Arc Minimization in Finite State Decoding Graphs with ... - Microsoft


               "!#  $ %&
'(*) +-,. ) /0
12++4365 '
! 7 8 +9 :/; ?1@BADCEGF4HJILKMNFNC"OQPSR"T UVFXWY@ZUG[]\_^LU6Ha`cbdT#UeFN@Z`XUdfADFNCb g"hij ik lmjdnpo6q>rDktsYlu9j'rDv w6xy{zG|~} n yy n z€S‚„ƒ…†‡ ˆŠ‰Š‹pŒ n y{Ž ‘ v }'’ j9“”“ •–n ‚„˜— os || n yš™{› r | o ‚J|˜y  “œt“ }Y—ž ŸV—py¡ ‚a—p¢ o£ |{Ž¥¤Z›¦‚„ƒ k Ÿ§‹Q‰p¨ŠˆQ©pƒ«ª lG¬ ­®N¯°± ²G³B° È»Gʼ¾ÆV½´Y¶·Èʵ˜µ·¼¾ÆV¶·Á~¶·µ˜µ¸Š¿e¹Yº¶·ÄQºZ½pµÐ»GÒc»GÏÑ»e½¼¾ºp½Q¶˜¶˜ÆVºp¹c¶ÀÁ¾¿Vµ·ÈGÈ>µ·µ·Á_¶·½p½¹¾¸>½–ÈÊÉ¥¹šÂ¸G¿VºZÃ×¼šµÐÃQÃBÆVµ~¼ÀÁ¾ÄQºZµÐ½»G½Z¶¿VϺZÁÅGØÚÈGÙ'ÆGµ˜¿G¹¾ºZµ˜ÉÔ¼šÁмšÇ2Òc»eÈGÉ¥ºZ¸Gµ·»ÛÉ¥¶·Ó µ˜½ºZ¼cÈʹšºpÉÔÉ¥½p¸GÈG¸ÕÃcÈʼ¾Ë̺Zµ·¸VÉ¥Á¾¹šÈÖÁ¾¿µ·ÁÐÒcË1¹šÉ¥µ˜¸G¿VÉ¥ÃBÉ¥µÒc¿¦»G¹¾É¥Ó µ·¼¾ºZ½pÈL¹šÅGÉÔÍVÂÔ½pµ˜¸G¸ÕÒÜÉ¥¹¾ºZµ{½ZÂ¥ÎJÃQÁšÏt¹À½pºZ¶·¼š½p¹¾É¥¹šµÒc¿G¹šÒ»G¼ÀÉ¥ºZÁ~¥ɥ¸V¸G¹¾ÁšÃ½ Î ÈÒGµ·½¶·ÈG½µ˜ÈÊÂÔÉ¥Á¸GØÊÃ#ÙX½–ÃB¼À¹šºZ¿G»GÉÔ¿VÁÌÁ–µ˜¸VËÌÈãÉ¥¹šâ¿ÝË1µÂÔ½pµ{¸GßÊà ¹¾µ˜Áš¸V»eÈ2ºZ¸Ý¹š¿V¶˜µY¼¾½BÍVÁ¾¸GÁÞÉ¥Îa¹¾Ëµ{ÎJ½pÁš¼¾¹ÀÈݺZ¹¾¶·µ½pºZ¸Š»G¹¾µ{»Gßʼ¾¹½QºpÈG¶¾µ˜¿»ÛŦµ˜Ç¸VÈGÈGµ˜µ˜¸VÄQ¶˜µ˜ÇÕÂÔ½pÅÛ»GÉ¥µ˜¸G¹àË1Ãäµ·¶·µ˜½p¸áÒcºp»G¶·ÂÔµ˜½pÒÆVÁ¾µ˜¹š¸ÊÉԶΠ¹À½ZºZϼš¹šÇL¿VºZµ·¼¾Á¾¶tµ"Ïa¹¾ºpµ·¶˜¶¾¹¾¿G½p¸G¼šÉ¥ÉÔÓ å¦ºZÆV¹šµ·ÉÔÁ2½p¸¸ÊÈGÎJÈGµ·µ˜¶·¹¾½¦µ˜ÈʼšÉ¥Òc¸GÃçÉ¥¸GÉÔÃBÁš¼À¹šºZÉÔ¶»G¿VÃBÁä¼ÀºZÉ¥»G¸d¿VÁËÌØG¿GÙ'ÉÔ¶¾¿V¿èµ ÆV¹š¿VÁ¾µµ ¹šºpºZ¼À¼¾¶·ºp¶{½pÁšÎaÆVÒc¹'Áš¹¾¹šÉ¥¸GÉԽж«É¥¹JÒcÒǁɥ»G½¦Ó ÉÔºZÈG¶¹šºZµ˜ÉÔÂÔÂD½pÁY¸>ÁšÆGÇÊ»G¹šÁšÉ¥¹¾¼¾Â¥µ˜½pÉ¥ÓÒÅGµéÂÔÁµ˜º–ÒíËÌτ¿GÆG¹šÉÔÂ¥¿e¶¾ÂN¿,3' 0&

(-4' .#  :  :? #,1 :@): 
8
$-4
 -.A ,1# B,
1#1=CB'

D&  "' > 8E ,1#1#


9
F&  1-= " "G 5
H& ">$ " ,61 "

%

 )   6:
$,(
- .? ,- / FE "
   " $GHE
"  
 $ D*$+ + M F< N @1 "'
 E* "J     /*+
1  $
  " (
-O. Q ,(: "C1$->) " ,$ .- '& 
 $ "% #    "  ., €)  
1#- . )  " N~ L
 
  -. 
O

.  
" :
($ 
 = $0$ "6 
 
 
 " .  $,1# ? 
   5-- :,< # " (- BE   "$
  "$ #( "-/$ .  |K*+(:-- &ZB
 *S  ,
t& !,
  (
A$ " J L "|3'
 ": (:1A S$8*!  8 
;(   "= $0
  
 8)  .6-
'+ 
S, " -

P;( G* "V,3 :(-4 .
O

. F   1A( E K1# 1O

.  >< Nj

1


 > QB9%0-, 9N,
 5 . 5 " G

"%
$-  "$

S " *
=:   





( $A
(:-F&

,
/ 


 "(

*+,

;(1A  )*Q
$ & "1#\ 


 &  :( $N  
ÿ ÿ Êþ Õþ ÿ þ ÿ Êþ ÿ þ ÿ þ Àÿ þ dþ Êþ ÿ „þ ÿ "ÿ ÿ Êþ cÿ
 ! 



!,
7


 :( $

"


N '
6P8
   K


  1  "A 


 9 
    "


:

":7; 

 :

.





$ ( 
 ?17



$  $
$

" )-4 (,81# - 
 0&

 :- " \'
E-  3 -.# ,
  -  B3.#
1#-
G- ,(', 1$-

-0,7,& 3'

"$5 O(: 

8 "1

  )-d  -($

,
, -- . 
S,   * 
,
O.3
 V*  

q:. 1#

G  V   " " $ Q* + +* H
 (5  
  1 /.  " 9 %1# 1O3  . 
 /< 
 (   " %. -:
 -j:   =,




p11 p12

w1

p21 p22

w2 w3

QÄ4ÈG½½pÉ¥ÃB¶¹šÆG¹¾ºZµ·ÅG¼¾Èáµ
ÆGÊØÂ¥ºZÉ¥¼š¸VÇLµ·Á¼ÀË1غZ½p»GY¼¾¿äÈG¼¾¶·Á¼¾Á䵘âG»Gµ½p¼¾ºpÆGµ·¶À¹2ÁÀ¿µ˜¸Š½ZËÌϹšÉ¥É¥¹š¸G¹š¿¿VÃе¹JÂÔ˵{ÄBτ½¹ÞºZÎa¼šË¶·ÉºZ½p½p¸Š¸Š¼¾¹Þ¹¾È2ÎJµ{Ášßʺp¹À¹Þ¶·ºZÎJ½p¹¾Á¾ÆVµ·µ˜Á

(

'*KL-H* & $

.*+$! @   "

F T

>DCV  

V  B) %* ' "
 >
 "$
1# O.3
 A(:
 @~,$

N G "? 
=$, 7 ~

",(:,  -

" {
  1 /.  "

 q,S$
* E :

1~.



" 3
 

0 

E--1 / "  F  6


4--.

"E 


I

G

"" 0&

*S1# 1#, .G 

, 1='-!- S$-Z
ÆG¼¾ÂÔµ
½½pVØ» dÅeºpÃB¶¾¼ÀòèºZ»G¹¾¿½ÝËÌÁšÉ¥¹À¹šºZ¿c¹¾µ·¼šÁB?
-,7; 9*+,V 3.

.#

" K

" A' 4

-$* & $

" 0:(  6 "
# 5
G)!6



5  B @  


 5-@*


? -B $0 L,
/
>B

" 1 1#/.  " {
,"1


 0$4
 ?)
 ~





E1 1#/.  " 9 , -$1

 /: -%,

" {

S


 )

"
($?$


BM- "$ 


"(: " 9*j,( $(

 $


A

 



"9 A1# 1O.  % "A (1

- F


 Q  ,(  H
ÿ ÿ ÿ ÿ –ÿ Šÿ–ÿ Lÿ Àÿ þ ÿ Êþ „þÝÿ ÊþÝÿ ÿ ÿ ÊþGÿ 6ÿ þGÿ æýÞÿ ~ÿ Êþ cÿ cÿ ¦ÿÿ „þ ÿ þ þ ÿ ÿ  eÿ þ „þ ÿ ZþGÿ ÿ ÿ þ Êþ ÊþGÿ eÿ ÿ ÿ þ þGÿ „þ §ÿ „þ „þ ÿ ÿ Àÿ ÿ ~ÿ ¦ÿ Êþ „þ

ÿ ÿ ÿ ÿ þ ÿ  ¦ÿ ÿ ¦ÿ Êþ Ðÿ eÿ   " „þçÿ ¦ÿ Zþ ÿ  )  "!  )  Àÿ þ „þ çÿ çÿ „þ Êþ æþ Àÿ ¦ÿ Ûÿ Êþ  ÿ þ  þ „þ >þ ¦ÿ{ÿ Àÿ

ÿ    "   ÿ
  þVÿ ÿ ÿ ÿ Ðÿ ÿ ÿ ZþGÿ „þ 8(!  $ ?$(

     j,( 

C
 -$ 
q*+--~) K,    '
 0K!,
 
  

$
   " "K-$* !  "% )
 )'*€A
 ;( : 4 "   :1A( , ,(

B
@3 K ,1# 
1#-
 .8)
"

-1# ,     

1A(   -H* & $

' 4


   $ ":A "  1#A3'
A*


$  "

B= 

(:

( ,"1

&  5
H& S$ & !, 
,-( " * j,( 

 $-(:G


(:-$1

)


:$



/ 5  € , 
  S  :

A


  " L 
|


" .#,$
 $ "

"

,

ÿ „þGÿ „þ þ  ÿ Àÿ ÿ ÿ ¦ÿ Êþ ZþGÿ  ÿ     „þ ÿ 2ÿ þ  ÿ „þ 
$ * "8$~, $ 2 ,
1A(1

: '*
  )5

 ( , >*+,8 1=--$)'-( |*

4|#BN--(
"
9

 $
 
 N'-(${*

)#*+,q 3>$


8 : "-- .91#,



4--.#
$($ 

"# SV 35$N ,( 

"

)  8 $
 
 

   C,("

-


  


8 #



,0

    "

,



C) "

,
1-  B$
ÿ „þ þ þ ¦ÿ Êþ  ÿ þ ¦ÿ þ „þ ¦ÿ éÿ „þ „þ çý ~ÿ Ûþ  ÿ ¦þ þ
¦þ þ )
% -.?{1 , '-> : 
 
V* ":

;(1G S$q'*Q 5
 
$
 : 

"%
37'  $S 

M

*+,--~) M , S"

B
9*


$
 "G:( - - .M~'-4 :-A*+
1 $)@!,
@  -H'

"

)
5; S '


" 
1# 
 C
$(
  #  .
 1

 'G
1-4E (

1$-  

M I .K

N 

"%




5, 

'& "1

-4 &

6M (  N'
K;t ,1#  ",!-4

#

 (
  8!,



{"1#A1# 1O.3
  , - 1




Q& 
/< !.KH, -, ) (  "$/*+,J$ ,1#S
 : "@ 

*+,

 5
?F&

3  $,1#1
{ ,(: "1# -

"% "(-J:     


  : *Q- A: " $K 

-$*  H
  

"V3'
*j! , "$6,
$
S /I I