In this paper we give an Immerman's Theorem for real-valued computation. We define circuits operating over real numbers and show that families of such circuits of polynomial size and constant depth decide exactly those sets of vectors of reals that can be defined in first-order logic on R-structures in the sense of Cucker and Meer. Our characterization holds both non-uniformily as well as for many natural uniformity conditions.

翻译：在本文中,我们给出了 Immerman 的理论, 用于实际估价计算。 我们定义了比实际数字操作的电路, 并显示这种多面体大小和持续深度的电路的组合, 确切地决定了Cucker 和 Meer 意义上的R 结构的第一阶逻辑中可以定义的一组真实矢量。 我们的描述既不统一,也符合许多自然统一条件。