DeepAI AI Chat
Log In Sign Up

Exploring Rulial Space: The Case of Turing Machines

by   Stephen Wolfram, et al.

As an example of the concept of rulial space, we explore the case of simple Turing machines. We construct the rulial multiway graph which represents the behavior of all possible Turing machines with a certain class of rules. This graph (which is a Cayley graph of a "Turing machine group") gives a map of the space of non-deterministic Turing machines. We investigate the subgraph formed by deterministic machines, and explore the relationship to the P vs. NP problem. We also consider the implications of features of rulial space for physics, including estimating the maximum speed h̊o̊ in rulial space, relations between rulial black holes and computational reducibility, and interpretations of hypercomputation.


page 8

page 19

page 20

page 21

page 24

page 32

page 33

page 36


Encoding Turing Machines into the Deterministic Lambda-Calculus

This note is about encoding Turing machines into the lambda-calculus....

Multiway Turing Machines

Multiway Turing machines (also known as nondeterministic Turing machines...

Notes on kAExp(pol) problems for deterministic machines

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

A Log-Sensitive Encoding of Turing Machines in the λ-Calculus

This note modifies the reference encoding of Turing machines in the λ-ca...

Computation with Large Advice

In this paper, we consider a new direction of computation, which we call...

Machines as Programs: P ≠ NP

The Curry-Howard correspondence is often called the proofs-as-programs r...

What Next? A Dozen Information-Technology Research Goals

Charles Babbage's vision of computing has largely been realized. We are ...