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"path": "/abs/2605.03306v1",
"publishedAt": "2026-05-06T00:00:00.000Z",
"site": "https://arxiv.org",
"tags": [
"John M. Hitchcock"
],
"textContent": "**Authors:** John M. Hitchcock\n\nLutz (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.",
"title": "Exponential-Size Circuit Complexity is Comeager in Symmetric Exponential Time"
}