Bell eats counter: Difference between revisions

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== Definition ==
{{Stub}}
Bell eats counter is a informal class of Turing machines. A typical Turing machine in this class has the following behavior:
'''Bell eats counter''' is an informal class of Turing machines. A typical Turing machine in this class has the following behavior:


* It has both a bell and a counter on the tape.
* It has both a bell and a counter on the tape.
* Increment: when the bouncer in the bell finish a period, the counter is increased by one.
* Increment: when the bouncer in the bell finishes a period, the counter is increased by one.
* Overflow: when the bouncer in the bell overflows, the bell eats the lowest digit of the counter (the counter is halved), and the bouncer in the bell is reset.
* Overflow: when the bouncer in the bell overflows, the bell eats the lowest digit of the counter (the counter is halved), and the bouncer in the bell is reset.
[https://github.com/ccz181078/busycoq/blob/BB6/verify/BECv1.v A Rocq proof of a kind of typical behavior doesn't halt.]


== Examples ==
== Examples ==
[https://bbchallenge.org/1RB1RE_0RC1RD_1LA1RC_1LC---_1LF0RE_0LF0LA 1RB1RE_0RC1RD_1LA1RC_1LC---_1LF0RE_0LF0LA]
{{TM|1RB1RE_0RC1RD_1LA1RC_1LC---_1LF0RE_0LF0LA}}


[https://bbchallenge.org/1RB---_1RC0RA_1LD1RA_1LE0LD_0RE1RF_0RB0LF 1RB---_1RC0RA_1LD1RA_1LE0LD_0RE1RF_0RB0LF]
{{TM|1RB---_1RC0RA_1LD1RA_1LE0LD_0RE1RF_0RB0LF}}


[https://bbchallenge.org/1RB0LE_0RC---_1LC0RD_0RB1RA_1LF1LE_0LA1LF 1RB0LE_0RC---_1LC0RD_0RB1RA_1LF1LE_0LA1LF] (more complex than typical ones)
{{TM|1RB0LE_0RC---_1LC0RD_0RB1RA_1LF1LE_0LA1LF}} (more complex than typical ones)


[https://bbchallenge.org/1RB3LB---3RA0LA_2LA3LB4RB1RB2RA 1RB3LB---3RA0LA_2LA3LB4RB1RB2RA]
{{TM|1RB3LB---3RA0LA_2LA3LB4RB1RB2RA}}
 
{{TM|1RB0RB_0RC1RB_1LD1RC_0LE0LD_1RA1LE}}
 
[[Category:Zoology]]

Latest revision as of 16:37, 26 August 2026

Bell eats counter is an informal class of Turing machines. A typical Turing machine in this class has the following behavior:

  • It has both a bell and a counter on the tape.
  • Increment: when the bouncer in the bell finishes a period, the counter is increased by one.
  • Overflow: when the bouncer in the bell overflows, the bell eats the lowest digit of the counter (the counter is halved), and the bouncer in the bell is reset.

A Rocq proof of a kind of typical behavior doesn't halt.

Examples

1RB1RE_0RC1RD_1LA1RC_1LC---_1LF0RE_0LF0LA (bbch)

1RB---_1RC0RA_1LD1RA_1LE0LD_0RE1RF_0RB0LF (bbch)

1RB0LE_0RC---_1LC0RD_0RB1RA_1LF1LE_0LA1LF (bbch) (more complex than typical ones)

1RB3LB---3RA0LA_2LA3LB4RB1RB2RA (bbch)

1RB0RB_0RC1RB_1LD1RC_0LE0LD_1RA1LE (bbch)

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