Continuing where we left off last time https://its101010.com/2020/10/06/the-turing-machines/
The Pinnacle of Human Accomplishment in 1992-1994 CE
The Non-Deterministic Calculus is NOT simply Non-Deterministic Turing Machine. NTM’s have some magical mechanism using which it guesses the right choices at each step to end up finding the solution eventually in polynomial time. It is this kind of guessing which is esoteric. This is the reason NTM’s have never been implemented in practicality before 1992 by anyone.
Non-Deterministic Calculus is that special ingredient that delivers these esoteric guesses. Which ‘help’ the NTM’s find a solution.
Non-Deterministic Calculus is actually the underlying algorithm of the functioning of the universe. Which Automatski discovered in 1990’s.
Non-Deterministic Calculus has since been used to solve Exponential Time & Space Problems. It is used by Automatski in the implementation of its Quantum Computer. Quantum Many Body Simulations etc. So its tried, verified and tested. And it is demonstrable. This is the first public demo of Automatski’s Circuit Based Quantum Computers v2014/2015 CE
The Birth of Determinism
To understand how Non-Deterministic Calculus works we have to first understand how and why a Probabilistic Turing Machine doesn’t work.
A PTM basically samples choices from Probability Distributions at each step of the solution algorithm. And as such doesn’t help in reducing the Exponential Time Complexity in anyway. It just reduces Exponential Space complexity into a manageable Polynomial Space Complexity. So its basically a pile of crap.
The Non-Deterministic Calculus works like the underlying algorithm of the universe. It does have and use Probability Distributions. But these PD’s collectively evolve and lead to Aggregate Determinism. Something like how Quantum Bodies lead to the universe or Quantum Qubits lead to solution.
This is exactly how the universe functions. It converts micro Non-Determinism to macro Determinism. An NTM is only useful if it can use Non-Determinism and yet deliver for us a Deterministic Answer. An thats what The Non-Deterministic Calculus does for us. It sits inside a NTM and helps it guess the right choices. And arrive at the Deterministic solution.
Non-Deterministic Calculus has been verified with Optimization and Constraint Solving Problems. K-CSP & K-CSO
It has been used in Quantum Many Body Simulations and to implement The Worlds First Billion Qubit and Infinite Precision Quantum Computer at Automatski.
It solves Exponential Time and Space Problems in Polynomial Time and Space. At Automatski we are still researching and analysing our NTM Implementation for the last 30+ years. And it never fails to amaze us. We are still discovering how it can be applied in various situations and solve previously unsolvable problems.