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ΠΛΗ30 ΜΑΘΗΜΑ 5.2 (ΕΚΤΥΠΩΣΗ)

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ΠΛΗ30 ΜΑΘΗΜΑ 5.2 (ΕΚΤΥΠΩΣΗ)

  1. 1. 30 5: 5.2: !"# $ %& ! " # $ %&'## ( )# " # #) *&'## + () % ," -.- ) -/- + 0 & % 1 # 2 3# 4 % , + & % 4 % , 4 )# 5 6 &) 0 ) 7 1 ) *&'## 4 / ) )# ) 2 ! %) , # + ! # )' ) 6 5 1& )# # ) " # #) *&'## 1& )# # 8 # + 1& )# # 2 4 1& )# # & 5 1& )# # 6 , # 7 1& )# # # ) 9:;; ; * # # ) ! "#$ ! . ' " ( ! " "') " ( ! " & : * * + " (! . . ( , (& + & SOS + " " - . " * / " " # & " - . . "'" " # . 0& " * (-) ! "#$ ! B. 1 0# 1. ) &- Turing ( , (& + 1. # ' (& " ' & %& + 0 & ( " & " %& "0& 0& + 0 & + " ( #) ) &! Turing ( " , . %! "#$ ! ) &! Turing - '" + & + ( 2 # '* ( w: # " , ) " ' (h, #Y#) & # " , ) " ' (h, #N#) & & + + L ( #) ) &! Turing ( " & , Turing- (! & *# ! ! % ! ) # &0 "( ' # ' + *% * % 2 " 2 " Y,N " ( 2 , (& &" " ) " & &" – Y(es) 3 – ( ). • (& * ( ( #- & & ( & % " 2 ( & ( 2 # '* ( &! ! ') " & + . • 2!& " & " & & +# " % 2 Y " & # ! #Y# & ( 2 # '* ( &! " & + . • 2!& " & " & & +# " % 2 " & # ! # # & ( 2 # '* ( * & &! " & + .
  2. 2. B. 1 0# 1. ) &- Turing ( , (& + 2. ) &- ( +# (& #Y# #N# ! "#$ ! . • ' ( ) &! ( " & ( 2 , ( MY) * #w# 2!& " & * " -#& " & " & " & # ! #4# • ' ( ) &! ( " & ( 2 , ( MN) * #w# 2!& " & * " -#& " & " & " & # ! #N# # * + : * " + : " ( " &" " # & " ! ) &! Turing M, 2 " ={0,1,#,$,4, } ( & , " & + . 1 0#! " '" * . & " " (#+ " ' " ) " ' #x#. " "( # +# ! " " (+ " ) &! " * +# # ! " . !"#: ‘ "( # +# ! " " (#+ " . .: ) &! " & " & ! " & #)! " " & - " # & & " " & * ' # " # # " * . &" " &" & 0 $ & 1 $. 5" & ' * + & $, ) &! " # " , &" &" YES. # "0 &" . * +# # ! " ) &! & " ' ( : B. 1 0# 2. * + " (! . . 1. '" " 3 # + "0& &! "#$ ! 6 : * " + : " ( " &" " # & " ! ) &! Turing M, 2 " ={a,b,c,#,$,4, } ( & , " & + . 1 0#! " '" * . & " " (#+ " ' " ) " ' #x#. " "( # +# ! " " (+ " ) &! " * +# # ! " . B. 1 0# 2. * + " (! . . 1. '" " 3 # + "0& '! "#$ ! # * + : * " + : ! " ( " &" " # & " ! ) &! Turing M, 2 " ={0,1,#,$,4, } ( & , " & + . 1 0#! " '" * . & " " (#+ " ' " ) " ' #x#. " "( # +# ! " " (+ " ) &! " * +# # ! " . !"#: ‘ "( # +# ! " " (#+ " . .: ) &! " & " & ! " & #)! " " & - " # & & " " & * ' # " # # " * . &" " &" *% & 0 $ "# & 1 $. 5" & ' * + & $, ) &! " # " , &" &" YES. # "0 &" . * +# # ! " ) &! & " ' ( : B. 1 0# 2. * + " (! . . 2. & + 3 # + "0& (! "#$ !
  3. 3. 6 : * " + : ! " ( " &" " # & " ! ) &! Turing M, 2 " ={a,b,c,#,$,4, } ( & , " & + . 1 0#! " '" * . & " " (#+ " ' " ) " ' #x#. " "( # +# ! " " (+ " ) &! " * +# # ! " . B. 1 0# 2. * + " (! . . 2. & + 3 # + "0& )! "#$ ! # * + : * " + : " " ( " &" " # & " ! ) &! Turing M, 2 " ={0,1,#,$,4, } ( & , " & + . 1 0#! " '" * . & " " (#+ " ' " ) " ' #x#. " "( # +# ! " " (+ " ) &! " * +# # ! " . !"#: ‘ "( # +# ! " " (#+ " . .: & ( " # " ( # " #'" # ( " * . '" # % 2 , " "#- &" " $ ' & (" & * . & * & & * " # " , ( &" &" NO. 5" & ' * + & $, " # " , ( &" &" YES. * +# # ! " ) &! & " ' ( : B. 1 0# 2. * + " (! . . 3. &*# '" " *! "#$ ! 6 : * " + : " " ( " &" " # & " ! ) &! Turing M, 2 " ={a,b,c,#,$,4, } ( & , " & + . 1 0#! " '" * . & " " (#+ " ' " ) " ' #x#. " "( # +# ! " " (+ " ) &! " * +# # ! " . B. 1 0# 2. * + " (! . . 3. &*# '" " **! "#$ ! # * + : * " + : # $ #%&'(&)&(#*+# " ( " &" " # & " ! ) &! Turing M, 2 " ={0,1,#,4, } ( & , " & + . 1 0#! " '" * . & " " (#+ " ' " ) " ' #x#. " "( # +# ! " " (+ " ) &! " * +# # ! " . !"#: + & & & ! , " ' " ' ( : B. 1 0# 2. * + " (! . . 4. & & - *! "#$ ! + + 0 0,11 +* 0 1 * + : # & ( " & " (#+ " ( ) &! Turing " ( ' ( ( &'& : • " & % " & ! " & #)! " " & ( & " " ) • " " + & " R • / , ( " 2 # " & 4 ' " ! " " . • / , ( " 2 # " & ' " ! " " .
  4. 4. !"# ( ): " (#+ " ( # & " ' " & ' ( ) &! Turing: B. 1 0# 2. * + " (! . . 4. & & - *! "#$ ! , 6 : * " + : # $ #-&.#*&/&(0.&(#1&# " ( " &" " # & " ! ) &! Turing M, 2 " ={0,1,#,4, } ( & , " & + . 1 0#! " '" * . & " " (#+ " ' " ) " ' #x#. " "( # +# ! " " (+ " ) &! " * +# # ! " . B. 1 0# 2. * + " (! . . 4. & & - *%! "#$ ! B. 1 0# 3. " " # & " - ) &- Turing 1. " " # & " - ) &- Turing *! "#$ ! *- " ( &" " # & % # %& & " %& " ) &- Turing. 7" # % & # ( Turing : # %& & # , &" - " 2 " * % 2 # , &" - &! ( &! )0# * 2 ( 2' () &" " # & " ! ) &! Turing: • &" , & ( #) - "0 -& & " ( + % ( & * + * )!. • &" 53 , & * & ( #) & " ( + % ( & * + * )!. # * + : * " + : " ( " &" " # & " ! ) &! Turing M, 2 " ={0,1,#,$,4, } ( & , " & + . 1 0#! " '" * . & " " (#+ " ' " ) " ' #x#. " "( # +# ! " " (+ " ) &! " * +# # ! " . !"#: ‘ "( # +# ! " " (#+ " . .: ) &! Turing * 2 , " # " % 2 " ( 2 # '* ( &" " # & " -+ " ( #) , # " ' ( 2 # . 7 " + & " " %" "0& -&0& ( 2' 0& "0& *% ' 0& ( 2 # & B. 1 0# 3. " " # & " - ) &- Turing 1. # * + " *&! "#$ !
  5. 5. 6 : * " + : #23$2##-&.#*&/&(0.&(#1&# 3#-&.# ')(4&(#1&# " ( " &" " # & " ! ) &! Turing M, 2 " ={0,1,#,4, } ( & , " & + . 1 0#! " '" * . & " " (#+ " ' " ) " ' #x#. " "( # +# ! " " (+ " ) &! " * +# # ! " . B. 1 0# 3. " " # & " - ) &- Turing 1. # * + " *'! "#$ ! # * + : * " + : 5 6 7 5 6 7 # " ( " &" " # & " ! ) &! Turing M, 2 " ={0,1,#,4, } ( & , " & + . 1 0#! " '" * . & " " (#+ " ' " ) " ' #x#. " "( # +# ! " " (+ " ) &! " * +# # ! " . !"#: + & & & ! , " ' " ' ( : B. 1 0# 3. " " # & " - ) &- Turing 2. ) &! Turing ( # & *(! "#$ ! + + 0 0,10,1 +* 1 * + : # & ( " & " (#+ " ( ) &! Turing " ( ' ( ( &'& : • " & % " & ! " & #)! " " & ( & " " ) • " " + & " R • / , ( " 2 # " & 4 ' " ! " " . • / , ( " 2 # " & ' " ! " " . !"# ( ): " (#+ " ( # & " ' " & ' ( ) &! Turing: B. 1 0# 3. " " # & " - . . 2. ) &! Turing ( # & *)! "#$ ! , B. 1 0# 4. "'" " "0& 0& 0 & ! "#$ ! 7 "0 *% + -&0 " ( & + # " ( & + " ! " ( & + "-# Kleene + & + ( !#0 + & + 6# -) ( "'" " ' " # . " + . 5 "'" " * ) %& - 0 ) & & Turing.
  6. 6. B. 1 0# 4. "'" " "0& 0& 0 & 1. "'" " " & 7&0 *! "#$ ! 1 # ( "'" " "0& 0& 0 & " & 7&0 ) & L1 & L2 & "'" L1 U L2 & '* . L1 & , # ( #) ) & Turing ( " & , - "0 1 L2 & , # ( #) ) & Turing ( " & , - "0 2 " ( , ( ) &! Turing, - "0 ’ * w " (#+ 0 .! : 1. #-) " & M1 * w. & 1 &"! , "'" ’ &" " # " , . & 1 &"! 53 # )0# " 2! 2: 2. #-) " & 2 * w. & 2 &"! , "'" ’ &" " # " , . & 2 &"! 53 "'" &" 53 " # " , . B. 1 0# 4. "'" " "0& 0& 0 & 2. "'" " " & ! ! "#$ ! 1 # ( "'" " "0& 0& 0 & " & !) & L1 & L2 & "'" 8 9 & '* . L1 & , # ( #) ) & Turing ( " & , - "0 1 L2 & , # ( #) ) & Turing ( " & , - "0 2 " ( , ( ) &! Turing, - "0 ’ * w " (#+ 0 .! : 1. #-) " & M1 * w. & 1 &"! 3 , "'" ’ &" 3 " # " , . & 1 &"! # )0# " 2! 2: 2. #-) " & 2 * w. & 2 &"! 3 , "'" ’ &" 3 " # " , . & 2 &"! "'" ’ &" " # " , . B. 1 0# 4. "'" " "0& 0& 0 & 3. "'" " " ( !#0 ! "#$ ! 1 # ( "'" " "0& 0& 0 & " ( !#0 ) & L & : & '* . L & , # ( #) ) & Turing ( " & , - "0 " ( , ( ) &! Turing, - "0 ’ * w " (#+ 0 .! : 1. #-) " & M * w. • & &"! 3 , "'" ’ &" NAI " # " , . • & &"! OXI, "'" ’ &" 53 " # " , . B. 1 0# 4. "'" " "0& 0& 0 & 4. "'" " " & # %! "#$ ! 1 # ( "'" " "0& 0& 0 & " & # ) & L1 & L2 & "'" 8 & '* . L1 & , # ( #) ) & Turing ( " & , - "0 1 L2 & , # ( #) ) & Turing ( " & , - "0 2 " ( , ( ) &! Turing, - "0 ’ * w " (#+ 0 .! : 1. # " ) &! Turing * )0# "! D # + ' ( " ( *(& " % * )0# % " ( 2 # w " & # *% ( 2 # & w1 w2 (* *! ' ( " ( *(& " % * )0# % " w 0 w1w2.) 2. *(& "' * )0# ': 1. #-) " & M1 * w1 " & M2 * w2. & *% ) &- &"! (& , "'" ’ " # " , &" &" & ' *(& " * )0# &" %& 53 , "'" ’ " # " , &" &" 53 .
  7. 7. B. 1 0# 4. "'" " "0& 0& 0 & 5. "'" " " "-# Kleene ! "#$ ! 1 # ( "'" " "0& 0& 0 & " "-# Kleene) & L & & '* . L & , # ( #) ) & Turing ( " & , - "0 " ( , ( ) &! Turing, - "0 ’ * w " (#+ 0 .! : 1. # " ) &! Turing * )0# "! D # + ' ( " ( *(& " % * )0# % " ( 2 # w " & # 1..|w| ( 2 # & (* *! ' ( " ( *(& " % * )0# % " w 0 w1w2…wk k=1,2,…|w|) 2. *(& "' * )0# ': 1. #-) " & M * * ) '* ( w1,w2 , … , wk. & &"! + ' " ( 2 #- "'" ’ " # " , &" &" . & ' *(& " * )0# &" %& 53 , "'" ’ " # " , &" &" 53 . . ! # +! 1 (2009 ) "0 2 " = {0,1} + : L = {w ∈ * : " w # -) " ( ) " & *% 0 ( (& )' & ! ') )}. " ( " ) &! Turing 2 " 0 = {0, 1, #, Y, N} ( , " & + L. ) &! . & ) " ': #w# + w ∈ *. " "( # +# ! " # &0 ) &! Turing (" & +'# * ) # " " & ) " (&-) "( ! # +# ! - 0 +# ! " # ! . &! "#$ ! . ! # +! 2 (2009/) 7 "0 2 " = {0,1} + : L = {w ∈ * : " w # -) " ( ) " & *% (& )' & 0 (* *!: 00)}. " ( " ) &! Turing 2 " 0 = {0, 1, #, Y, N} ( , " & + L. ) &! . & ) " ': #w# + w ∈ *. " "( # +# ! " # &0 ) &! Turing (" & +'# * ) # " " & ) " (&-) "( ! # +# ! - 0 +# ! " # ! . '! "#$ ! . ! # +! 3 (2010 ) . +! " + " " #'2 " ( " ' & ( 2 # " 2 " {0,1} # -) " & * # ' 0 1 & % ( ). (! "#$ !
  8. 8. . ! # +! 4 (2011 ) " ( " &" " # & " ! ) &! Turing M, 2 " = {0, 1, #, Y, N}, ( & , " & + L = { x ∈ {0,1}* | x & &*# }. &*# & ( 2 #- ( * 2 , &" " * ' * . ' # " # . 1 0#! " '" * x∈{0,1}* . & " & " (#+ " ' " & ) " ' #x#. ) # "!# 4 (YES) (NO) )# %&" " + " & " *'" " * )! ! " '## 8 " '* (, &" " ) . (1) " "( # +# ! " " (#+ " (-& & +'# * ) # " " & " ). )! "#$ ! . ! # +! 4 (2) " " +# # ! " ( ) " ! & # " )#! +&0 " & ) & &). (3) " " & ( + ' " + " ( # "0 #) % " ) " % : (i) #01010# (ii) #1001# (iii) #1101# (iv) ## ! "#$ !

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