New Conjecture in the Theory of Computation and the P vs. NP problem
I recently published an algorithm on here which has efficiency O(N) and which decides the answer to the boolean satisfiability problem. This new algorithm led directly to this conjecture after having many discussions with various experts in their fields.
Introduction
I have invented a new theory of computation which I have named “The Theory of Self Reproducing Machines” and have discovered a very interesting infinite family of self reproducing machines, as well as a new set of mathematical laws which govern these types of systems, which extends Cellular Automata and John Conways “The Game of Life” using my new methods of “computer virus techniques” to write regular non-malicious computer programs. Since I am inventor I have a lot of crazy ideas. This one is really it and I am going with it and I desperately need help from experts.
Conjecture 1
The Theory of Self Reproducing Turing Machines or The Theory of Self Reproducing Machines is a Turing Complete theory of computation which generalizes the previous theory of computation. It’s possible to solve problems in the “complexity class” NP-Complete (a term I will define in my next conjecture). This new theory of computation involves adding a new axiom to the previous theory of computation which will result in a violation of the church-turing thesis and enable an algorithm which I have already written in javascript and tested in my debugging tool, namely, that Turing Machines have a magic axiomatic feature where they can self-replicate.
Conjecture 2
According to my new theory of computation, the class (according to class as defined by class theory in the sense of von neumann) of problems NP, can be partitioned into distinct subsets which i just named “complexity classes” of which NP-complete is the least level, these complexity classes can be mapped 1–1 to other problems by a type of isomorphism I name “complexity-class homomorphisms” and we can understand the different types of exponential growth in the complexity Big-O estimate by this type of operation. Furthermore, the different types of Big-O efficiency notation in use must be expanded to include the orders of infinity according the Cantors theory of infinite sets using a new Axiom that states there is no infinite set with complexity class between the integers and the real numbers. Furthermore, the types equivalence relation I just conjectured can by mapped 1–1 by a complexity class homomorphism to these orders of infinity I just described Furthermore, the complexity class of the integer factorization problem is of the same order as the chess engine problem, in other words, what makes chess hard is its strategy involves the mathematical problem of prime factorization.
Conjecture 3
Any computational problem should be able to be reduced to solving a Tree Search Optimization Problem, and a complexity class homomorphism is an isomorphisms between Tree Graphs which preserves the “branching amount” of the Tree, or in other words, the order of the exponential type of growth in the Big-O Estimate is related to the fundamental properties of different families of infinite Tree Graphs, and this “branching amount” is a measurable quantity that takes values in the set of orders of infinity.
Remarks
These conjectures are the result of 15 years of work on the theory of self reproducing machines which John Von Neumann invented and which inspired 3 fields, computer science, biology (via the discover of DNA that Watson and Crick knew to look for because of the theory of self reproducing machines) and game theory. His method for inventing entirely new fields of mathematics was to study nature, evolution, and the human nervous system. This is also the basis for my new discovery which results from analyzing the energy in the work done by cells in the human body as a result of cell self-replication in the human nervous system, which has tended to show that it is possible to make an exponential gain in energy for computer science purposes by understanding the computational power of the human nervous system from a theoretical physics perspective.
I have been working on various strategies to prove the 2nd conjecture since last night when I thought of this idea, and if I come up with anything good, I will publish it on here to let you all know.
Wish me luck!
P.S. If anyone has any comments, insights, objections, they would be much appreciated. I look forward to any replies to this post.
