30 3:

3.4:

.

.

1.

1.

2.

2 , 30, 3.4:

3. Kleene

4.

5.

1.

2.

1.

2.

.

.

:

3 , 30, 3.4:

(-)

B. 1.

4 , 30, 3.4:

.

..

..

x,y x+y

:

x,y x*y

:

x,y x-y

B. 1.

5 , 30, 3.4:

.

L1 L2 . ( ..) ( .) Kleene L ( .) Kleene L1 ( .) L1 ( ) ( )

B. 1. 1.

6 , 30, 3.4:

( )

L1 L2 L1 U L2

L1 , , r1 L1 , , r1 L2 , , r2

L1 U L2 r1+r2, .

B. 1. 2.

7 , 30, 3.4:

( )

L1 L2 L1L2 .

L1 , , r1 L1 , , r1 L2 , , r2

L1L2 r1r2, .

B. 1. 3. Kleene

8 , 30, 3.4:

( Kleene)

L L* .

L , , r

L* r*, .

B. 1. 4.

9 , 30, 3.4:

B. 1. 4.

10 , 30, 3.4:

A B 0 0

0,11 1

0,1

A B 0 0

0,1

0,1

1 1

B. 1. 5.

11 , 30, 3.4:

( )

L1 L2 L1L2 .

L1,L2 , L1,L2 , , 1,2.

L1L2 1,2 : 1,2 (

)

.

,

L1L2, .

B. 1. 5.

12 , 30, 3.4:

:L1={w{0,1}*| w 0} L2={w{0,1}*| w 1}

A B0

1 1

1

0 0

L1L2 = {w{0,1}*| w 0 1} :

A B

A

0 1

00

00

1 1 1 1

B. 1. 5.

13 , 30, 3.4:

2:L1={w{0,1}*| w 00} L2={w{0,1}*| w 1}

A B0

1 0,1

1

0 1

0

L1L2 = {w{0,1}*| w 00 1} :

A B

A

0

0

0 01 11

1

0

1

0

1 0

1

B. 1. 5. ( 1)

14 , 30, 3.4:

:

A 0

0 01 11

0 0

1 0

1

1: ( BY ):

1

1 1

A

0

01 1

0

1

0

1 0

1

B. 1. 5. ( 2)

15 , 30, 3.4:

A

0

01 1

0 0

1 0

1

2: , : ( )

.

AX AY ( AX):

1 1

A 0

0 0

1 0

11

1

B. 1. 5. ( 2)

16 , 30, 3.4:

L1L2 = {w{0,1}*| w 00 1}:

0 0

0

10

1

1

1

, ,

. ,

.

! .

01

B. 2.

.

:

( )

17 , 30, 3.4:

.

:

( ) L1 U L2

1 2 L1 - L2

B. 2. 5.

18 , 30, 3.4:

:L1={w{0,1}*| w 0} L2={w{0,1}*| w 1}

A B0

1 1

1

0 0

L1 U L2 = {w{0,1}*| w 0 1} :

A B

A

0 1

00

00

1 1 1 1

L1 (A) L2 (Y)

AX,,

B. 2. 5.

19 , 30, 3.4:

:L1={w{0,1}*| w 0} L2={w{0,1}*| w 1}

A B0

1 1

1

0 0

L1 - L2 = {w{0,1}*| w 0 1} :

A B

A

0 1

00

00

1 1 1 1

L1 (A) L2 (X) AX

. 1

() L={w{0,1}*| w 1}() L={w{0,1}*| w 0}() L1L2

20 , 30, 3.4:

. 2 1 2

L1 L2 1 2

21 , 30, 3.4:

() .

() .

() L1L2, L1L2,L1 - L2.

22 , 30, 3.4:

() .

23 , 30, 3.4: