43+Slides--Decidability

# 43+Slides--Decidability - CS103 HO#43 Slides-Decidability...

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CS103 HO#43 Slides--Decidability 5/11/11 1 Monday Weeks of 5/9, 5/23 Kevin 10 - 12 Gates 200 Bob 3:45 - 5:00 Gates 178 4:00 – 5:30 Tuesday Ryan 1:15 - 3:15 Gates 100 Hrysoula 7 - 9 Gates B12 Wednesday Conal 12:15 - 2:15 Gates 200 Bob 3:45 - 5:30 Gates 178 4:30 – 5:30 Thursday Evan 2:15 - 4:15 Gates 400 Mingyu 7 - 9 200-201 Sunday Neel 1 - 3 Gates B12 Karl 5 - 7 Gates B12 Office Hour Schedule Coding a Turing Machine state symbol write move new state q 1 S 2 S 2 R q 1 q 1 S 1 S 2 R q 3 q 3 S 1 S 2 L q 3 q 3 S 0 S 2 L q 2 The behavior of a machine can be described by a table like this. (A transition to state 2 means HALT.) q 1 S 2 S 2 Rq 1 ;q 1 S 1 S 2 Rq 3 ;q 3 S 1 S 2 Lq 3 ;q 3 S 0 S 2 Lq 2; A more compact form: Coding a Turing Machine q 1 S 2 S 2 Rq 1 ;q 1 S 1 S 2 Rq 3 ;q 3 S 1 S 2 Lq 3 ;q 3 S 0 S 2 Lq 2 ; Replace: q i by D followed by A i S i by D followed by C i to get the standard description of the machine: DADCCDCCRDA;DADCDCCRDAAA;DAAADCDCCLDAAA;DAAADDCCLDAA; Replace: A by 1 C by 2 D by 3 L by 4 R by 5 ; by 7 to get the description number of the machine: 31322322531731323225311173111323224311173111332243117 Standard descriptions are in the language R = (31*32*32*(4 5)31*7)* Using a Turing Machine to Simulate a Turing Machine M q \$3132232253173132322531117311132322431. .. Description of Machine M \$ 0010100001110101000101010110101010. .. Machine M's Tape \$31 Machine M's State \$ . . . . . . . . . . . . . . . . . Scratch A machine like this is called a Universal Turing Machine . 02895462 PC Program Counter IR 000 0165371 001 5720973 002 0000000 003 0042001 004 8463203 005 ... 006 ... 007 ... 008 ... 009 ... 010 ... ... ... ... ... ... LD R1,(R2) ... ST R1,(IR) ... ... ... ... 00050034 R1 00000020 R2 00010000 R3 00000450 R4 00000006 Index Register Registers How Does A Computer Work? Memory Using a Turing Machine to Simulate a Computer q \$*0# 165371 *1# 5720973 *2# 0 *3# 42001 * . . . Memory \$ 02895462 * PC \$*1# 20 *2# 10000 *3# 450 *4# 6 *IR# 50034 * Registers \$ . . . . . . . . . . . . . . . . . Scratch

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CS103 HO#43 Slides--Decidability 5/11/11 2 Decidability Now that we have a model of a computation, we will now turn our attention to the question of decidability: What is the power of algorithms to solve problems? What problems are unsolvable? Recognizer Decider input w input w Yes, w L Yes, w L No , w L Decidable Languages Can we determine whether a particular DFA accepts a given string? We state the problem as a language: A DFA = { B, w | B is a DFA and B accepts string w } and try to specify a Turing machine that decides it. If the language is decidable, then the original question is decidable. This one is easy since we are talking about a DFA. Build a TM M that simulates B operating on w. Accept if the simulation ends in an accept state; otherwise, reject. Acceptance Problems for Regular Languages Can we determine whether a particular NFA accepts a given string?
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43+Slides--Decidability - CS103 HO#43 Slides-Decidability...

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