This document contains formal definitions and notations related to context-free languages and pushdown automata. It defines various symbols and sets out rules for generating strings using a pushdown automaton. It also provides examples of context-free languages and how they are generated by a pushdown automaton through transitions involving the stack.

1. 1
:5
version 1
24.11.06
CFL
PDA
),,,( SRV Σ
•V
•Σ
•R
•S
•}1#:#}1,0{{ 01
*
+=∈= ww
wL
SEMSE
M
MMEM
SME
SSES
1/0
/0/1
0/1
→
→
→
ε
•PDA}1#:#}1,0{{ 01
*
+=∈= ww
wL

2. 2
•}0,:{ >= +
mncbaL mnmn
bcbAcA
aAcaScS
/
/
→
→
•}0:{ ≥= nbaLofcomplement nn
***
)()()(}:{}:{ baababbajibajibaL jiji
∪∪∪∪<∪>=
ε////
//
//
//
3
222
111
321
babXaXX
XbXaXS
bbSbaSS
aaSbaSS
SSSS
→
→
→
→
→
aA
BCA
→
→
aABCBC
ε→SS
ε→A
BA →
•
ε
ε
/00
//
→
→
B
BBABA

3. 3
Lp
Lzxyuvi
pvxy
vy
uvxyzw
pwLw
ii
∈Ν∈∀
<
>
=
⇒>∈∀
:
||)2
0||)1
||,
G
ww

4. 4
b
G
b
ii
b
1|| +
= V
bp
wpw|V|+1
w
|V|+1
R
w
Rvxy
Rx
RR
RRuxz
vy
wR
R
uxzp
|V|+1p
CFL}:{ Ν∈= ncbaL nnn
LCFLpppp
cbaw =
uvxyzw =
vy
vy
vy
*** cba

5. 5
L
CFL}}1,0{|{ *
∈= wwwL
LCFLp1100 pp
w =
LCLFpppp
w 1010=
vxywvxy
i=2
L
vxywi=0
pjip
1010pji ==L
L
L
2
1L

6. 6