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ΠΛΗ30 ΜΑΘΗΜΑ 3.4 (ΕΚΤΥΠΩΣΗ) Slide 1 ΠΛΗ30 ΜΑΘΗΜΑ 3.4 (ΕΚΤΥΠΩΣΗ) Slide 2 ΠΛΗ30 ΜΑΘΗΜΑ 3.4 (ΕΚΤΥΠΩΣΗ) Slide 3 ΠΛΗ30 ΜΑΘΗΜΑ 3.4 (ΕΚΤΥΠΩΣΗ) Slide 4 ΠΛΗ30 ΜΑΘΗΜΑ 3.4 (ΕΚΤΥΠΩΣΗ) Slide 5 ΠΛΗ30 ΜΑΘΗΜΑ 3.4 (ΕΚΤΥΠΩΣΗ) Slide 6
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ΠΛΗ30 ΜΑΘΗΜΑ 3.4 (ΕΚΤΥΠΩΣΗ)

  1. 1. 30 3: 3.4: ! " # $ % # ! " # ! " #$ % " $ $ % &'(()( * + , -" ! % % -" . / ! -" . 0 1 # . & # ' " # ( ' " # ) : &)& * # &)& * + & & ) ! " #$ % " $ & & ) &)& * (-) B. , ) 1. ! " #$ % " $ - # # ) " . / / # & - # & # ' ) * & ' -( ' ( ) & ) . & . .(. - -( ' & # & # '# .' %# %#.%#. ! -( ' *% .' %# x,y & - x+y ) & .' # & ' & & % '# .' %# %#: ! -( ' *% .' %# x,y & - x*y ) & .' # ( & # . ) # '# .' %# %#: ! -( ' *% .' %# x,y & - x-y * ) ’ / .' # #
  2. 2. B. , ) 1. &! " #$ % " $ - # # 0 ) . /" # / #. , % *% / # L1 L2 & ' ) -#. - '# ) " ( & * ) ' - . .) & '# ) " ( & * ) ' - . ) - Kleene # L ) " ( & * ) ' - . )- Kleene # L1 ) " ( & * ) ' - . ) ' & " # L1 ) " ( & * ) ' ) " '# ) " ( & * ) ' ) B. , ) 1. 1. 1 '! " #$ % " $ , ( 1 ) L1 ) " L2 ) " L1 U L2 ) " & * L1 ) ", & / . & ) " - . , - r1L1 ) ", & / . & ) " - . , - r1 L2 ) ", & / . & ) " - . , - r2 L1 U L2 & / . & " - . r1+r2, ) " / . B. , ) 1. 2. (! " #$ % " $ , ( ) L1 ) " L2 ) " L1L2 ) " . & * L1 ) ", & / . & ) " - . , - r1L1 ) ", & / . & ) " - . , - r1 L2 ) ", & / . & ) " - . , - r2 L1L2 & / . & " - . r1r2, ) " / . B. , ) 1. 3. - Kleene )! " #$ % " $ , ( - Kleene) L ) " L* ) " . & * L ) ", & / . & ) " - . , - r L* & / . & " - . r*, ) " / .
  3. 3. B. , ) 1. 4. ' & " *! " #$ % " $ B. , ) 1. 4. ' & " +! " #$ % " $ , - % 0 0 0,1 1 1 0,1 , - % 0 0 0,1 0,1 1 1 B. , ) 1. 5. " ++! " #$ % " $ , ( ") L1 ) " L2 ) " L12L2 ) " . & * L1,L2 ) -#, '& ( ' & & - ' & ' #L1,L2 ) -#, '& ( ' & & - ' & ' # & . )3 ' , - 1, 2. ' 3 ' 4 & & - ' / L12L2 & ' & - 1, 2 # "#: • 1( # # '# '# ' *' %# 1, 2 ( / *% ' ) • ' 0 # 0 ) & - 3 %/ # & & # ' ( # *% " # ' • ( " ) 3 %/ # ( *% ' • -# # ) 3 %/ *% ' . & *" ' & ' ( ' /) *% ' , & . )3 / L12L2, ' " ) ". B. , ) 1. 5. " +! " #$ % " $ * / : L1={w∈{0,1}*| w & -( 0} L2={w∈{0,1}*| w & -( & 1} , - 0 1 1 . / 1 0 0 ' & # & - ' # / # L12L2 = {w∈{0,1}*| w & -( 0 & 1} ) ' : , - ,. 0. 0/ 0 . / 1 1/ 0 0 0 0 1 1 1 1
  4. 4. B. , ) 1. 5. " +! " #$ % " $ * / 2: L1={w∈{0,1}*| w & -( 00} L2={w∈{0,1}*| w 1} , - 0 1 0,1 . / 1 0 1 % 0 ' & # & - ' # / # L12L2 = {w∈{0,1}*| w & -( 00 1} ) ' : , - ,. 0. 0/ . / 0 1/ 0 0 01 1 1 1 % %. %/ 0 1 0 1 0 1 B. , ) 1. 5. " ( & & ) – # 1) +! " #$ % " $ ' & ' & %& & / '"# / " & *-( & & " #: ,. 0. 0 0 01 1 1 %. 0 0 1 0 1 # & & " # 1: # & ' * -( ' ( 0- # & % / % ( BY & ) / )): 0/1/ 1 %/1 1 ,. 0. 1/ 0 0 1 1 %. %/ 0 1 0 1 0 1 B. , ) 1. 5. " ( & & ) – # 2) +&! " #$ % " $ ' & ' & - '5 & % . ' * % & & ) # ,. 0. 1/ 0 0 1 1 %. %/ 0 0 1 0 1 # & & " # 2: # & ' -( ' )* ' & . , * *": • ) *% -# (" -#) • / ) ' # )* # # )* % 0 & % ' & '( % ) . & * / & % # AX AY ) - (- AX): 1/ %/1 1 ,. 0. 0 %. %/ 0 0 1 0 1 1 1 B. , ) 1. 5. " ( & & ) – # 2) +'! " #$ % " $ ' & ' & %& / / ) L12L2 = {w∈{0,1}*| w & -( 00 1}: 0 0 0 1 0 1 1 1 *% # & & ) # * ' & & , * *" 0 ) ' . /", ' ()3 ' '# . 3 ' . 6 * 0 ) ' & - . /", -( & %5 ( *' & " # . ( & ) ' ' ' * ) '& ( "! . 3 ' . # 3 . # #. 01
  5. 5. B. , ) 2. & & - '-# 3 '" ' / ". '/ - ' % 0 # '# )* '# # / : • '" ( # / *% ' ) • # 0 # & ' ' /) *% ' +(! " #$ % " $ • ( " # ' *' ( *% ' . & & % & /" : • & -/ ' # -# ' -# & ' & -( ' ' ( ) " ( ' & ' " ' * % ' " *% ) • -( ' / - *% / L1 U L2 • & -/ ' # -# ' -# & ' & -( ' " ' 1 " ' 2 • -( ' / * . *% / L1 - L2 B. , ) 2. & & - '-# 5. '" / 1 +)! " #$ % " $ * / : L1={w∈{0,1}*| w & -( 0} L2={w∈{0,1}*| w & -( & 1} , - 0 1 1 . / 1 0 0 ' & # & - ' # / # L1 U L2 = {w∈{0,1}*| w & -( 0 " & 1} ) ' : , - ,. 0. 0/ 0 . / 1 1/ 0 0 0 0 1 1 1 1 -# ' L1 (A) -# ' L2 (Y) - # -# & -( ) ' ( & ' -# 7 -# ) AX, 8,+8 B. , ) 2. & & - '-# 5. '" / ! . +*! " #$ % " $ * / : L1={w∈{0,1}*| w & -( 0} L2={w∈{0,1}*| w & -( & 1} , - 0 1 1 . / 1 0 0 ' & # & - ' # / # L1 - L2 = {w∈{0,1}*| w & -( 0 ( & 1} ) ' : , - ,. 0. 0/ 0 . / 1 1/ 0 0 0 0 1 1 1 1 -# ' L1 (A) -# ' L2 (X) 7 " ) AX !. " # . /" 1 ( ) ! / / L={w∈{0,1}*| w & -( ' ( - 1} (+) ! / / L={w∈{0,1}*| w ()3 0} ( ) ' / L12L2 ( & # / # # "# ! " #$ % " $
  6. 6. !. " # . /" 2 !)* & & - ' 1 2 & ' / )3 ' # / # L1 L2 ) ( 1 2 +! " #$ % " $ ( ) / 5 # / # & ' / )3 & *% ' . (+) ! # ) ( # -# . #. ( ) ' & & - ' & ' / )3 ' # / # L1∪L2, L12L2,L1 - L2. ! " #$ % " $ (!) & & " # "#. ! " #$ % " $

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