TM_Universal

Turing Machines and Regular Languages
We’ll do this on a 4 tape TM. Our TM’s ﬁrst task is to move
things onto the right tapes:
Tape 0: Transition function
Tape 1: Accepting states
Tape 2: Current state (starts at 0)
Tape 3: Input to DFA
t 0 : 1 = 1 , 0 = 0 ; 1 : 1 = 0 , 0 = 1 t
t 1 t t t t t t t t t t t t t t t t t t t
t 0 1 1 0 1 t t t t t t t t t t t t t t t
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t 0 : 1 = 1 , 0 = 0 ; 1 : 1 = 0 , 0 = 1 t
We search tape 0 for the current state (as recorded on tape 2)
Here, we already found it.
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Tapes:
t 0 : 1 = 1 , 0 = 0 ; 1 : 1 = 0 , 0 = 1 t
Then we search tape 0 for the input symbol (as found on tape 3)
We use the TM’s state to keep track of whether we are after a ,
or an =.
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Tapes:
t 0 : 1 = 1 , 0 = 0 ; 1 : 1 = 0 , 0 = 1 t
Then we move across the = on tape 0, ﬁnd the state number
and update Tape 2
(no change on tape 2: already in state 0)
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Tapes:
t 0 : 1 = 1 , 0 = 0 ; 1 : 1 = 0 , 0 = 1 t
Then we scan back to the start of Tape 0, and advance Tape 3
by one position
Tape 3’s movement is the DFA going to the next character of
input.
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Tapes:
t 0 : 1 = 1 , 0 = 0 ; 1 : 1 = 0 , 0 = 1 t
Already at state 0’s description, so ﬁnd 1
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Tapes:
t 0 : 1 = 1 , 0 = 0 ; 1 : 1 = 0 , 0 = 1 t
Go after the =, and update state number (tape 2)
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Tapes:
t 0 : 1 = 1 , 0 = 0 ; 1 : 1 = 0 , 0 = 1 t
Scan to left of Tape 0, advance on Tape 3.
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Tapes:
t 0 : 1 = 1 , 0 = 0 ; 1 : 1 = 0 , 0 = 1 t
Now, we search for state 1’s description on Tape 0
Use TM state to remember if we just crossed a ;
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Tapes:
t 0 : 1 = 1 , 0 = 0 ; 1 : 1 = 0 , 0 = 1 t
Find input symbol (1 from Tape 3)
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Tapes:
t 0 : 1 = 1 , 0 = 0 ; 1 : 1 = 0 , 0 = 1 t
Find destination state (0) and update tape 2.
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Tapes:
t 0 : 1 = 1 , 0 = 0 ; 1 : 1 = 0 , 0 = 1 t
Scan to left on Tape 0 and move right one on Tape 3.
We’ll skip to the end now...
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Tapes:
t 0 : 1 = 1 , 0 = 0 ; 1 : 1 = 0 , 0 = 1 t
When Tape 3 sees t, we have reached the end of the DFAs
input
We need to see if the current state (recorded on Tape 2) is
accepting (listed on tape 1)
If we ﬁnd it, we accept, if not, we reject (here we accept)
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TM_Universal

TM_Universal

Tiffany

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