We introduce a new bounded theory RS^1_2 and show that the functions which are Sigma^b_1-representable in it are precisely random functions which can be computed in polynomial time. Concretely, we pass through a class of oracle functions over string, called POR, together with the theory of arithmetic RS^1_2. Then, we show that functions computed by poly-time PTMs are arithmetically characterized by a class of probabilistic bounded formulas.

翻译：我们引入了一个新的约束理论 RS1__2, 并显示Sigma_b__1在其中代表的函数正是随机函数, 可以在多数值时间内计算。 具体地说, 我们通过字符串上的甲骨文函数类别, 称为 POR, 以及算术 RS_1_2的理论。 然后, 我们显示, 由多时 PTM 计算出来的函数, 具有一种概率约束公式的算术特征 。