DeepAI AI Chat
Log In Sign Up

After 100 Years, Can We Finally Crack Post's Problem of Tag? A Story of Computational Irreducibility, and More

by   Stephen Wolfram, et al.

Empirical, theoretical and historical aspects of Post's "problem of tag" from 1921 are explored. Evidence of strong computational irreducibility is found. Despite their deterministic origin, the lengths of successive sequences generated seem to closely approximate random walks. All 10^25 smallest initial conditions are found to eventually halt, although sometimes in > 6*10^11 steps. Implications of the Principle of Computational Equivalence are discussed, along with examples of identifiable computational capabilities of tag systems. Various minimal examples of complex behavior are found, including a less-biased analog of the 3n+1 Collatz problem. There is also discussion of the history of Emil Post and of tag systems in the context of ideas about the foundations of mathematics and computation.


page 6

page 12

page 18

page 19

page 20

page 26

page 38

page 40


Infinitely growing configurations in Emil Post's tag system problem

Emil Post's tag system problem is the question of whether or not a tag s...

A Low Computational Approach for Price Tag Recognition

In this work we discuss the task of search, localization and recognition...

A new TAG Formalism for Tamil and Parser Analytics

Tree adjoining grammar (TAG) is specifically suited for morph rich and a...

Scalable Fiducial Tag Localization on a 3D Prior Map via Graph-Theoretic Global Tag-Map Registration

This paper presents an accurate and scalable method for fiducial tag loc...

Tag Embedding and Well-defined Intermediate Representation improve Auto-Formulation of Problem Description

In this report, I address auto-formulation of problem description, the t...

Socializing the Semantic Gap: A Comparative Survey on Image Tag Assignment, Refinement and Retrieval

Where previous reviews on content-based image retrieval emphasize on wha...