3.1.  -

                    -  祬? , ⥩... -, .
                     室   誮  ஬ .
                                   쭨 稭  㡡


   ,   ண 뢠 㣨 모, 뢠
몮. ⭮,  ᪨   몮. 
 ⮬ 몥  뢠, ਬ,   ᯮ⥫ 㪠-
.  ᪨  ,    㣮 ⢥ ,
᫨誮 祭  ᫮  ண ଠ ᠭ.
    ணࠬ஢ 祭  ਬ  --
  ᠭ ଠ 権.     
ᯮ짮  ᠭ 몠 ணࠬ஢ -60.
    몥 - ᯮ  ᫥騥  ᨬ (-
ᨬ):
<>    - ᪮, 뤥騥 ।塞 ⨥;
::=   - ⠢ ᨬ,  ⠥ " । ";
|     - ᨬ, 騩 ୠ⨢, ⠥ "".

   ਬ ।.

   ਬ 1
    < ᫮> ::= +
 ᫮  ।  ᨬ "+".

   ਬ 2.

    <> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

     ।  0   1,  2,  3,  4, 
5,  6,  7,  8,  9.

       ᯮ짮 몠 --
  ᮧ ४ᨢ ।.

   ਬ 3.

  <᫮> ::= <㪢> | <᫮><㪢>             (1)
  <㪢> ::=  |                                 (2)

     ।  ⠪:
   ""    । :  "㪢",  ꥪ,  
  ,   "᫮",  ᫥      ᠭ
"㪢".
   "㪢" -   ᨬ "",  ᨬ "".
    , ࢠ ப  । ᮤন ४!
   ஢ਬ,  ᮮ⢥   ।  "᫮"  ᫥騥
ꥪ: "", "", "".
   1) ꥪ "" - ᫮, ⮬ :
    - 㪢 (ࠢ 2),  㪢  ᫮ (ࠢ 1).
   2) ꥪ "" - ᫮, ⮬ :
   "" -  ᫮ (⠪    ""  -   㪢  ࠢ 2, 
, ᫮  ࠢ  1).  ,   ᫥ 㪢,
 ᫮ (ࠢ 1), , "" - ᫮.
   3) ꥪ "" -  ᫮, ⮬    ᫮ "" ᫥
 㪢  ᫥ ࠢ 2.

    ஢ ᮮ⢥⢨ ꥪ ।? 㦭 ᫥-
 ࠢ,   ⮬ ।. ᫨ ࠢ ४-
ᨢ,     ஢ઠ 㤥 ᮤঠ ४. ஢ਬ,
ਬ,  ꥪ ""  ᫮.

   ꥪ "" - ᫮, ᫨ ᫮  "" (ࠢ 1
 2).
   ꥪ "" -  ᫮, ᫨ ᫮  ""(ࠢ 1 
2).
   ꥪ ""  - ᫮, ᫨  ᫮  "" (ࠢ 1 
2).
   ꥪ "" - ᫮ (ࠢ 2).

   ⨬,   । 1 ᫮   ( -
!)  ᫥⥫쭮   㪢 ""  "".   
 ᯮ ⮤ ⥬᪮ 樨.

   .  ⥬᪠   -    㭨ᠫ
ᯮᮡ ⥫⢠ ⢥ত F, ᮤঠ饥 ᨬ  
楫 ᫠ n. ᨬ 砥  F(n).
   ⥫⢮ ⮤ ⥬᪮  樨 ஢ 
 蠣.
  1)  樨.
   ⢥ত F(n) ஢  ஬ 砫쭮  n = n0
(ਬ,  n0 = 1).
  2) ⨢ ।.
   뤢  ⨢ ।.    砥  
⮬,  ⢥ত F(n-1) ⠥ ࠢ (n > n0).
  3) ⨢ 室.
   뢠 ࠢ F(n)  ⮬ ⨢ ।-
,   ।  ࠢ F(n-1). -
⥫⢮ ᭮뢠  ⪥ ।⠢ ᨬ F(n)
१ F(n-1).
   ⠪,  ⮤ ⥬᪮ 樨,   -
,  F(n) ࠢ, ᫨ ࠢ  F(n-1).  -
⥫⢮,   ஢મ F    ⭮ -
 n0  ⢥ত,  F(n) ࠢ ᥣ. -
?
    ,  ⢥ত F(n) ࠢ, ᫨ ࠢ-
 F(n-1). ⮣ 筮 ⮡ ⢥ত,   F(n) -
    n > n0, ᫨ F(n0) ஢७ ।⢥-
.

....
F(5) ࠢ, ᫨ ࠢ F(4)
F(4) ࠢ, ᫨ ࠢ F(3)
F(3) ࠢ, ᫨ ࠢ F(2)
F(2) ࠢ, ᫨ ࠢ F(1)
F(1) -  樨, ࠢ ஢७ ।⢥.

       ⠢塞 ࠡ ண ᯮ⥫ 
஢ન ࠢ ⢥ত F   ⭮ n
 ᫥饩 ४ᨢ ணࠬ:

  (n)
  n = 1
    ("F - ࠢ   n")
    (n-1)


   ਬ, 楤 (3) ४ᨢ 믮 楤-
 (2).    ⥫⢠  樮 室
᫥,  F(3) ࠢ, ᫨ ࠢ F(2). 楤
(2), 筮, 믮 楤 (1).  -
 楤 ४ 稢:  F(1)  ࠢ
-  ஢७  樨.
   ਢ ணࠬ, 筮, 襭 类 ࠪ᪮
᫠.       ⥬  
४ᨢ , ,    ⨢
室 ᢮ ஢ F(n)  ஢થ F(1).

   ୥   襩  . ,   ᫥⥫-
 F(n),   n ᨬ,    ਭ-
 祭 "",   "",   ᫮  ᫥ 
।.

   1)  樨. F(1) ⮨   ᨬ ""  ""
   ᨫ ࠢ (2)  㪢,     ᨫ ࠢ
(1) - ᫮.
   2) 樮 ।. ⠥,  F(n-1) - ᫮.
   3) 樮 室. ,  F(n) - ⮦ ᫮.
   ।⠢ F(n)      ⥩: ᫥ ᨬ  
⠫쭮.  F(n)   :

                     F(n)  = F(n-1) s                 (*)

    s  -  ᫥ ᨬ   F(n),    ਭ
祭 "a"  "m",    㪢  ᨫ (2).
   ⠪,  ।⠢ F(n)  ᫮ F(n-1)   ᫥-
 㪢.  ⮣  ᨫ (1) - F(n) ⮦ ᫮.

    ᫥ ᯨ᮪     ⢥⠬.    -
짮    誮쭨  ࠪ᪮ ࠡ 
।ﬨ, 묨  樨 -.

  1.
   । 1
   -------------
<> ::= <㪢> | <><㪢> | <><>
<㪢> ::= x | y
<> ::= 1 | 2

   ஢,     ਢ   ꥪ  
᫥ । 1.

1) x   2) xy    3) x1    4) 2y    5) xxxxxxx  6) y321  7) 1212
8) x21    9) X21

⢥:    ꥪ 4), 6), 7), 9)

    ᫥饥 ⢥ত.
      ᫥⥫쭮  㪢  , 
稭  㪢.

  2.
   । 2
   -------------
<> ::= <㪢> | <><㪢> | <><>
<㪢> ::= <> | x | y
<> ::= 1 | 2
<> ::=
   ஢,     ਢ   ꥪ  
᫥ । 2.

1) x   2) xy    3) x1    4) 2y    5) xxxxxxx  6) y321  7) 1212

⢥:    ꥪ 6)

   ୮  ᫥騥 ⢥ত.
   )  ᫥⥫쭮    ᨬ "x"  "1" 
  ᫥ । 2.
   )    ⢮  ⠪ ""  ⢮ ,
 । 2?

 3.
   । 3
   -------------
<ࠦ> ::= <᫮> |(<ࠦ>) | <᫮> + <ࠦ>
<᫮> ::= 20 | 30
   ஢,   ਢ  ꥪ  ࠦﬨ
 ᫥ । 3.
1) 2  2) 20  3) 2030 4) 20+30 5) (20) 6) (20+30) 7) 20 + (30+30)
8) 20 +
9) + 30
10) (20+(30+(20+20)))

⢥: ࠦﬨ   ꥪ 1), 3), 8), 9)

 4.
    ᫥饥 ।     몠 --
.
   ਬ -  ᪮쪮 , ᮥ   ᮡ 
"-".

⢥:
<ਬ> ::= <> - <> | <ਬ> - <>
<> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

 5.
      몠 - । ࠫ-
 ᫠.

⢥:
<ࠫ쭮 ᫮> ::= <㫥 > |
                        <ࠫ쭮 ᫮> <>
<㫥 > ::= 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
<> ::= 0 |<㫥 >

 6.
        몠  - । 楫
᫠.

 ⢥:
<楫> ::= <楫  > | +<楫  > | -<楫  >
<楫  > ::= <> | <楫  ><>
<> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

 7.
। 4
-------------
<ࠦ> ::= <> | <ࠦ> + <>
<> ::= <ࢨ> | <> * <ࢨ>
<ࢨ> ::= x | y | z
   ஢,   ਢ  ꥪ  ࠦﬨ
 ᫥ । 4.
1) z   2) x*y+z  3) x+y+z  4)  (x+y)*z  5) x*x  6) y+y*y+y
7) xy  8) +x     9) z+

⢥: ࠦﬨ   ꥪ 4), 7), 8), 9)

 8.

। 5
-------------
<ꥪ> ::= <⮩> | <⠢>
<⮩> ::= <ꥪ  > | <맮 楤> | <ࠧ> | <横>
<⠢> ::= { <஡> <楯窠 ꥪ⮢> <஡> }
<楯窠 ꥪ⮢> ::= <ꥪ> | <楯窠 ꥪ⮢> <஡> <ꥪ>
...

     ꥪ  । 5 (।  )?

   ⢥. ꥪ -  ᠭ   "" 몠 ࠢ-
 ᯮ⥫ﬨ ( 㪠  ४).
