DeepAI AI Chat
Log In Sign Up

Machines as Programs: P ≠ NP

by   Jonathan J. Mize, et al.
University of North Texas

The Curry-Howard correspondence is often called the proofs-as-programs result. I offer a generalization of this result, something which may be called machines as programs. Utilizing this insight, I introduce two new Turing Machines called "Ceiling Machines." The formal ingredients of these two machines are nearly identical. But there are crucial differences, splitting the two into a "Higher Ceiling Machine" and a "Lower Ceiling Machine." A potential graph of state transitions of the Higher Ceiling Machine is then offered. This graph is termed the "canonically nondeterministic solution" or CNDS, whose accompanying problem is its own replication, i.e., the problem, "Replicate CNDS" (whose accompanying algorithm is cast in Martin-Löf type theory). I then show that while this graph can be replicated (solved) in polynomial time by a nondeterministic machine – of which the Higher Ceiling Machine is a canonical example – it cannot be solved in polynomial time by a deterministic machine, of which the Lower Ceiling Machine is also canonical. It is consequently proven that P ≠ NP.


page 1

page 2

page 3

page 4


Diagonalization of Polynomial-Time Turing Machines Via Nondeterministic Turing Machine

The diagonalization technique was invented by Georg Cantor to show that ...

Exploring Rulial Space: The Case of Turing Machines

As an example of the concept of rulial space, we explore the case of sim...

Descriptive complexity of real computation and probabilistic independence logic

We introduce a novel variant of BSS machines called Separate Branching B...

Doubly-Efficient Pseudo-Deterministic Proofs

In [20] Goldwasser, Grossman and Holden introduced pseudo-deterministic ...

A polynomial time parallel algorithm for graph isomorphism using a quasipolynomial number of processors

The Graph Isomorphism (GI) problem is a theoretically interesting proble...

Notes on kAExp(pol) problems for deterministic machines

The complexity of several logics, such as Presburger arithmetic, depende...

A Simple Elementary Proof of P=NP based on the Relational Model of E. F. Codd

The P versus NP problem is studied under the relational model of E. F. C...