Sync bi-counter

A sync bi-counter is an informal class of Turing machines. A typical Turing machine in this class has the following behavior:

• It has two counters on the tape, and the lowest digit of both counters are adjacent.
• In each round, both of the two counters are increased by one, and they count in the same base. Both counters count to the same number after each round (i.e. they are synchronized).

Examples

• Skelet #10 (Proof of non-halt)
• 1RB1LA_1LA0RC_1RB0RD_1LE1RD_0LC0LF_---0LA (bbch)
• 1RB0LE_0LC---_1LA0RD_1RC0RC_1LF1LE_0LA1RF (bbch)

Decider

For typical cases, we can fold the tape so that two counters overlap as one counter, and then it's usually decidable by CTL.

Inductive decider can deal with some more complex situations.