标题： Psi图灵机：复杂性障碍和预言机分离的有界内省 显示英文标题

标题： Psi-Turing Machines: Bounded Introspection for Complexity Barriers and Oracle Separations

摘要： 我们引入Psi-Turing机（Psi-TM）：配备常数深度内省接口$ \iota $和显式每步信息预算$ B(d,n)=c\,d\log_2 n $的经典图灵机。 在接口冻结的情况下，我们开发了一个信息论下界工具包：预算计数、$ \Psi $-欺骗和$ \Psi $-法诺，带有工作示例$ L_k $和$ L_k^{\mathrm{phase}} $。 我们证明了一个相对预言机的分离$ P^{\Psi} \neq NP^{\Psi} $和一个严格的深度层次结构，由一个反模拟钩子强化，该钩子在预算制度下通过使用许多对$ \iota_{k-1} $的调用，排除了对$ \iota_k $的多项式模拟。 我们还介绍了两个独立的平台（Psi-决策树和接口约束电路 IC-AC$^{0}$/IC-NC$^{1}$）以及在机器、树和电路之间转移界限的桥梁，具有显式的多项式/对数损失。 该模型在$ \iota $之外保留了经典的计算能力，同时能够关于障碍（相对化；自然证明和证明复杂性的部分/条件进展）做出精确的预言机感知陈述。 目标是一个标准化的最小内省接口，其信息预算明确计算。 显示英文摘要

摘要： We introduce Psi-Turing Machines (Psi-TM): classical Turing machines equipped with a constant-depth introspection interface $ \iota $ and an explicit per-step information budget $ B(d,n)=c\,d\log_2 n $. With the interface frozen, we develop an information-theoretic lower-bound toolkit: Budget counting, $ \Psi $-Fooling, and $ \Psi $-Fano, with worked examples $ L_k $ and $ L_k^{\mathrm{phase}} $. We prove an oracle-relative separation $ P^{\Psi} \neq NP^{\Psi} $ and a strict depth hierarchy, reinforced by an Anti-Simulation Hook that rules out polynomial emulation of $ \iota_k $ using many calls to $ \iota_{k-1} $ under the budget regime. We also present two independent platforms (Psi-decision trees and interface-constrained circuits IC-AC$^{0}$/IC-NC$^{1}$) and bridges that transfer bounds among machine, tree, and circuit with explicit poly/log losses. The model preserves classical computational power outside $ \iota $ yet enables precise oracle-aware statements about barriers (relativization; partial/conditional progress on natural proofs and proof complexity). The aim is a standardized minimal introspection interface with clearly accounted information budgets.