Repeated Word List: Difference between revisions
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'''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 by multiplicity. 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 group's 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 (called macro steps) and regex branching up to a predefined limit on the amount of nodes which are allowed to be visited, <math>N</math>. If | [[File:RepWL 0RB0LC 1LA1RB 1RD0RE 1LC1LA ---0LD.png|thumb|500px|RepWL diagram for non-halting TM {{TM|0RB0LC_1LA1RB_1RD0RE_1LC1LA_---0LD}} showing a closed graph.]] | ||
'''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 by multiplicity. 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 group's 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 (called macro steps) and regex branching up to a predefined limit on the amount of nodes which are allowed to be visited, <math>N</math>. If the 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. | |||
== History == | == History == | ||
Revision as of 23:52, 20 February 2026
0RB0LC_1LA1RB_1RD0RE_1LC1LA_---0LD (bbch) showing a closed graph.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 by multiplicity. 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 group's 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 (called macro steps) and regex branching up to a predefined limit on the amount of nodes which are allowed to be visited, . If the 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.
History
- In April 2024, RepWL is first introduced by mxdys as part of Coq-BB5.[1]
- In May 2024, Repeated Word List is reproduced by savask.[2]
- In October 2024, Tristan Stérin reproduces Repeated Word List again.[3]