Assembly Theory of Bitstrings

Credit to Information Physics Institute
• Assembly Theory of Bit...
The bit is the smallest amount and the quantum of information. We used assembly theory to investigate the assembly pathways of binary strings 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. The string assembly index (the smaller amount of steps required to assemble a string of length N) is bounded from below by the shortest addition chain for N. We conjecture about the form of the upper bound. We define the degree of causation for the minimum assembly index that happened to reveal regularities for certain N that can be used to determine the length of the shortest addition chain for N. We explored the idea of assembling bitstrings by other bitstrings (binputation), and it turned out that a bitstring with the smallest assembly index for N can be assembled by a binary program of length equal to this index if the length of this bitstring is expressible as a product of Fibonacci numbers. The results confirm that four Planck areas provide a minimum information capacity that corresponds to a minimum thermodynamic (Bekenstein-Hawking) entropy. Knowing that the problem of determining the assembly index is at least NP-complete, we conjecture that this problem is, in fact, 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.