Shift overflow counter: Difference between revisions
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'''Shift overflow counter''' is an informal class of Turing machines. A typical Turing machine in this class has the following behavior: | '''Shift overflow counter''' is an informal class of Turing machines. A typical Turing machine in this class has the following behavior: | ||
* | * It represents digits as short fixed-length blocks of symbols. | ||
* | * It spends most of its time implementing basic double counter until one of the sides overflows (expands) which leads to changing the offsets of blocks, making them non-valid representations of digits. | ||
* | * After “Counter Phase” there is a “Reset Phase” where the contents are “reparsed”, creating a new double counter configuration. The new configuration could lead to halting. | ||
Note: some examples (like the halting shift-overflow counters below) use a counter on one side and a [[bouncer]] (sometimes called unary counter) on the other. | Note: some examples (like the halting shift-overflow counters below) use a counter on one side and a [[bouncer]] (sometimes called unary counter) on the other. | ||
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== Examples == | == Examples == | ||
* Skelet holdouts: [[Skelet 34]], [[Skelet 33]], [[Skelet 35]], [[Skelet 15]], [[Skelet 26]] | * Skelet holdouts: [[Skelet 34]], [[Skelet 33]], [[Skelet 35]], [[Skelet 15]], [[Skelet 26]] | ||
* {{TM|1RB0RF_1LC1RB_0RD0LB_---0LE_1RE0RA_1RD1RE}} | * {{TM|1RB0RF_1LC1RB_0RD0LB_---0LE_1RE0RA_1RD1RE}} | ||
Halting shift-overflow counters: | Halting shift-overflow counters: | ||
* Current longest running [[BB(2,5)]] TM: {{TM|1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ}} | * {{TM|1RB1LD_1RC0RB_1LA0LE_1LC0LA_1RZ1RB|halt}} | ||
* Current | * {{TM|1RB1LD_1RC0RB_1LA1LE_1LC0LA_1RZ0RD|halt}} | ||
* Current longest running [[BB(2,5)]] TM: {{TM|1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ|halt}} | |||
* Current seventh longest running [[BB(6)]] TM: {{TM|1RB1RC_1LC1RE_1LD0LB_1RE1LC_1LE0RF_1RZ1RA|halt}} | |||
== Related links == | == Related links == | ||
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* [https://discuss.bbchallenge.org/t/skelet-33-doesnt-halt-coq-proof/180 Skelet #33 doesn’t halt - Coq proof] | * [https://discuss.bbchallenge.org/t/skelet-33-doesnt-halt-coq-proof/180 Skelet #33 doesn’t halt - Coq proof] | ||
[[Category:Zoology]] | [[Category:Zoology]] | ||
Latest revision as of 18:39, 16 August 2025
Shift overflow counter is an informal class of Turing machines. A typical Turing machine in this class has the following behavior:
- It represents digits as short fixed-length blocks of symbols.
- It spends most of its time implementing basic double counter until one of the sides overflows (expands) which leads to changing the offsets of blocks, making them non-valid representations of digits.
- After “Counter Phase” there is a “Reset Phase” where the contents are “reparsed”, creating a new double counter configuration. The new configuration could lead to halting.
Note: some examples (like the halting shift-overflow counters below) use a counter on one side and a bouncer (sometimes called unary counter) on the other.
Examples
- Skelet holdouts: Skelet 34, Skelet 33, Skelet 35, Skelet 15, Skelet 26
1RB0RF_1LC1RB_0RD0LB_---0LE_1RE0RA_1RD1RE(bbch)
Halting shift-overflow counters:
1RB1LD_1RC0RB_1LA0LE_1LC0LA_1RZ1RB(bbch)1RB1LD_1RC0RB_1LA1LE_1LC0LA_1RZ0RD(bbch)- Current longest running BB(2,5) TM:
1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ(bbch) - Current seventh longest running BB(6) TM:
1RB1RC_1LC1RE_1LD0LB_1RE1LC_1LE0RF_1RZ1RA(bbch)