Shift overflow counter
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
1RB1LD_1RC0RB_1LA0LE_1LC0LA_1RZ1RB(bbch)1RB0RF_1LC1RB_0RD0LB_---0LE_1RE0RA_1RD1RE(bbch)1RB1LD_1RC0RB_1LA1LE_1LC0LA_1RZ0RD(bbch)
Halting shift-overflow counters:
- Current longest running BB(2,5) TM:
1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ(bbch) - Current seventh longest running BB(6) TM:
1RB1RC_1LC1RE_1LD0LB_1RE1LC_1LE0RF_1RZ1RA(bbch)