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.]]{{Stub}} | [[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.]]{{Stub}} | ||
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. | 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 [[decider]] for cyclers works by memorizing all configurations which are visited by a TM. If a configuration is visited twice, the TM is shown to be non-halting. | ||
The rule for identifying cyclers is simple: | The rule for identifying cyclers is simple: | ||
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* [https://github.com/bbchallenge/bbchallenge-proofs/blob/build-latex-pdf/deciders/correctness-deciders.pdf Section 2] of bbchallenge's deciders write-up. | * [https://github.com/bbchallenge/bbchallenge-proofs/blob/build-latex-pdf/deciders/correctness-deciders.pdf Section 2] of bbchallenge's deciders write-up. | ||
[[Category:Zoology]] | [[Category:Zoology]][[Category:Deciders]] | ||
Latest revision as of 11:44, 28 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 decider for cyclers works by memorizing all configurations which are visited by a TM. If a configuration is visited twice, the TM is shown to be non-halting.
The rule for identifying cyclers is simple:
û → û
where û is any headed tape segment.
Related Functions
- Busy Preperiodic Beaver (BBS(n,m)): The longest possible preperiod of a cycler or translated cycler with n states and m symbols.
- Busy Periodic Beaver (BBP(n,m)): The longest possible period of a cycler or translated cycler with n states and m symbols.
See also
- Translated cycler
- Section 2 of bbchallenge's deciders write-up.