grammar - Chomsky Normal Form Rules -


in old exam-question need convert grammar cnf, suspect provided solution wrong.

grammar:

s -> aab|a|aa|ab|abb|b|ab|bb -> aa|a|cc|c b -> bb|b|dd|d c -> cc|c d -> dd|d

in first step set variables 4 terminals:

v -> x -> b y -> c z -> d

in second step replace terminals variables(only productions in s now):

s -> vab|a|va|vb|axb|ax|xb

in third step replace ab in vab u -> ab get:

s -> vu|a|va|vb|axb|ax|xb

in solution, don't understand what's happening s-productions abb , bb(which have set axb , xb). provided answer s-productions:

s → vu|a|va|vb|ux|b|ax|bx

how come abb set ux , bb bx? should not bb set xb @ least?


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