We already know that several problems like the inequivalence of P and EXP as well as the undecidability of the acceptance problem and halting problem relativize. However, relativization is a limited tool which cannot separate other complexity classes. What has not been proven explicitly is whether the Turing-recognizability of the acceptance problem relativizes. We will consider an oracle for which R and RE are equivalent; RA = REA, where A is an oracle for the equivalence problem in the class ALL, but not in RE nor co-RE. We will then differentiate between relativization and what we will call "semi-relativization", i.e., separating classes using only the acceptance problem oracle. We argue the separation of R and RE is a fact that only "semi-relativization" proves. We will then "scale down" to the polynomial analog of R and RE, to evade the Baker-Gill-Solovay barrier using "semi-relativized" diagonalization, noting this subtle distinction between diagonalization and relativization. This "polynomial acceptance problem" is then reducible to CIRCUIT-SAT and 3-CNF-SAT proving that these problems are undecidable in polynomial time yet verifiable in polynomial time. "Semi-relativization" does not employ arithmetization to evade the relativization barrier, and so itself evades the algebrization barrier of Aaronson and Wigderson. Finally, since semi-relativization is a non-constructive technique, the natural proofs barrier of Razborov and Rudich is evaded. Thus the separation of R and RE as well as P and NP both do not relativize but do "semi-relativize", evading all three barriers.

翻译：已知诸如P与EXP的不等价性、接受问题与停机问题的不可判定性等多个问题均具有相对化性质。然而，相对化是一种有限工具，无法分离其他复杂性类。尚未被明确证明的是接受问题的图灵可识别性是否具有相对化性质。我们将考虑一个使R与RE等价的神谕：RA = REA，其中A是类ALL中等价问题（但不在RE亦不在co-RE中）的神谕。进而区分相对化与我们称为“半相对化”的方法——即仅使用接受问题神谕进行类分离。我们认为R与RE的分离是仅能通过“半相对化”证明的事实。随后我们将“缩放”至R与RE的多项式类比，通过“半相对化”对角化规避Baker-Gill-Solovay障碍，并指出对角化与相对化之间的微妙差异。该“多项式接受问题”可归约至CIRCUIT-SAT与3-CNF-SAT，从而证明这些问题在多项式时间内不可判定却在多项式时间内可验证。“半相对化”未采用算术化方法规避相对化障碍，因此本身也规避了Aaronson与Wigderson的代数化障碍。最后，由于半相对化是非构造性技术，故亦规避了Razborov与Rudich的自然证明障碍。由此可见，R与RE的分离以及P与NP的分离均不具有相对化性质，但具有“半相对化”性质，从而成功规避了所有三重障碍。