Repeated Word List: Difference between revisions
Added N |
Added mechanism for proving non-halting |
||
| Line 1: | Line 1: | ||
'''Repeated Word List''' (short '''RepWL''') is a [[decider]]. It works by splitting the tape contents into blocks ("words") of a given length <math>l</math>. Consecutive blocks grouped into powers. If there are more consecutive repeating blocks than a predefined repeat threshhold <math>T</math>, the exponent is given as <math>T+</math>. Consecutive blocks with no <math>+</math> in their exponent are called constant blocks. When the TM head is facing a constant block, the TM is simulated until it either leaves the constant block, halts, or exceeds a predefined step limit <math>B</math>. This simulation inside a constant block is called block simulation. Once the TM has left the constant block, identical contiguous blocks are regrouped into powers. If the TM head is facing a group of blocks with a <math>+</math> in its exponent, the block directly faced by the TM head is separated from the group and the simulation splits into two branches: One where the original groups multiplicity is reduced to <math>T-1</math> and one where it stays at <math>T+</math>. This splitting is called regex branching. The decider constructs a graph of all instances of block simulation and regex branching up to a predefined limit on the amount of nodes which are allowed to be visited, <math>N</math>. | '''Repeated Word List''' (short '''RepWL''') is a [[decider]]. It works by splitting the tape contents into blocks ("words") of a given length <math>l</math>. Consecutive blocks grouped into powers. If there are more consecutive repeating blocks than a predefined repeat threshhold <math>T</math>, the exponent is given as <math>T+</math>. Consecutive blocks with no <math>+</math> in their exponent are called constant blocks. When the TM head is facing a constant block, the TM is simulated until it either leaves the constant block, halts, or exceeds a predefined step limit <math>B</math>. This simulation inside a constant block is called block simulation. Once the TM has left the constant block, identical contiguous blocks are regrouped into powers. If the TM head is facing a group of blocks with a <math>+</math> in its exponent, the block directly faced by the TM head is separated from the group and the simulation splits into two branches: One where the original groups multiplicity is reduced to <math>T-1</math> and one where it stays at <math>T+</math>. This splitting is called regex branching. The decider constructs a graph of all instances of block simulation and regex branching up to a predefined limit on the amount of nodes which are allowed to be visited, <math>N</math>. If a graph of a TM contains less than <math>N</math> nodes, the graph is closed. If the graph of a TM is closed and contains no halting configurations, the TM is proven non-halting. | ||
[[Category:Deciders]] | [[Category:Deciders]] | ||
{{Stub}} | {{Stub}} | ||
Revision as of 22:30, 20 February 2026
Repeated Word List (short RepWL) is a decider. It works by splitting the tape contents into blocks ("words") of a given length . Consecutive blocks grouped into powers. If there are more consecutive repeating blocks than a predefined repeat threshhold , the exponent is given as . Consecutive blocks with no in their exponent are called constant blocks. When the TM head is facing a constant block, the TM is simulated until it either leaves the constant block, halts, or exceeds a predefined step limit . This simulation inside a constant block is called block simulation. Once the TM has left the constant block, identical contiguous blocks are regrouped into powers. If the TM head is facing a group of blocks with a in its exponent, the block directly faced by the TM head is separated from the group and the simulation splits into two branches: One where the original groups multiplicity is reduced to and one where it stays at . This splitting is called regex branching. The decider constructs a graph of all instances of block simulation and regex branching up to a predefined limit on the amount of nodes which are allowed to be visited, . If a graph of a TM contains less than nodes, the graph is closed. If the graph of a TM is closed and contains no halting configurations, the TM is proven non-halting.