What question did this study set out to answer?

The aim is to present a computational architecture designed to solve NP-Hard optimization problems efficiently.

February 16, 2026Open Access

A Generic Low-Level Solver for NP-Hard Instances (N=63) on Commodity 64-Bit Silicon Breaking the Tractability Barrier:

Key Points

The aim is to present a computational architecture designed to solve NP-Hard optimization problems efficiently.
Developed a silicon-native architecture for NP-Hard problems.
Focused on the Hamiltonian Path Problem in directed graphs.
Utilized bitwise operations and hardware-level nondeterminism for algorithm design.
Implemented in C/C++ for deployment on low-memory platforms.
Successfully solved instances of the directed Hamiltonian Path Problem with N=63 in 0.116 seconds.
Exploited real silicon characteristics, such as capacitive noise and L1 cache timing jitter, to escape local optima.
Demonstrated improved performance over conventional software approaches.

Abstract

⚠️ Author’s Note (Language and Tooling Disclosure) The author is a native Spanish speaker. A Large Language Model (LLM) was used exclusively for academic translation, grammar, and formatting, with the sole purpose of communicating the results clearly and efficiently to the international research community.All algorithmic design, implementation, experimental methodology, and results are entirely human-derived and original. Abstract / Description This work presents and validates a silicon-native computational architecture for addressing NP-Hard optimization problems, with a specific focus on the Hamiltonian Path Problem on directed (unilateral) graphs, which constitute one of the most restrictive and computationally demanding problem classes due to asymmetric edge constraints and reduced combinatorial symmetry. Unlike conventional approaches that treat the CPU as a high-level software execution platform, the proposed system models the processor as a physical substrate of logic gates, leveraging strictly bitwise operations and hardware-level nondeterminism arising from real silicon behavior. Key Results • Execution PerformanceDirected Hamiltonian Path instances with N = 63(search space ≈ 10⁸⁷) were solved in 0.116 seconds on a standard commercial mobile processor. • Algorithmic MechanismThe method incorporates hardware race conditions, capacitive noise, and L1 cache timing jitter as controlled entropy sources to facilitate escape from local optima, effectively exploiting non-ideal physical characteristics of silicon rather than abstract randomness. • Problem ClassAll reported results correspond to directed (unilateral) graphs, which are strictly harder than undirected variants due to directionality constraints and reduced path equivalence. • Implementation and PortabilityThe implementation is written in pure C / C-style C++, requires zero dynamic memory allocation, and is suitable for deployment on bare-metal microcontrollers, embedded platforms, and DSP architectures with limited memory availability. Reproducibility and Review The author welcomes independent verification, critical review, and replication attempts.All feedback is appreciated. ✉️ Contact: lctrnc1@gmail.com

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