with respect to resource-bounded category.

翻译：Lutz (1987) 引入资源有界范畴，并证明在ESPACE中电路规模类SIZE($\frac{2^n}{n}$)是稀的。Li (2024) 建立了对称交替类$S^E_2$包含需要规模为$\frac{2^n}{n}$的电路的问题。在本注记中，我们通过在Banach-Mazur博弈中相对于单值$FS^P_2$策略定义稀性，将资源有界范畴扩展到$S^E_2$。我们证明Li针对Range Avoidance问题的$FS^P_2$算法产生了一个获胜策略，从而证实在$S^E_2$中SIZE($\frac{2^n}{n}$)是稀的。因此，在$S^E_2$中需要指数级规模电路的语言是余稀的：它们相对于资源有界范畴而言是典型的。