Cycler: Difference between revisions
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[[File:1RB0LB 1LB1LC 0RC1RA.png|alt=1RB0LB_1LB1LC_0RC1RA|thumb|upright=1.5|The record 3-state 2-symbol cycler {{TM|1RB0LB_1LB1LC_0RC1RA}}, which has period 18 and preperiod 4.]] | [[File:1RB0LB 1LB1LC 0RC1RA.png|alt=1RB0LB_1LB1LC_0RC1RA|thumb|upright=1.5|The record 3-state 2-symbol cycler {{TM|1RB0LB_1LB1LC_0RC1RA}}, which has period 18 and preperiod 4.]] | ||
A '''cycler''' is a Turing machine that eventually enters a repeating cycle. Such a Turing machine runs forever | A '''cycler''' is a Turing machine that eventually enters a repeating cycle. Such a Turing machine runs forever and thus is a [[non-halting Turing machine]]. A cycler may be seen as a special case of a [[translated cycler]] which has offset zero. | ||
The rule for identifying cyclers is simple: | The rule for identifying cyclers is simple: | ||
Revision as of 10:22, 10 August 2025
1RB0LB_1LB1LC_0RC1RA (bbch), which has period 18 and preperiod 4.A cycler is a Turing machine that eventually enters a repeating cycle. Such a Turing machine runs forever and thus is a non-halting Turing machine. A cycler may be seen as a special case of a translated cycler which has offset zero.
The rule for identifying cyclers is simple:
û → û
where û is any headed tape segment.
See also
- Translated cycler
- Section 2 of bbchallenge's deciders write-up.