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    will block the  won  Tij and  none  of them  can  be  performed  simultane-
    ously with Tip [Wi),  I  = I,  2.  .  ,  mlij.  is  the  set of  mating  tasks  (ilud-
    ing real  and  pseudo) such that  the esrabllshing  of any one  of them  will block
    the operation Tij and  all  of them can  be performed  simultaneously with Tij.
    Then the  pt-condition of operation  Tij  is
    Rij=MP(  Tij ,  zlSy )ANL( Tij, V Vi).  (6)
    For task Tij  to  be performed  successfully,  at  least one of its opemtions  is not
    blocked;  i.e..
    ”*  ..  I”*
    1-1
    is the postcondition of task Ti. Its  equivalent disassembly  form is
    Equations  (7)  and  (8)  an two  formulas representing  pmedence
    knowledge of assembly and disassembly respectively. It can  be shown  that
    they can  be  derived from each other.  The  equivalence of (7)  and  (8) sug-
    gests that either  assembly approach or  disassembly  appaach can  be  used  in
    acquiring precedence knowledge of an embly. Following  is a prowdm
    which obtains the assembly postconditions  for mating tasks,  it can  easily
    be  modified to  obtain disassembly preconditions.
    Algorithm  ACQUISITION-FOSr  (Acquire  assembly  post-
    conditions).  Given  an  assembly with ne  components and n  real mating
    tapirs  and the  number  ofopaaio~  for each  nal matins  Ti  is 4.
    i = 1,2, *-  ,  n. this a@”  obtains  the ansanbly postanditions  fix the
    product with the  time complexity  to  be a polymmialof the  number of  mat-
    ing tasks  of the  product  It is assumed that  Ti’s with i gmte~  than n am
    pseudomatingtasks.
    Al.  ~~tspLindex.lSetit1.RtTRUE.
    A2.
    A4.  [Loop2fa~operstiOna]Ifjisg~?aterthan~,then  (iti+l.
    AS.  [Initialize  relaion indcx.] Sett t  1. Rj?’ t  TRUE ,  Rd  t  TRUE.
    A6. [Loop  3  form  rela1ions.1  Ift  is g”  than  I)! =(ne  -  1  )  n,  12. thea  [
    Ri tRi  V (RY  ARd  )  .  j  t  j + Land go  to
    A7. rrajectory is blocked.]  If  T  is blocked by Sf  and cannot  be pa-
    formed simularneously  with $,  thenRr +R*  AMP( 4,  s!);  else
    if  Tij  is blocked  by Wi  but can  be performed  imultaneowly wth w,
    thenR$  t  R#  AM(  Ti/,  Wi  ).
    1 for n tasks.] Ifi  isg”  than  n,  then exit
    AX  Fitializc-On  indcx.1 Seti  t  1,Ri t  TRUE.
    R t  R  ARi 1, and go (0 step  A2
    1.
    AS. End of loop 3.1 A  t  A + 1 and  go to step A6.
    END  ACQvrSmON_POST.
    The result and output of this  algorithm will be the  expressiOn shown  in
    (7).  There are  three  loops in the algorithm, at steps A2.  A4. and  A6.  The
    loop in step A2  has  n iterations; the  hp  in step A4 has  mi Mons;  and
    the loop  in step  A6 has  (ne  -  1 )  n,  I2  iterstions.  The  total  number of itera-
    tions  in this  algorithm is then  n (h-  1)n, mi n.  Suppose M  = max (mi ),
    then  the  total number of  iterations in  the above algorithm  is less than
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