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Solving NP-Complete Problems by Self-Supervised Dynamics.

Michail A. Zak

Published Feb 1, 2017• 0 citations
OpenAlex

Abstract

The challenge of this paper is to relate quantum-inspired dynamics represented by a self- supervised system, to solutions of noncomputable problems. In the self-supervised systems, the role of actuators is played by the probability produced by the corresponding Liouville equation. Following the Madelung equation that belongs to this class, non- Newtonian properties such as randomness, entanglement, and probability interference typical for quantum systems have been described in [1]. It has been demonstrated there, that such systems exist in the mathematical world: they are presented by ODE coupled with their Liouville equation, but they belong neither to Newtonian nor to quantum physics. The central point of this paper is the application of the self-supervised systems to solve traveling salesman problem.

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The challenge of this paper is to relate quantum-inspired dynamics represented by a self- supervised system, to solutions of noncomputable problems. In the self-supervised systems, the role of actuators is played by the probability produced by the corresponding Liouville equation. Following the Madelung equation that belongs to this class, non- Newtonian properties such as randomness, entanglement, and probability interference typical for quantum systems have been described in [1]. It has been demonstrated there, that such systems exist in the mathematical world: they are presented by ODE coupled with their Liouville equation, but they belong neither to Newtonian nor to quantum physics. The central point of this paper is the application of the self-supervised systems to solve traveling salesman problem.
The challenge of this paper is to relate quantum-inspired dynamics represented by a self-supervised system, to solutions of noncomputable problems. In the self-supervised systems, the role of actuators is played by the probability produced by the corresponding Liouville equation. Following the Madelung equation that belongs to this class, non-Newtonian properties such as randomness, entanglement, and probability interference typical for quantum systems have been described in [1]. It has been demonstrated there, that such systems exist in the mathematical world: they are presented by ODE coupled with their Liouville equation, but they belong neither to Newtonian nor to quantum physics. The central point of this paper is the application of the self-supervised systems to finding global maximum of functions that is no-where differential, but everywhere continuous (such as Weierstrass functions)
A new class of dynamical system described by ODE coupled with their Liouville equation has been introduced and discussed. These systems called self-controlled, or self-supervised since the role of actuators is played by the probability produced by the Liouville equation. Following the Madelung equation that belongs to this class, non- Newtonian properties such as randomness, entanglement, and probability interference typical for quantum systems have been described. Special attention was paid to the capability to violate the second law of thermodynamics, which makes these systems neither Newtonian, nor quantum. It has been shown that self-controlled dynamical systems can be linked to mathematical models of livings as well as to models of AI. The central point of this paper is the application of the self-controlled systems to NP-complete problems known as being unsolvable neither by classical nor by quantum algorithms. The approach is illustrated by solving a search in unsorted database in polynomial time by resonance between external force representing the address of a required item and the response representing location of this item.
The challenge of this paper is to relate artificial intuition-based intelligence, represented by self-supervised systems, to solutions of NP-complete problems. By self-supervised systems we understand systems that are capable to move from disorder to order without external effort, i.e. in violation of the second law of thermodynamics. It has been demonstrated, [1], that such systems exist in the mathematical world: they are presented by ODE coupled with their Liouville equation, but they belong neither to Newtonian nor to quantum physics since they are capable to violate the second law of thermodynamics. That suggests that machines could not simulate intuition-based intelligence if they are composed only of physical parts, but without digital components. Nevertheless it was found such quantum-classical hybrids, [1], that simulates some of self-supervised systems. The main achievement of this work is a demonstration that self-supervised systems can solve NP-complete problems in polynomial time by replacing an enumeration of exponentially large number of possible choices with a short cut provided by a non-Newtonian and non-quantum nature of self-supervised systems.
This work is inspired by the discovery of a new class of dynamical system described by ODE coupled with their Liouville equation. These systems called self-controlled since the role of actuators is played by the probability produced by the Liouville equation. Following the Madelung equation that belongs to this class, non-Newtonian properties such as randomness, entanglement, and probability interference typical for quantum systems have been described. Special attention was paid to the capability to violate the second law of thermodynamics, which makes these systems neither Newtonian, nor quantum. It has been shown that self-controlled dynamical systems can be linked to mathematical models of livings. The discovery of isolated dynamical systems that can decrease entropy in violation of the second law of thermodynamics, and resemblances of these systems to livings implies that Life can slow down heat death of the Universe, and that can be associated with the Purpose of Life.
This work is inspired by the discovery of a new class of dynamical system described by ODE coupled with their Liouville equation. These systems called self-controlled since the role of actuators is played by the probability produced by the Liouville equation. Following the Madelung equation that belongs to this class, non-Newtonian properties such as randomness, entanglement, and probability interference typical for quantum systems have been described. Special attention was paid to the capability to violate the second law of thermodynamics, which makes these systems neither Newtonian, nor quantum. It has been shown that self-controlled dynamical systems can be linked to mathematical models of livings. The discovery of isolated dynamical systems that can decrease entropy in violation of the second law of thermodynamics, and resemblances of these systems to livings implies that Life can slow down heat death of the Universe, and that can be associated with the Purpose of Life.
A new type of correlation has been developed similar to quantum entanglement in self-supervised dynamics (SSD). SSDs have been introduced as a quantum-classical hybrid based upon the Madelung equation in which the quantum potential is replaced by an information potential. As a result, SSD preserves the quantum topology along with superposition, entanglement, and wave-particle duality. At the same time, it can be implemented in any scale including the Newtonian scale. The main properties of SSD associated with simulating intelligence have been formulated. The attention with this innovation is focused on intelligent agents interaction based upon the new fundamental non-New tonian effect; namely, entanglement.