Designing a Sequence detector
Yes, the "Match" row gives the logical expressions that match the table data immediately above. Keep in mind that the table is not showing all of the possible values for "PS" (present state), and the missing rows are being treated as "don't cares" when creating the expressions.

For example, here's the part of the table for Y2, showing the missing rows, and replacing the X values with values that show how the expression below works.

Y2
PS      Next State
Y2Y1Y0   X=0  X=1
 0 0 0   0    0
 0 0 1   0    0
 0 1 0   X(1) X(0)
 0 1 1   1    0
 1 0 0   0    1
 1 0 1   0    0
 1 1 0   X(1) X(1)
 1 1 1   X(1) X(0)

 Match   Y1   Y2*Y0'