Definition 2.2.1: Let K,L_ _*. The left-quotient of K by L is K\L = {y__* | _x_K so that xy_L}. The right- quotient of K by L is K/L = {x__* | _y_L so that xy_K}.
Examples
(01)*/1 = (01)*0
(01)*/11 = _
0*\0*1* = 0*1* 0*1\0*1* = 1*
Theorem 2.2.1: If K_ _* is regular and L_ _* is
arbitrary, then K/L and L\K are regular (but L/K
and K\L may not be).
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