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Assembly Theory of Binary Messages

- Subjects: Physics, Mathematical
- |
- Submitted by:

- assembly theory
- emergent dimensionality
- shortest addition chains
- P versus NP problem
- mathematical physics

Video Introduction

This video is adapted from 10.3390/math12101600

Using assembly theory, researchers investigate the assembly pathways of binary strings (bitstrings) of length N formed by joining bits present in the assembly pool and the bitstrings that entered the pool as a result of previous joining operations. Researchers show that the bitstring assembly index is bounded from below by the shortest addition chain for N, and researchers conjecture about the form of the upper bound. Researchers define the degree of causation for the minimum assembly index and show that, for certain N values, it has regularities that can be used to determine the length of the shortest addition chain for N. Researchers show that a bitstring with the smallest assembly index for N can be assembled via a binary program of a length equal to this index if the length of this bitstring is expressible as a product of Fibonacci numbers. Knowing that the problem of determining the assembly index is at least NP-complete, researchers conjecture that this problem is NP-complete, while the problem of creating the bitstring so that it would have a predetermined largest assembly index is NP-hard. The proof of this conjecture would imply P ≠ NP since every computable problem and every computable solution can be encoded as a finite bitstring. The lower bound on the bitstring assembly index implies a creative path and an optimization path of the evolution of information, where only the latter is available to Turing machines (artificial intelligence). Furthermore, the upper bound hints at the role of dissipative structures and collective, in particular human, intelligence in this evolution.

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Łukaszyk, S.; Bieniawski, W. Assembly Theory of Binary Messages. Encyclopedia. Available online: https://encyclopedia.pub/video/video_detail/1314 (accessed on 12 August 2024).

Łukaszyk S, Bieniawski W. Assembly Theory of Binary Messages. Encyclopedia. Available at: https://encyclopedia.pub/video/video_detail/1314. Accessed August 12, 2024.

Łukaszyk, Szymon, Wawrzyniec Bieniawski. "Assembly Theory of Binary Messages" *Encyclopedia*, https://encyclopedia.pub/video/video_detail/1314 (accessed August 12, 2024).

Łukaszyk, S., & Bieniawski, W. (2024, July 12). Assembly Theory of Binary Messages. In *Encyclopedia*. https://encyclopedia.pub/video/video_detail/1314

Łukaszyk, Szymon and Wawrzyniec Bieniawski. "Assembly Theory of Binary Messages." *Encyclopedia*. Web. 12 July, 2024.

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