Chen
October 06, 2022
76

# TM_multitape

October 06, 2022

## Transcript

1. ### Multi-tape TM 0: t 0 0 0 1 + 1

0 0 1 = 1 0 1 0 t 1: t t t t t t t t t t t t t t t t 2: t t t t t t t t t t t t t t t t We start with input on tape 0. Other tapes are blank. 10 / 27
2. ### Multi-tape TM 0: t t t t t + 1

0 0 1 = 1 0 1 0 t 1: t 0 0 0 1 t t t t t t t t t t t 2: t t t t t t t t t t t t t t t t We can copy the ﬁrst operand to tape 1, crossing it off as we go 11 / 27
3. ### Multi-tape TM 0: t t t t t t t

t t t = 1 0 1 0 t 1: t 0 0 0 1 t t t t t t t t t t t 2: t 1 0 0 1 t t t t t t t t t t t We can copy the second operand to tape 2, crossing it off as we go 12 / 27
4. ### Multi-tape TM 0: t t t t t t t

t t t t 1 0 1 0 t 1: t 0 0 0 1 t t t t t t t t t t t 2: t 1 0 0 1 t t t t t t t t t t t We scan to the end 13 / 27
5. ### Multi-tape TM 0: t t t t t t t

t t t t 1 0 1 0 t 1: t 0 0 0 1 t t t t t t t t t t t 2: t 1 0 0 1 t t t t t t t t t t t Move left once on all tapes, and then just check each digit one by one, moving left. Remember carry in state. Carry in = 0 Carry out = 1 14 / 27
6. ### Multi-tape TM 0: t t t t t t t

t t t t 1 0 1 0 t 1: t 0 0 0 1 t t t t t t t t t t t 2: t 1 0 0 1 t t t t t t t t t t t Carry in = 1 Carry out = 0 15 / 27
7. ### Multi-tape TM 0: t t t t t t t

t t t t 1 0 1 0 t 1: t 0 0 0 1 t t t t t t t t t t t 2: t 1 0 0 1 t t t t t t t t t t t Carry in = 0 Carry out = 0 16 / 27
8. ### Multi-tape TM 0: t t t t t t t

t t t t 1 0 1 0 t 1: t 0 0 0 1 t t t t t t t t t t t 2: t 1 0 0 1 t t t t t t t t t t t Carry in = 0 Carry out = 0 17 / 27
9. ### Multi-tape TM 0: t t t t t t t

t t t t 1 0 1 0 t 1: t 0 0 0 1 t t t t t t t t t t t 2: t 1 0 0 1 t t t t t t t t t t t Carry in = 0 All tapes on t Accept! 18 / 27