### Improving NP-complete algorithms

Suppose we have an (efficient) NP-complete algorithm. I remind that proving a provable theorem isn’t an NP problem, because there are theorems whose shortest proof is of super-exponential length. However, finding a proof that is below a given “threshold” length is an…

### Halting problem is essentially solvable

I have some error: from the below it follows that if the formal system found is distinct from the original one then it’s provable that the input algorithm does not halt (if it halts, it’s provable that it halts in Peano arithmetic)…

### Circumventing First Godel Incompleteness Theorem

A statement equivalent to First Incompleteness theorem There are theorems that can be neither proved nor disproved in a given formal system (containing arithmetic). This theorem makes people sad: There are “problems” that cannot be solved. But God teaches me that there…

### [ERRONEOUS] A proof of P=NP using a Merkle tree – a new version

I’ve produced a short and much elementary proof of P=NP (without an efficient algorithm presented). I sent it to a reputable CS journal and insofar there were no errors noticed by the editor. Here is an updated version of my proof with…

### [ERRONEOUS] A proof of P=NP using a Merkle tree

I denote s(X) the size of data X (in bits). I denote execution time of an algorithm A as t(A,X). Using a Merkle tree technology similar to one of the Cartesi crypto (but with a true random number generator, and possibly the…

### What if somebody discovers and publish an efficient P=NP solution

Lemme model what happens if somebody finds an efficient NP-complete algorithm. In layman terms (you are now studying things like this in the university, so you will soon know the formulas) an efficient NP-complete algorithm is: an algorithm that reaches any given…

### I’ve Proved Constructivity of P=NP

I’ve found (and proved) an algorithm that is NP-complete in the assumption that P=NP. In other words, if P=NP has a positive solution, my algorithm is its solution. I was kinda afraid if I already have almost solved P=NP as an easy…