Expression 6: "P" left parenthesis, "x" , "y" , right parenthesis equals "d" left parenthesis, "H" left parenthesis, "x" , "y" , right parenthesis , "f" left parenthesis, left bracket, "x" , "y" , right bracket , right parenthesis , right parenthesis times "f" Subscript, 3 , Baseline left parenthesis, negative "x" , right parenthesis "f" Subscript, 3 , Baseline left parenthesis, negative "y" , right parenthesis positive "d" left parenthesis, "H" left parenthesis, "x" plus 1 , "y" , right parenthesis , left bracket, negative "f" left parenthesis, negative "x" , right parenthesis , "f" left parenthesis, "y" , right parenthesis , right bracket , right parenthesis times "f" Subscript, 3 , Baseline left parenthesis, "x" , right parenthesis "f" Subscript, 3 , Baseline left parenthesis, negative "y" , right parenthesis positive "d" left parenthesis, "H" left parenthesis, "x" , "y" plus 1 , right parenthesis , left bracket, "f" left parenthesis, "x" , right parenthesis , negative "f" left parenthesis, negative "y" , right parenthesis , right bracket , right parenthesis times "f" Subscript, 3 , Baseline left parenthesis, negative "x" , right parenthesis "f" Subscript, 3 , Baseline left parenthesis, "y" , right parenthesis positive "d" left parenthesis, "H" left parenthesis, "x" plus 1 , "y" plus 1 , right parenthesis , negative "f" left parenthesis, left bracket, negative "x" , negative "y" , right bracket , right parenthesis , right parenthesis times "f" Subscript, 3 , Baseline left parenthesis, "x" , right parenthesis "f" Subscript, 3 , Baseline left parenthesis, "y" , right parenthesisPx,y=dHx,y,fx,y·f3−xf3−y+dHx+1,y,−f−x,fy·f3xf3−y+dHx,y+1,fx,−f−y·f3−xf3y+dHx+1,y+1,−f−x,−y·f3xf3y
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Expression 7: 1 greater than 0 left brace, "P" left parenthesis, "x" , "y" , right parenthesis less than or equal to 0.6 times left parenthesis, 2 StartFraction, left bracket, 0 , ... , 8 , right bracket Over 8 , EndFraction minus 1 , right parenthesis , right brace1>0Px,y≤0.6·20,...,88−1
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Expression 8: "H" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis equals "H" left parenthesis, "x" , 0 , right parenthesis left bracket, 1 , right bracketH1x=Hx,01
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Expression 9: "P" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis equals left parenthesis, "H" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis times "f" left parenthesis, "x" , right parenthesis , right parenthesis "f" Subscript, 3 , Baseline left parenthesis, negative "x" , right parenthesis plus left parenthesis, "H" Subscript, 1 , Baseline left parenthesis, "x" plus 1 , right parenthesis times negative "f" left parenthesis, negative "x" , right parenthesis , right parenthesis "f" Subscript, 3 , Baseline left parenthesis, "x" , right parenthesisP1x=H1x·fxf3−x+H1x+1·−f−xf3x
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Expression 10: "P" Subscript, 1 "b" , Baseline left parenthesis, "x" , right parenthesis equals "H" Subscript, 1 , Baseline left parenthesis, "x" , right parenthesis "f" Subscript, 3 , Baseline left parenthesis, negative "x" , right parenthesis plus "H" Subscript, 1 , Baseline left parenthesis, "x" plus 1 , right parenthesis "f" Subscript, 3 , Baseline left parenthesis, "x" , right parenthesisP1bx=H1xf3−x+H1x+1f3x
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Expression 11: "y" equals 1 plus "P" left parenthesis, "x" , 0 plus "t" , right parenthesisy=1+Px,0+t