Skip to main content
Notice removed Draw attention by Thomas
Bounty Ended with Adam P. Goucher's answer chosen by Thomas
LaTeX italic
Source Link
Carlo Beenakker
  • 188.1k
  • 18
  • 448
  • 651

Has the 3-tag system investigated by Emil Post $(0\to00, 1\to1101)$ been solved? Is there a decision algorithm to determine which starting strings terminate, which end up in a cycle, and which (if any) grow without bound?

Also, what cycle structures are there? Setting a='00'$a=$ '00' and b='1101'$b=$ '1101', the only cycles I know of begin with $ab, b^2 a^2$, combinations of these, and $a^2 b^3 (a^3 b^3)^n$. Are there any more?

Has the 3-tag system investigated by Emil Post $(0\to00, 1\to1101)$ been solved? Is there a decision algorithm to determine which starting strings terminate, which end up in a cycle, and which (if any) grow without bound?

Also, what cycle structures are there? Setting a='00' and b='1101', the only cycles I know of begin with $ab, b^2 a^2$, combinations of these, and $a^2 b^3 (a^3 b^3)^n$. Are there any more?

Has the 3-tag system investigated by Emil Post $(0\to00, 1\to1101)$ been solved? Is there a decision algorithm to determine which starting strings terminate, which end up in a cycle, and which (if any) grow without bound?

Also, what cycle structures are there? Setting $a=$ '00' and $b=$ '1101', the only cycles I know of begin with $ab, b^2 a^2$, combinations of these, and $a^2 b^3 (a^3 b^3)^n$. Are there any more?

Notice added Draw attention by Thomas
Bounty Started worth 200 reputation by Thomas
edited tags
Link
David Roberts
  • 35.5k
  • 11
  • 124
  • 349
fix confusing markup
Source Link
Emil Jeřábek
  • 47.1k
  • 4
  • 147
  • 208

Has the 3-tag system investigated by Emil Post $(0->00, 1->1101)$$(0\to00, 1\to1101)$ been solved? Is there a decision algorithm to determine which starting strings terminate, which end up in a cycle, and which (if any) grow without bound?

Also, what cycle structures are there? Setting a='00' and b='1101', the only cycles I know of begin with $ab, b^2 a^2$, combinations of these, and $a^2 b^3 (a^3 b^3)^n$. Are there any more?

Has the 3-tag system investigated by Emil Post $(0->00, 1->1101)$ been solved? Is there a decision algorithm to determine which starting strings terminate, which end up in a cycle, and which (if any) grow without bound?

Also, what cycle structures are there? Setting a='00' and b='1101', the only cycles I know of begin with $ab, b^2 a^2$, combinations of these, and $a^2 b^3 (a^3 b^3)^n$. Are there any more?

Has the 3-tag system investigated by Emil Post $(0\to00, 1\to1101)$ been solved? Is there a decision algorithm to determine which starting strings terminate, which end up in a cycle, and which (if any) grow without bound?

Also, what cycle structures are there? Setting a='00' and b='1101', the only cycles I know of begin with $ab, b^2 a^2$, combinations of these, and $a^2 b^3 (a^3 b^3)^n$. Are there any more?

edited tags
Link
Thomas
  • 2.8k
  • 16
  • 29
Loading
Source Link
Thomas
  • 2.8k
  • 16
  • 29
Loading