2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155872In this paper, we use resource-bounded dimension theory to investigate polynomial size circuits. We show that for every $i\geq 0$, $\Ppoly$ has $i$th order scaled $\pthree$-strong dimension 0. We also show that $\Ppoly^\io$ has $\pthree$-dimension 1/2, $\pthree$-strong dimension 1. Our results improve previous measure results of Lutz (1992) and dimension results of Hitchcock and Vinodchandran (2004).11 pagesComputational ComplexityF.1.3text