ΠΛΗ30 ΜΑΘΗΜΑ 3.1

30 3:

3.1:

.

.

1.

1.

2.

2 , 30, 3.1:

3.

2.

1.

2.

3.

4.

5. :

.

.

:

3 , 30, 3.1:

(-)

B. 1. 1.

4 , 30, 3.1:

: .

: ={0,1} ={a,b} ={A,B,,,}

: .

, *.

* Kleene 0

={0,1} *={,0,1,00,01,10,11,000,001,010,011,100,101,110,111,}

: 0

B. 1. 2.

5 , 30, 3.1:

: *.

L. ={0,1}:

L1={ w | w 00}

.

1

L2={ w | w 11} L3={ w | w 01} L4={ w | w 2} L5={ w | w 1} L6={ w | w } L7={ w | w } .

B. 1. 3.

6 , 30, 3.1:

B. 2. 1.

7 , 30, 3.1:

.

.

: L={w{0,1}*|w 1}; 1(0+1)* 1(0+1)*

.

1 1. (0+1)* 0 1 ( 0+1) 0 .

Kleene 0,1,2, : 1 1(0+1)=10 11 1(0+1)(0+1)=100 101 110 111 .

B. 2. 1.

8 , 30, 3.1:

:

:

1. 2. + 3. * Kleene. 0 .4.

.. 11*+(00)* :

( ) ( )

4. 5.

( ) .

Kleene, +, .

B. 2. 2. : {0,1}:

9 , 30, 3.1:

L1={ w | w 1 } L2={ w | w 00 } L3={ w | w 01 } L4={ w | w 2 } L5={ w | w 2 } L6={ w | w 2 } L7={ w | w } L8={ w | w } L9={ w | w 00} L10={ w | w 01} L11={ w | w 01} L12={ w | w 0}

B. 2. 3.

.

:

10 , 30, 3.1:

*

rL

B. 2. 4.

.

:

11 , 30, 3.1:

:

.

.

.

. (.3) ( 4) Turing ( 5) ( 5)

B. 2. 4. : :

12 , 30, 3.1:

1. (0+1)*11(0+1)*2. 0(0+1)*103. 00(0+1)*11(0+1)*114. 0(0+1)*0 + 1(0+1)*15. 1(0+1)*0 + 0(0+1)*16. 0*(10*10*)*7. 0(0+1)*+(0+1)*18. 1(00+01+10+11)*9. (0+10*1)*10. 0*(10*10*10*)*

B. 2. 5.

13 , 30, 3.1:

:

: +

:

L={,0,1,00,01,10,11}

L :+0+1+00+01+10+11

. 1

14 , 30, 3.1:

,*

1L *2L

. 1 :

L1={w{0,1}*| w 00 10}

L2={w{0,1}*| w 11, 00 10}

L ={w{a,b}*| w aabb}

15 , 30, 3.1:

L3={w{a,b}*| w aabb}

L4={w{a,b}*| w a}

L5={w{a,b}*| w a b}

. 2 :

L1={w{0,1}*| w 01}

L2={w{0,1}*| w 01}

L ={w{0,1}*| w 01}

16 , 30, 3.1:

L3={w{0,1}*| w 01}

L4={w{0,1}*| w 01}

L5={w{0,1}*| w 01}

L6={w{0,1}*| w 01}

. 3 {0,1} :

1. L = 0*1(0*10*1)*0*

2. L = 1* + 1*01* + 1*01*01*

17 , 30, 3.1:

2. L = 1* + 1*01* + 1*01*01*

3. L = (0 + 1)* 11 + (0 + 1)* 10 + (0 + 1)* 01 + 0 + 1 +

4. L = 1(0 + 1)* + 0(0 + 1)*

5. L = 1*(01*01*01*)*

. 41. = {a,b}

ab ba.

2. b*a(b*ab*a)*b*.

3. = {a,b} L={aibi |0 i3}

18 , 30, 3.1:

3. = {a,b} L={a b |0 i3}4. = {0,1} L = {(00111)n | n 0} n

;

5. = {a,b} ={(a+b)i |i>2}