Bell eats counter: Difference between revisions
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* Increment: when the bouncer in the bell finishes 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 | [https://github.com/ccz181078/busycoq/blob/BB6/verify/BECv1.v A Rocq proof of a kind of typical behavior doesn't halt.] | ||
== Examples == | == Examples == | ||
Latest revision as of 09:06, 25 August 2025
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
1RB---_1RC0RA_1LD1RA_1LE0LD_0RE1RF_0RB0LF
1RB0LE_0RC---_1LC0RD_0RB1RA_1LF1LE_0LA1LF (more complex than typical ones)