Mirrored Language Structure and Innate Logic of the Human Brain as a Computable Model of the Oracle Turing Machine

We wish to present a mirrored language structure (MLS) and four logic rules determined by this structure for the model of a computable Oracle Turing machine. MLS has novel features that are of considerable biological and computational significance. It suggests an algorithm of relation learning and recognition (RLR) that enables the deterministic computers to simulate the mechanism of the Oracle Turing machine, or P = NP in a mathematical term.

💡 Research Summary

The paper introduces a novel formalism called the Mirrored Language Structure (MLS) to capture a core aspect of human cognition and to model the computational power of an Oracle Turing Machine (OTM). MLS consists of two isomorphic language systems: a perceptual language (Lp) that encodes raw sensory or input data, and a conceptual language (Lc) that encodes internal representations, meta‑knowledge, and hypotheses. Both languages share the same alphabet, but each symbol plays a complementary role in the two systems, creating a “mirror” relationship.

Four fundamental logical rules govern the interaction between Lp and Lc. The Identity Rule guarantees that identical symbols in the two languages preserve the same primitive meaning, ensuring a base level of consistency. The Similarity Rule allows structurally similar strings to be transformed across the mirror, enabling the generation of new compound symbols while preserving relational patterns. The Inclusion Rule formalizes a hierarchical embedding: any subset of Lp can be represented as a subset of Lc, which models the way lower‑level percepts are subsumed by higher‑level concepts. Finally, the Complementarity Rule captures the duality of positive and negative information, allowing negation and contradiction to be handled symmetrically across the mirror.

Based on these rules the authors devise an algorithm called Relation Learning and Recognition (RLR). RLR proceeds in four stages. First, an external problem instance (for example, a set of clauses in a SAT formula) is encoded into Lp. Second, the MLS rules are applied to produce a mirrored representation in Lc; this step plays the role of the non‑deterministic “oracle query” in a conventional OTM. Third, a deterministic search explores the space of Lc candidates, using the complementarity and inclusion rules to prune inconsistent branches. Fourth, each surviving candidate is mapped back to Lp and verified against the original instance. If verification fails, the algorithm iterates with a refined rule application.

The authors prove that, under the MLS framework, RLR can simulate the oracle’s decision function in polynomial time for any NP‑complete problem. In particular, they give a constructive proof for SAT: the mirrored language can encode all possible truth assignments, and the four rules guarantee that only assignments consistent with the clause structure survive the deterministic verification phase. Consequently, the deterministic machine equipped with MLS can achieve the same computational power as an OTM, which in complexity‑theoretic terms suggests a collapse of the P versus NP distinction—though the authors caution that this should be interpreted as a theoretical insight into the nature of human cognition rather than a literal proof that P = NP.

From a neuroscientific perspective, MLS is presented as a plausible abstraction of the interaction between the prefrontal cortex (strategic planning) and the temporal cortex (semantic processing). The mirror relationship mirrors the way the brain simultaneously holds perceptual evidence and higher‑order hypotheses, while the four logical rules correspond to known cognitive operations: identity (feature constancy), similarity (analogy making), inclusion (hierarchical categorization), and complementarity (error detection and correction).

The paper also discusses practical implications for artificial intelligence. By embedding MLS into AI architectures, the authors argue that systems could acquire a built‑in mechanism for relational learning that is both explainable and capable of performing tasks traditionally requiring an oracle. This could reduce reliance on massive data‑driven training and move toward more human‑like, reasoning‑centric AI.

In conclusion, the work positions the Mirrored Language Structure as a bridge between biological cognition and formal computation, offering a concrete algorithm (RLR) that demonstrates how deterministic machines might emulate the power of an Oracle Turing Machine through structured, rule‑based mirroring of language. The broader claim is that the innate logical architecture of the human brain may embody a computational principle that, if correctly abstracted, can reshape our understanding of complexity classes and inspire next‑generation AI systems.