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Clearly, the rst step requires 
           
  
  
      

        

  
                  
               

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         roduce the denition of MME for QCSPs.

Denition 9.                     ** 
Following the methods discussed in Denition 8, we give a similar denition on extended MME for QCSPs.

Denition 10.                      
        **                 **            
                
Thus, given the above two denitions, we can identify a new tr     
         *be a binary quantied arc consistent QCSP whose variable dom*   
 *is satisable if there exists a mapping* 
 *For each existentially quantied x*      **                   
       **     
                      
              

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       have presented the denition of the QBTP on binary QCSPs, whi
         o the ordering in the prex of the QCSP, and proved that a binar QCSP can be solved in polynomial time if it satises the QBTP.          
of the QBTP differs from the ordering in the prex. One simple           
         uantied variables can be shifted out of their blocks has bee We regard this work as the rst step on hybrid tractable class           
                  
                   