{
  "$type": "site.standard.document",
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  "path": "/report/2026/068",
  "publishedAt": "2026-05-04T18:51:18.000Z",
  "site": "https://eccc.weizmann.ac.il",
  "textContent": "Lutz (1987) introduced resource-bounded category and showed the circuit size class SIZE($\\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.",
  "title": "TR26-068 |  Exponential-Size Circuit Complexity is Comeager in Symmetric Exponential Time | \n\n\tJohn Hitchcock"
}