Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

ΠΛΗ30 ΜΑΘΗΜΑ 5.3 (ΕΚΤΥΠΩΣΗ)

3,141 views

Published on

.

Published in: Education
  • Be the first to comment

  • Be the first to like this

ΠΛΗ30 ΜΑΘΗΜΑ 5.3 (ΕΚΤΥΠΩΣΗ)

  1. 1. 30 5: 5.3: !!!! " # $ %& ! " # $%&'' ( #' " )%&'' * +, - ' '# )%&'' # " * + %# ! ( #' %$ * . ' /0 102 ! 3 !"#$$ 3 4 + %# ! 3 . $%&'' 5678 ! ( #' * " #9 # " # - ' '# 3 " #9 # # " 4 +% #' ' # " )%&'' +% #' ' : ' * +% #' ' ; 3 +% #' ' < , ' 4 +% #' ' ' # =7>> > ? @AB +% #' ' % ) ' ' # . ' ( " ! ') ( " *& : * (-) * + , !! Halting !"#$$ , !! Halting ' - ' * , !! *& ". ! ' .& & , .!! &. * ' - ' Halting & *& / !*! B. 0 .#* 1. ) & Turing ( ) & , !! 1. # ! ' " !! %!"#$$ (& ' & !%& , .!! & ( *& !%& .& & , .!! & , * ( #) ) &" Turing ( - / !*1 . ', * " , !! ) & ' & : • # *1 '& & !( 2 ! # !' ( &" ! & , !! . • !( 2 ! # ( & &" ! & , !! , # ( )# . ) &" & & # *1 (& / ! 2#') ).
  2. 2. B. 0 .#* 1. ) & Turing ( ) & , !! 2. / !*! , !! *& ". !"#$$ : Turing- / !*! , !! *& Turing- " , !! . ' - : 3! . / !*! , !! L. / % *& / !*! , ( #) * ) &" Turing ( & / !*1 , ! . M. ! ( 1 ( ) &" Turing ’ ( - / !*1 & , !! . -" : • # ) &• # ) & • & & "! NAI ( " # *! !) ! ' #Y#), ' ’ # *1 . • & M & "! 45 ( " # *! !) ! ' # #) ' ’ / ! # & 2#') ( .). & & & / " !(& ) - ) 6# ’ / !*1 & , !! L, # L *& " , !! . ( ’ ! ( 1 !. ( -" ,# # " : B. 0 .#* 2. " ) &" Turing 1. # ! ' ( , #* ( &!"#$$ D.Knuth (The Art of Computer Programming) & ,'# # & ) # #*1 ' -" : • : 2" # & *& ! /". • : & ! ! *& & , *! ( & # * & # %7 (& / # & ! ! , & * *! )* *! ) • : # & *& # ! & . " # ,'# ! , " & & , ' # ! & # ' 2 .&. • : ,'# # & (#, * , ' !' ( &' !(, # & ( % (. • - : ,'# # & *#& *! & # , * & " - , *! . # # % ' ) &" Turing # * ' # "# ( # ! % &' , #* (! B. 0 .#* 2. " ) &" Turing 2. 0 ! Church-Turing '!"#$$ ! : ) &" Turing ( *1 ! ' ! * & # ! ' ( , #* (. 6# : CHURCH – TURING: ! TURING *& !(& &( && " # $ # & # &. ! (& * && % ' ' ! %& && ,'# *& ) &" Turing. *! ! %& && ( , #* ( *& && &' # ,# ( ( (#, * !.! ) .). ! , !! C. 6# , ' & : 5 -TURING = 8 0 = 8 8 # ! )"! 3& ,'# # *1 & ! 6# « ,'# » *& . . ( ( ,*1 (& !(& # "! " / !*1 (& , !! . 4) . ( ) & , !! . ! TURING *& !(& &( && " # $ # B. 0 .#* 2. " ) &" Turing 2. 0 ! Church-Turing (!"#$$ )# !" # & ) 2# * ( , ! ' & !)(#' # ' ) &" Turing: CHURCH – TURING: ! TURING *& !(& &( && " # $ # ) &" Turing: " & ) 2# * #'2 ( & & %& ' ) &" Turing & %& ' ( , ! ' & . & ', ( ' ! .& Church – Turing ( & ' & 2# * !)(#' # & ' & ) &" Turing. ! '! *& ! ( !* ) & ) ) * ' #' . 6#! ! .& Church-Turing ,"! ! & %#, ( , ! & !
  3. 3. B. 0 .#* 2. " ) &" Turing 3. # ,# ( ) & . *! # ,# . )!"#$$ 0 .# % -" % ( , ! # 2 " : 8 + 1: *! : &' # ,# ! , !! C. 3- : NAI/OXI & , & #',# *& !(& # ' ( & ! 2 ( &'& ( !(& % ! C) #'2 1 *& ,&.! " !* ( & , . ! " *& & / !*! #'2 ( ) ( * " , *& & %$"& $ # #'2 ) #'2 2 & ) 2# * ,'# ( %& . *- ( ' & # * & ( * ! ( *& & %$"& $ # #'2 ) 0 % & & * ! .& # 2 .& ) & Turing! 8 + 2: *! : &' # ,# ! , !! C * *! ( !(, # & ( # ,# . 3- : NAI/OXI & , & #',# # *1 & !(, # & *! . B. 0 .#* 2. " ) &" Turing 4. " ) &" Turing U *!"#$$ ' ( ) ( Turing U " «* ( » *& * . . 3 & & * : 2 & . *! * !( 2 ! # <M,w> ' ( " # ,# /" . . w *! ) &" . # ! & & ! *! w. # *1 & '& & M # *1 *& & . & ! & *# *1 & '& & M # *1 *& & . & ! & * & ! ( *& *! w. B. 0 .#* 2. " ) &" Turing 4. " ) &" Turing U **!"#$$ # ! *.! ( = #' (#,* U) *& -" : & # &* ) & # ) (! ! ! &* ( #) * ,# / *! w) & % # &* ,# / " # ,# /" & #* &* . * # ) (! ! ! . 2" U 1 & ! ! ( ' & #* &* ),2" U 1 & ! ! ( ' & #* &* ), !% 2 &* ( ' & # &* ) * & 2 ! ( # ,# / " # ,# /" * 2#*! ! & % # &* . #' (#,* U *& ! %& ( ( , ! ": • 6# 2 ! & ! .& Church-Turing & ! # &' ( , ! " *& ! (& & " ) &" Turing. • 9 ' # !!' # ! # &' : , ! " & *& !)(#' # ' ) &" Turing. B. 0 .#* 3. , !! Halting 1. # ! ' *!"#$$ , !! Halting (= # ! ' ) #*1 . -" : # 2 & " ' 1 %, : " # ,# /" * ) &" Turing M * *! w M* *! w M 3 ! ! : ) &" Turing M # *1 *! w. 3& # , ) &" Turing !' ( w ( &" ! & H *& .). . . ( * ! # , % & ( / !*1 & , !! L={0n1n|n;0} & *! w=0011 & ' ( ) &" Turing & *! w=11 & &" ! & H, / % & # *1
  4. 4. B. 0 .#* 3. , !! Halting 2. ' - ' , !! H & *& / !*! . *!"#$$ 0 *- ( ' , !! H & *& / !*! , !! : ! : ' - ( " *& (- & (! * , ! #*1 ! & )& " ,.& * ! ( "! ( ! ' & ' - ( 0 .#" :' - ( 0 .#" : • + 2 2 * ! .107-108. ( # * ) B. 0 .#* 3. , !! Halting 2. ' - ' , !! H *& ".. *%!"#$$ 0 *- ( ' ( #) ) &" Turing ( - / !*1 & Halting: ' - ( 0 .#" : *)& ( ' H *& " , !! ! ( 1 & * ) &" Turing ’*)& ( ' H *& " , !! ! ( 1 & * ) &" Turing ’ * - / !*1 & H . -" . ’ *! < ,w> (#, * ' . " ) &" Turing U, " # ! & & (#,* ) &" Truing *! w. *& # / & ' : • & *! w # *1 , ' ( & ’ & # *1 . • & *! w # , # % & « ! ( » ( .). & & & ) # "# ! # ! #' # &* & 2 ! * ( ' ) # "# , ' ’ / ! # & 2#') . • & *! w & # *1 , ' ’ & # *1 . (& ’ - / !*1 & H, # H *& " , !! . B. 0 .#* 4. ! ' .& & .!! & *!"#$$ 3! . % , !! &.! ( *& " , !! # ! ( *& " , !! " ( *& " , !! ! # Kleene * , !! *& " , !! & * ( % ! & ') & ) ( ! ' ! & # - ( !( # B. 0 .#* 4. ! ' .& & .!! & 1. ! ' ! & 3&.! *&!"#$$ 0 # ( ! ' .& & .!! & ! & 3&.! ) & L1 *& " !! L2 *& " !! ' L1 U L2 *& " !! ' - L1 *& " !! , # ( #) * ) & Turing ( & - / !*1 ! . 1 L *& " !! , # ( #) * ) & Turing ( & - / !*1 ! .L2 *& " !! , # ( #) * ) & Turing ( & - / !*1 ! . 2 ! ( 1 ( * ) &" Turing, ! . ’ * *! w (#, * . -" : • * '' M1 M2, " # ) & - & 2" ! & 1, & 2" ! & 2 . . . 3 & ! 2" * ' % # *! , ' ( & ’ & # *! . (& : • & # *! 1 ( # !( 2 ! # &" ! & L1), ' ’ # *1 • & # *! 2 ( # !( 2 ! # &" ! & L2), ' < # *1 . • & 1 & # *1 2 & # *1 ( # !( 2 ! # & &" % ! & L1 % ! & L2, # % ! & &.!" ( ), ' M’ & # *1 . ) &" Turing M’ - / !*1 & , !! L1 U L2 , # ( " *& " , !! .
  5. 5. B. 0 .#* 4. ! ' .& & .!! & 2. ! ' ! & " *'!"#$$ B. 0 .#* 4. ! ' .& & .!! & 4. ! ' ! & # ! *(!"#$$ B. 0 .#* 4. ! ' .& & .!! & 4. ! ' ! ! # Kleene *)!"#$$ B. 0 .#* 4. ! ' .& & .!! & 5. 45 ! ' ! ( "#. !"#$$ & *- ( ' & ) ( ! ' ! !( "#. , - & % ' -" ! & ' # :
  6. 6. B. 0 .#* 4. ! ' .& & .!! & 5. 45 ! ' ! ( "#. *!"#$$ ' # , % & # # % & ' ( #* ! & #*! . %#+ $ $ " %#, -. " " 8 8 0 " TURING 8 0 " TURING " 8 w Y . . ( ) # *1 & # *1 ' : ( # & .!! & : $ : %#+ $ $ " " 8 " : " = 8 TURING 8 0 " TURING ' : !' 3 # , .& & ,* 3 # , .& # ! & ww « " # * & ( , ! * ' & #',# .).! C» w Y N . . ( / !*1 . ! "! / # ," 1 *& , !! 5 = {c(M) | ) &" Turing # *1 *! & &" !( 2 ! # } *- ' , !! 5 *& !"#$$ . ! "! / # ," 2 *& , !! 5 = {c(M) | ) &" Turing # *1 *! & !( 2 ! # 0011} *- ' , !! 5 *& %!"#$$
  7. 7. . ! "! / # ," 3 *& , !! 5 = {c(M,q) | ) &" Turing #& ' & ! ! q ' & - & *! & &" !/! # } !"#$$ *- ' , !! 5 *& . ! "! / # ," 4 *& , !! 5 = {c(M) | ) &" Turing & # *1 *! & !( 2 ! # } *- ' , !! 5 & *& % & Turing- ". &!"#$$

×